XSProc.rst 138 KB
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.. _7-1:

XSPROC: The Material and Cross Section Processing Module for SCALE
==================================================================

*M. L. Williams, L. M. Petrie, R. A. Lefebvre, K. T. Clarno, J. P.
Lefebvre, U. Merturyek, D. Wiarda, and B. T. Rearden*

ABSTRACT

The modern material and cross section processing module of SCALE
(XSProc) was developed for the 6.2 release to prepare data for
continuous-energy and multigroup calculations. XSProc expands material
input from Standard Composition Library definitions into atom number
densities and, for multigroup calculations, performs cross section
resonance self-shielding, energy group collapse, and spatial
homogenization. XSProc implements capabilities for problem-dependent
temperature interpolation, calculation of Dancoff factors, resonance
self-shielding using Bondarenko factors with full-range intermediate
resonance treatment, as well as use of continuous energy resonance
self-shielding in the resolved resonance region. XSProc integrates and
enhances the capabilities previously implemented independently in
BONAMI, CENTRM, PMC, WORKER, ICE, and XSDRNPM, along with some
additional capabilities that were provided by MIPLIB and SCALELIB. The
use of the modern XSProc sequence instead of the legacy codes of
previous versions of SCALE generally results in the preparation of cross
sections in less time, with substantial speedups for more I/O bound
problems. Additionally, the memory requirements of XSProc are improved
by generating only the data needed for a particular calculation instead
of generating a general-purpose library that contains substantial
amounts of data that are not needed for a particular calculation.

ACKNOWLEDGMENTS

XSProc has evolved from the concept of a Material Information Processor
library (MIPLIB) that used alphanumeric material specifications, which
was initially proposed and developed by R. M. Westfall. J. R. Knight and
J. A. Bucholz expanded and refined MIPLIB in early SCALE releases.
Through SCALE 6.1, many enhancements were made by S. Goluoglu, D. F.
Hollenbach, N. F. Landers, J. A. Bucholz, C. F. Weber, and C. M. Hopper,
with L. M. Petrie taking the lead responsibility. With the SCALE
modernization initiative beginning in SCALE 6.2, MIPLIB is no longer
part of the XSProc analysis, but the original concepts and input
formatting were preserved in the new implementation. The authors wish to
thank Dan Ilas for helping convert the original MIPLIB documentation and
Sheila Walker for editing and formatting this document. Special thanks
to Don Mueller for his detailed review and checking of the document.

.. _7-1-1:

Introduction
------------

Self-shielding of multigroup cross sections is required in SCALE
sequences for criticality safety, reactor physics, radiation shielding,
and sensitivity analysis. In all previous versions of SCALE, resonance
self-shielding calculations were done by executing a series of
stand-alone executable codes, each dedicated to a specific aspect of the
self-shielding operations. Each sequence had its own unique internal
coding to launch the executable codes. Multigroup (MG) and
continuous-energy (CE) cross sections and other data were passed between
the individual executable codes by external I/O, which could require a
substantial amount of clock time. In the modern version of SCALE, all
self-shielding operations are consolidated into a single driver module
named XSProc, and the stand-alone executable codes have been transformed
into callable computational modules" :cite:`rearden_modernization_2015`. The
functions of XSProc are to (a) read input data, (b) generate in-memory
data structures (objects) containing problem-definition information
(compositions, cell geometries, computation options), as well as
self-shielding information (MG and CE cross sections and fluxes), and
(c) execute appropriate computational modules for the requested
self-shielding option. Calculated results produced by one module may be
stored in the internal data objects and passed to other modules through
application program interfaces (APIs). At the completion of XSProc the
self-shielded MG cross sections on the data objects can be passed along
to transport solvers for continued execution of the control sequence or
can be written to an external AMPX library file.

In the future, XSProc will be extended to parallel computations in which
self-shielding calculations are done simultaneously for multiple types
of unit cells. At the present time, however, XSProc is limited to serial
computations; but even in serial mode it typically requires less time
than older versions of SCALE to process shielded cross sections, and
significant speedups have been observed for heavily I/O bound problems.
Integrating the self-shielding capabilities into a single module has a
number of additional benefits as well, including maintainability,
extensibility, and the ability to easily replace an entire computational
module with a future implementation containing new features.
Additionally, the size of the problem-dependent MG library generated by
XSProc may be greatly reduced compared to previous versions of SCALE
because macroscopic cross sections are stored rather than a
general-purpose library of microscopic data.

.. _7-1-2:

Techniques
----------

XSProc integrates and enhances the capabilities previously implemented
independently in BONAMI, CENTRM, PMC, WORKER, ICE, and XSDRNPM, as well
as other capabilities formerly provided by MIPLIB and SCALELIB. It
provides capabilities for problem-dependent temperature interpolation of
both CE and MG nuclear data, calculation of Dancoff factors, and
resonance self-shielding of MG cross sections using several available
options. XSProc produces shielded microscopic data for each nuclide or
macroscopic data for each material. Additionally, a flux-weighting
spectrum can be applied to collapse cross sections to a coarser group
structure and/or to integrate over volumes for homogenized cross
sections. The flux-weighting spectrum can be input by the user or
calculated using one-dimensional (1-D) coupled neutron/gamma transport
model. These operations are performed by the sequences CSAS-MG, CSAS1,
CSASI, and T-XSEC described in :ref:`7-1-3-2`.

.. _7-1-2-1:

Overview of XSProc procedures
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

XSProc reads the COMPOSITION and CELL DATA blocks of the SCALE input,
which are described in the following sections. After reading the user
input data, XSProc loads the specified MG library to be self-shielded
and, depending on the selected self-shielding method, additional CE data
files for nuclides appearing in the problem specification. Finally
XSProc performs MG self-shielding calculations for all compositions by
calling APIs to computational modules such as BONAMI (**BON**\ darenko
**AM**\ PX **I**\ nterpolator), CRAWDAD (**C**\ ode to **R**\ ead
**A**\ nd **W**\ rite **DA**\ ta for **D**\ iscretized solution), CENTRM
(**C**\ ontinuous **EN**\ ergy **TR**\ ansport **M**\ odule), PMC
(**P**\ roduce **M**\ ultigroup **C**\ ross sections), CHOPS
(**C**\ ompute **HO**\ mogenized **P**\ ointwise **S**\ tuff), CAJUN
(**C**\ E **AJ**\ AX **UN**\ iter), WAX (**W**\ orking
**A**\ JA\ **X**), XSDRNPM (**X**\ ‑\ **S**\ ection **D**\ evelopment
for **R**\ eactor **N**\ ucleonics with **P**\ etrie
**M**\ odifications), and/or MIXMACRO to provide a problem-dependent
cross section library. Many computational modules have been modernized
compared to earlier executable codes distributed in previous versions of
SCALE.

Like earlier versions of SCALE, XSProc provides several options for
self-shielding an input MG library :cite:`williams_resonance_2011`. The first, based on the
Bondarenko method :cite:`ilich_bondarenko_group_1964`, uses the computational module BONAMI. BONAMI is
always used to compute self-shielded cross sections for all energy
groups. If *parm=bonami* is specified, the shielded cross sections
provided by BONAMI are the final values output from XSProc. However the
Bondarenko method has several limitations, especially in the resolved
resonance range. Therefore XSProc provides another self-shielding
method, with several computation options, which often produces more
accurate MG data in the resolved resonance and thermal energy ranges. If
*parm=centrm* or *parm=2region* is specified on the sequence line,
XSProc calls APIs for the modules CRAWDAD, CENTRM, and PMC to compute CE
flux spectra for processing problem-specific, self-shielded cross
sections “on the fly :cite:`williams_computation_1995`. CENTRM performs MG transport calculations in
the fast and lower energy ranges, coupled to pointwise (PW) transport
calculations that use CE cross sections in the resonance range. PMC uses
the PW flux spectra from CENTRM to compute MG values, which replace the
previous values obtained from BONAMI over the specified range of the CE
calculation. The original BONAMI shielded cross sections are retained
for all other groups.

The CENTRM/PMC approach is the default for criticality and lattice
physics calculations, while the BONAMI-only method is default for
radiation shielding calculations. The end results of an XSProc
calculation are self-shielded macroscopic and/or microscopic MG cross
sections stored in memory for subsequent transport calculations; or
alternatively a shielded MG AMPX library can be written to an external
file and saved for future use.

.. _7-1-2-2:

Standard composition material processing
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A primary function of the XSProc module is to expand user input in the
COMPOSITION block into nuclear number densities (nuclei/b-cm) for every
nuclide in each defined mixture. Mixtures can be specified through the
direct use of materials presented in the Standard Composition Library,
which includes individual nuclides, elements with natural abundances,
numerous compounds, alloys and mixtures found in engineering practice,
as well several variations of fissile solutions. Additionally, users may
define their own materials as atom percent or weight percent
combinations. Nuclear masses and theoretical densities are provided in
the Standard Composition Library, and methods are available to determine
equilibrium states for fissile solutions. Input options for composition
data are described in :ref:`7-1-3-3` with several examples provided in
Appendix A.

.. _7-1-2-3:

Unit cells for MG resonance self-shielding
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

XSProc utilizes a unit cell description to provide information for
resonance self-shielding calculations of the input mixtures. As many
unit cells as needed to describe the problem may be specified; however,
each mixture (other than 0 for a void mixture) can appear only in one
unit cell in the CELLDATA block. If a nuclide appears in more than one
mixture, multiple sets of self-shielded cross sections are calculated
for the nuclide—one for each mixture in each unit cell. Four types of
cells are available for self-shielding calculations: **INFHOMMEDIUM**,
**LATTICECELL**, **MULTIREGION**, and **DOUBLEHET**. The default
calculation type is CENTRM/PMC for CSAS (see :ref:`CSAS5`), TRITON, (see
:ref:`3-0`) and TSUNAMI (see :ref:`6-0`) sequences and BONAMI for MAVRIC.
All materials not specified in a unit cell are treated as infinite
homogeneous media and shielded with BONAMI only, unless the mixture
contains a fissionable nuclide, in which case an infinite medium
CENTRM/PMC model is used. Note that previous versions of SCALE used
infinite medium CENTRM/PMC calculations for all unassigned mixtures. The
default type of self-shielding calculation can be overridden, as
described in :ref:`7-1-3-2`. The following is a brief description of
the types of unit cells that can be input in CELLDATA and the
computation procedures used.

.. _7-1-2-3-1:

INFHOMMEDIUM (infinite homogeneous medium) Treatment
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The **INFHOMMEDIUM** treatment is best suited for large masses of
materials where the size of each material is large compared with the
average mean-free path of the material or where the fraction of the
material that is a mean-free path from the surface of the material is
very small. When **INFHOMMEDIUM** cell is specified, the material in the
unit cell is treated as an infinite homogeneous lump. Systems composed
of small fuel lumps or resonance nuclides sandwiched between moderating
regions should not be treated as infinite homogeneous media. In these
cases a MULTIREGION or LATTICECELL geometry should be used.

.. _7-1-2-3-2:

LATTICECELL Treatment
^^^^^^^^^^^^^^^^^^^^^^

The **LATTICECELL** model is appropriate for arrays of resonance
absorber mixtures—with or without clad—arranged in a square or a
triangular pitch configuration within a moderator. Annular fuel (e.g.,
with an internal moderator in the center) can also be addressed. Input
data for the **LATTICECELL** treatment are described in :ref:`7-1-3-5`.
Self-shielded cross sections are generated for each material zone in a
unit cell of the lattice. If a nuclide appears in more than one zone,
self-shielded cross sections are produced for each zone where the
nuclide is present. Limitations of the **LATTICECELL** treatment are
listed below.

1.    The cell description is limited to unit cells for arrays of
      spherical, plate (slab), or cylindrical fuel bodies. In the case
      of cylindrical pins in a square-pitch lattice, the default
      (*parm=centrm*) self-shielding calculation uses the CENTRM method
      of characteristics (MoC) option to represent the 2D rectangular
      unit cell with reflected boundary conditions. By default,
      self-shielding for all other arrays uses a CENTRM 1D S\ :sub:`N`
      calculation for the unit cell (spherical and cylindrical
      geometries use Wigner-Seitz cells). If *parm=bonami* is specified,
      heterogeneous self-shielding effects are treated by equivalence
      theory :cite:`williams_resonance_2011` The computation option *parm=2region*, described
      in :ref:`7-1-3-1`, can also be used for self-shielding lattice
      cells.

2.    Only predefined choices of cell configurations are available. The
      available options are described in detail in :ref:`7-1-3-5`.

3.    The basic treatment for **LATTICECELL** assumes an infinite, uniform
      array of unit cells. This assumption is a good approximation for
      interior fuel regions within a large, uniform array. The
      approximation becomes less rigorous for fuel regions on the
      periphery of the array or adjacent to a nonuniformity (e.g.,
      control rod, water hole, etc.) in the lattice. For some cases it
      may be desirable to address this issue by specifying a different
      lattice cell for this type of fuel pin and using a modified
      procedure to define an effective unit cell, as described below.

*\****\* LATTICECELL treatment for nonuniform arrays*.

Nonuniform lattice effects may be treated in CENTRM calculation by
specifying the keyword **DAN2PITCH=**\ *dancoff* in the optional CENTRM
DATA (see :ref:`7-1-3-9`). In this approach, the SCALE standalone code
MCDancoff must be run prior to the self-shielding calculation in order
to compute Dancoff factors for the fuel regions of interest in the
nonuniform lattice configuration. MCDancoff performs a simplified
one-group Monte Carlo calculation to compute Dancoff factors for complex
geometries (see :ref:`7-8`). The Dancoff value for the fuel region of
interest is assigned to the DAN2PITCH keyword in the input for the
corresponding cell. Using an iterative procedure, CENTRM computes the
pitch of a uniform lattice that has the same Dancoff value as the
nonuniform lattice.

.. _7-1-2-3-3:

MULTIREGION Treatment
^^^^^^^^^^^^^^^^^^^^^

The **MULTIREGION** treatment is appropriate for 1-D geometric regions
where the geometry effects may be important, but the limited number of
zones and boundary conditions in the **LATTICECELL** treatment are not
applicable. The **MULTIREGION** unit cell allows more flexibility in the
placement of the mixtures but requires all regions of the cell to have
the same geometric shape (i.e., slab, cylinder, sphere, buckled slab, or
buckled cylinder). Lattice arrangements can be approximated by
specifying a non-vacuum boundary condition on the outer boundary. See
:ref:`7-1-3-6` for more details. Limitations of the **MULTIREGION**
cell treatment are listed below.

1.    A **MULTIREGION** cell is limited to a 1-D approximation of the
      system being represented. An exact 1D model can be defined for the
      following multizone geometries with vacuum boundary conditions:
      spheres, infinitely long cylinders, and slabs; and for an infinite
      array of slabs with reflected or periodic boundaries.

2.    The shape of the outer boundary of the **MULTIREGION** cell is the
      same as the shape of the inner regions. Cells with curved outer
      surfaces cannot be stacked physically to create arrays; however,
      arrays can be approximated by a Wigner-Sietz cell with a white
      outer boundary condition, where the outer radius is defined to
      preserve the area of the true rectangular or hexagonal unit cell.

3.    Boundary conditions available in a **MULTIREGION** problem include
      vacuum (eliminated at the boundary), reflected (reflected about
      the normal to the surface at the point of impact), periodic
      (a particle exiting the surface effectively enters an identical
      cell having the same orientation and continues traveling in the
      same direction), and white (isotropic return about the point of
      impact). Reflected and periodic boundary conditions on a slab can
      represent real physical situations but are not valid on a curved
      outer surface. A single, non-interacting cell has a vacuum outer
      boundary condition. If the cell outer boundary condition is not a
      vacuum boundary, the unit cell approximates some type of array.

4.    When using the CENTRM/PMC self-shielding method, the MULTIREGION cell
      model must include fissionable material. This can be accomplished
      by adding a trace amount of a fissionable material to one or more
      mixtures, or by modeling a region of homogenized fuel and water,
      or by adding a thin (e.g., 1e-6 cm-thick) layer containing at
      least a trace of a fissionable nuclide on the periphery of the
      problem.

.. _7-1-2-3-4:

DOUBLEHET Treatment
^^^^^^^^^^^^^^^^^^^

**DOUBLEHET** cells use a specialized CENTRM/PMC calculational approach
to treat resonance self-shielding in “doubly heterogeneous” systems. The
fuel for these systems typically consists of small, heterogeneous,
spherical fuel particles (grains) embedded in a moderator matrix to form
the fuel compact. The fuel-grain/matrix compact constitutes the first
level of heterogeneity. Cylindrical(rod). spherical (pebble), or slab
fuel elements composed of the compact material are arranged in a
moderating medium to form a regular or irregular lattice, producing the
second level of heterogeneity. The fuel elements are also referred to as
“macro cells.” Advanced reactor fuel designs that use TRISO
(tri-material, isotopic) or fully ceramic microencapsulated (FCM) fuel
require the **DOUBLEHET** treatment to account for both levels of
heterogeneities in the self-shielding calculations. Simply ignoring the
double-heterogeneity by volume-weighting the fuel grains and matrix
material into a homogenized compact mixture can result in a large
reactivity bias.

In the **DOUBLEHET** cell input, keywords and the geometry description
for grains are similar to those of the **MULTIREGION** treatment, while
keywords and the geometry for the fuel element (macro-cell) are similar
to those of the **LATTICECELL** treatment. The following rules apply to
the **DOUBLEHET** cell treatment and must be followed. Violation of any
rules may cause a fatal error.

1. As many grain types as needed may be specified for each unique fuel
   element. Note that grain type is different from the number of grains
   of a certain type. For example, a fuel element that contains both
   UO\ :sub:`2` and PuO\ :sub:`2` grains has two grain types. The same
   fuel element may contain 10000 UO\ :sub:`2` grains and
   5000 PuO\ :sub:`2` grains. In this case, the number of grains of type
   UO\ :sub:`2` is 10000, and the number of grains of type PuO\ :sub:`2`
   is 5000.

2. As many fuel elements as needed may be specified, each requiring its
   own **DOUBLEHET** cell. This may be the case for systems with many
   fuel elements at different fuel enrichments, burnable poisons, etc.
   Each fuel element may have one or more grain types.

3. Since the grains are homogenized into a new mixture to be used in the
   fuel element (macro-cell) cell calculation, a unique fuel mixture
   number must be entered. XSProc creates a new material with the new
   mixture number designated by the keyword f\ *uelmix=*, containing all
   the nuclides that are homogenized. The user must assign the new
   mixture number in the transport solver geometry (e.g., KENO) input
   unless a cell-weighted mixture is created.

4. The type of lattice or array configuration for the fuel-element may
   be spheres on a triangular pitch (**SPHTRIANGP**), spheres on a
   square pitch (**SPHSQUAREP**), annular spheres on a triangular pitch
   (**ASPHTRIANGP)**, annular spheres on a square pitch
   (**ASPHSQUAREP)**, cylindrical rods on a triangular pitch
   (**TRIANGPITCH**), cylindrical rods on a square pitch
   (**SQUAREPITCH**),annular cylinderical rods on a triangular pitch
   (**ATRIANGPITCH)**, annular cylindrical rods on a square pitch
   (**ASQUAREPITCH)**, a symmetric slab (**SYMMSLABCELL)**, or an
   asymmetric slab (**ASYMSLABCELL)**.

5. If there is only one grain type for a fuel element, the user must
   enter either the pitch, the aggregate number of particles in the
   element, or the volume fraction for the grains. The code needs the
   pitch and will directly use it if entered. If pitch is not given,
   then the volume fraction (if given) is used to calculate the pitch.
   If neither the pitch nor the volume fraction is given, then the
   number of particles is used to calculate the pitch and the volume
   fraction. The user should only enter one of these items.

..

   If the fuel matrix contains more than one grain type, all types are
   homogenized into a single mixture for the compact. As for the one
   grain type case, the pitch is needed for the spherical cell
   calculations. However, the pitch by itself is not sufficient to
   perform the homogenization. Since each grain’s volume is known (grain
   dimensions must always be entered), entering the number of particles
   for each grain type essentially provides the total volume of each
   grain type and therefore enables the calculation of the volume
   fraction and the pitch. Likewise, entering the volume fraction for
   each grain type essentially provides the total volume of each grain
   type and therefore enables the calculation of the number of particles
   and the pitch. Therefore, one of these two quantities must be entered
   for multiple grain types. In these cases, since pitch is not given,
   the available matrix material is distributed around the grains of
   each grain type proportional to the grain volume and is used to
   calculate the corresponding pitch. Over-specification is allowed as
   long as the values are not inconsistent to greater than 0.01%.

6. For cylindrical rods and for slabs, fuel height must also be
   specified. For slabs the slab width must also be specified.

7. The CENTRM calculation option must be S\ :sub:`n`.

.. _7-1-2-4:

Cell weighting of MG cross sections
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Cell-weighted self-shielded cross sections are created when
**CELLMIX**\ = is specified in a **LATTICECELL** or **MULTIREGION** cell
input. In this case, after finishing the self-shielding calculations for
all mixtures in the cell, XSProc calls the computational module XSDRNPM,
which solves the 1-D MG transport equation to obtain k\ :sub:`∞` and
space-dependent MG fluxes for the cell. The resultant fluxes are used to
compute MG flux disadvantage factors for processing cell-weighted
cross sections of all nuclides in the cell. When the cell-weighted
cross sections are used with *homogenized* number densities of the cell
nuclides, the reaction rates of the homogenized mixture preserve the
spatially averaged reactions rates of the heterogeneous configuration.
The user must input a new mixture ID to identify the homogenized mixture
associated with the cell-weighted cross sections. **This homogenized
mixture should not be used in the heterogeneous geometry data for other
transport codes such as KENO, NEWT, etc.** Instead, the cell-homogenized
mixture that is created should be used at the location of the original
cell. Also, cell weighted homogenized cross sections should not be used
in MG sensitivity data calculations performed using the TSUNAMI
sequences.

.. _7-1-3:

XSPROC Input Data Guide
-----------------------

XSProc input data are entered in free form, allowing alphanumeric data,
floating-point data, and integer data to be entered in an unstructured
manner. Up to 252 characters per line are allowed. Data can usually
start or end in any column. Each data entry must be followed by one or
more blanks to terminate the data entry. For numeric data, either a
comma or a blank can be used to terminate each data entry. Integers may
be entered for floating values. For example, 10 will be interpreted as
10.0 if a floating point value is required. Imbedded blanks are not
allowed within a data entry unless an E precedes a single blank as in an
unsigned exponent in a floating-point number. For example, 1.0E 4 would
be correctly interpreted as 1.0 × 10\ :sup:`4`. A number with a negative
exponent must include an “E”. For example 1.0-4 cannot be used for
1.0E-4.

The word “END” is a special data item. An END may have a name or label
associated with it. The name or label associated with an END is
separated from the END by a single blank and is a maximum of
12 characters long. *At least two blanks or a new line MUST follow every
labeled and unlabeled END. WARNING: It is the user’s responsibility to
ensure compliance with this restriction. Failure to observe this
restriction can result in the use of incorrect or incomplete data
without the benefit of warning or error messages.*

Multiple entries of the same data value can be achieved by specifying
the number of times the data value is to be entered, followed by either
R, \*, or $, followed by the data value to be repeated. Imbedded blanks
are not allowed between the number of repeats and the repeat flag. For
example, 5R12, 5*12, 5$12, or 5R 12, etc., will enter five successive
12’s in the input data. Multiple zeros can be specified as nZ where n is
the number of zeroes to be entered.

.. _7-1-3-1:

XSProc data checking and resonance processing options
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. highlight:: scale

To check the XSProc input data, run CSAS-MG and specify PARM=CHECK or
PARM=CHK after the sequence specification as shown below.

::

  =CSAS-MG PARM=CHK

In this case the actual XSProc cross section processing calculations are
not performed. The input data are checked, the problem description is
printed, appropriate error and warning messages are printed, and a table
of additional data is printed.

Resonance processing will automatically be performed by the default
method for the sequence selected. The default methods are CENTRM/PMC for
CSAS, TRITON, and TSUNAMI sequences and BONAMI for the MAVRIC sequences.
Alternatively, a resonance processing procedure may be chosen by
entering PARM=\ *option*, where *option* CENTRM selects the recommended
CENTRM/PMC transport method for each cell type, *option* 2REGION selects
the CENTRM/PMC two-region calculation, and *option* BONAMI applies full
range Bondarenko factors to all energy groups without utilizing
CENTRM/PMC. For example, to run CSAS1X sequence using only BONAMI for
self-shielding, rather than the default CENTRM/PMC method, enter the
computational sequence specification shown below.

::

  =CSAS1X PARM=BONAMI

Multiple PARM options are specified by enclosing parameters in
parenthesis, such as

::

  =CSAS1X PARM=(CHK, BONAMI)

XSProc resonance self-shielding options are summarized below.

PARM=BONAMI.

  This is the fastest MG processing method. It performs
  resonance self-shielding for all energy groups using the Bondarenko
  method. BONAMI computes the appropriate background cross section of a
  given unit cell and then interpolates the corresponding shielding factor
  from Bondarenko factors on the MG library. Dancoff factors needed to
  evaluate the background cross section for lattices are computed
  internally, but these can be overridden by input values in the MORE DATA
  block. More details on this method are given in the BONAMI section of
  the manual.

PARM=CENTRM.

  This executes the CENTRM/PMC modules to process shielded MG
  cross sections using CE flux spectra calculated with the recommended
  type of CE transport solver for the designated type of cell. The
  CENTRM-recommended CE transport solvers are (a) infinite homogeneous
  medium calculation for INFHOMMEDIUM cells; (b) 2D MoC transport
  calculation for a LATTICECELL consisting of cylindrical fuel pins in a
  square lattice; and (c) 1-D discrete S\ :sub:`n` transport for all other
  LATTICECELLs and for all MULTIREGION cells. The recommended type of
  transport solver can be overridden for individual cells, as well as for
  selected energy ranges, by using the CENTRM DATA block described in
  :ref:`7-1-3-9`.

PARM=2REGION.

  The CENTRM two-region (2R) option computes the PW flux using a
  simplified collision probability method for an absorber (e.g., fuel)
  region surrounded by an external moderator region which has an
  asymptotic energy spectrum. To account for the heterogeneous effects of
  a lattice, a correction known as the Dancoff factor is applied to the
  escape probabilities in the 2R calculation (see the CENTRM chapter of
  the SCALE manual). These Dancoff factors are calculated internally by
  XSProc for a uniform array of mixtures in slab, spherical, or
  cylindrical geometries. These mixture-dependent Dancoff factors can be
  modified by user input using the DAN parameters contained in the MORE
  DATA block, as defined in :ref:`7-1-3-8`.

*Note on CENTRM/PMC self-shielding options:*

The energy range of the CENTRM flux calculation is subdivided into three
sections: fast, PW, and low energy. PMC only computes self-shielded
cross sections for groups within the PW range defined by parameters
*demax* and *demin*, which, respectively, define the upper and lower
energies of the CENTRM PW flux calculation. Problem-dependent cross
sections for groups in the fast and low energy ranges are obtained with
the more approximate BONAMI method. Default values for parameters
*demax* and *demin* are defined appropriately for self-shielding of
important resonance materials in thermal reactor systems. The PW
self-shielding range can be extended or decreased for individual cells
by modifying these parameters using CENTRM DATA.

.. _7-1-3-2:

XSProc input data
~~~~~~~~~~~~~~~~~

The types of input data required for XSProc are given in :numref:`tab7-1-1`,
and individual entries are explained in the text following the table.
The title, cross section library name (either CE or MG), and standard
composition specification data (**READ COMP** input block) are required
for all sequences that use XSProc. The name of the cross section library
is used to determine if the transport solver is executed using CE or MG
data (e.g., CE or MG KENO calculations). The unit cell descriptions
(**READ CELL** input block) are only used for MG self-shielding
calculations. If the specified sequence executes in CE mode, the cell
data input can be omitted, or it will be skipped if present. If the cell
data information is omitted for MG calculations, all mixtures are
self-shielded using the infinite medium approximation.

There are seven standard SCALE sequences that run just XSProc, and
produce a MG cross section library or libraries.

**=XSPROC** produces three libraries with an optional fourth library.

-  **sysin.microLib** is a self-shielded library of the individual
   nuclides in the problem for use in a later transport calculation,

-  **sysin.macroLib** is a self-shielded library of the mixture cross
   sections in the problem for use in a later transport calculation,

-  **sysin.smallMicroLib** is a self-shielded library of specific
   reaction rate cross sections and the elastic and total inelastic
   scattering transfer matrices for later use in calculating reaction
   rates and sensitivity values, and

-  **sysin.xsdrnWeightedLib** is an optional library produced if the
   input specifies having **XSDRN** do a weighting calculation. This can
   be a cell weighted and/or a group collapse calculation. The library
   can be either individual nuclides or mixtures, depending on input.

**=CSAS-MG** produces an **ft04f001** library that is equivalent to the
**sysin.microLib**. With appropriate input it can also produce an
**ft03f001** which is equivalent to **sysin.xsdrnWeightedLib** above.

**=CSASI** or **=CSASIX** produce an **ft04f001** library that is
equivalent to **sysin.microLib**, and an **ft02f001** library that is
equivalent to **sysin.macroLib**. CSASIX will run an **XSDRN** on the
first cell without any MOREDATA input. With appropriate input they both
can produce an **ft03f001** that is the equivalent of
**sysin.xsdrnWeightedLib**.

**=CSAS1** or **=CSAS1X** produce an **ft04f001** library that is the
equivalent of **sysin.microLib**. Both sequences will run an **XSDRN**
on the first cell. With appropriate input, they both can produce an
**ft03f001** that is the equivalent of **sysin.xsdrnWeightLib**.

**=T-XSEC** produces an **ft04f001** library that is equivalent to
**sysin.macroLib**. and an **ft44f001** library that is equivalent to
sysin.microLib.

The reactions (MT numbers) written to each library are listed in the
``SequenceNeutronMT.txt`` file located in the etc directory installed with
SCALE.

.. _tab7-1-1:

.. table:: Outline of XSProc input data
  :align: center

  +-----------------+-----------------+-----------------+-----------------+
  | Data Position   | Type of Data    | Data Entry      | Comments        |
  +=================+=================+=================+=================+
  | 1               | Title           | Enter title     | Limit to 80     |
  |                 |                 |                 | characters      |
  +-----------------+-----------------+-----------------+-----------------+
  | 2               | Cross section   |                 | The currently   |
  |                 | library name    |                 | available       |
  |                 |                 |                 | libraries are   |
  |                 |                 |                 | listed in the   |
  |                 |                 |                 | table *Standard |
  |                 |                 |                 | SCALE           |
  |                 |                 |                 | cross-section   |
  |                 |                 |                 | libraries* of   |
  |                 |                 |                 | the XSLib       |
  |                 |                 |                 | chapter.        |
  +-----------------+-----------------+-----------------+-----------------+
  | 3               | Standard        | Enter the       | | Begin this    |
  |                 | composition     | appropriate     |   data block    |
  |                 |                 | data            |   with          |
  |                 | specification   |                 | | **READ COMP** |
  |                 | data            |                 |                 |
  |                 |                 |                 | | and terminate |
  |                 |                 |                 |   with          |
  |                 |                 |                 | | **END COMP**. |
  |                 |                 |                 |                 |
  |                 |                 |                 | See Section     |
  |                 |                 |                 | :ref:`7-1-3-3`. |
  +-----------------+-----------------+-----------------+-----------------+
  | 4               | Unit cell(s)    |                 | Begin this data |
  |                 | description     |                 | block with      |
  |                 |                 |                 | READ CELL (or   |
  |                 | for MG          |                 | CELLDATA)       |
  |                 | calculations    |                 |                 |
  |                 |                 |                 |                 |
  |                 | only            |                 |                 |
  +-----------------+-----------------+-----------------+-----------------+
  |                 | a. Type of self | **INFHOMMEDIUM**| These are the   |
  |                 | shielding       |                 | available       |
  |                 | calculation     |                 | options.        |
  |                 |                 | **LATTICECELL** |                 |
  |                 |                 |                 | See the         |
  |                 |                 | **MULTIREGION** | explanation in  |
  |                 |                 |                 | Section         |
  |                 |                 | DOUBLEHET       | :ref:`7-1-3-2`. |
  +-----------------+-----------------+-----------------+-----------------+
  |                 | b. Unit cell    | Enter the       | See             |
  |                 | geometry        | appropriate     | :ref:`7-1-3-4`  |
  |                 | specification   | data            | **INFHOMMEDIUM**|
  |                 |                 |                 |                 |
  |                 |                 |                 |                 |
  |                 |                 |                 | See Section     |
  |                 |                 |                 | :ref:`7-1-3-5`  |
  |                 |                 |                 | **LATTICECELL** |
  |                 |                 |                 | .               |
  |                 |                 |                 |                 |
  |                 |                 |                 | See Section     |
  |                 |                 |                 | :ref:`7-1-3-6`  |
  |                 |                 |                 | **MULTIREGION** |
  |                 |                 |                 | .               |
  |                 |                 |                 |                 |
  |                 |                 |                 | See Section     |
  |                 |                 |                 | :ref:`7-1-3-7`  |
  |                 |                 |                 | DOUBLEHET.      |
  +-----------------+-----------------+-----------------+-----------------+
  |                 | c. Optional     | Enter the       | | Begin this    |
  |                 | MORE parameter  | desired data    |   data block    |
  |                 | data            |                 |   with          |
  |                 |                 |                 | | **MORE DATA** |
  |                 |                 |                 |   (or           |
  |                 |                 |                 |   **MOREDATA**) |
  |                 |                 |                 |                 |
  |                 |                 |                 | | and terminate |
  |                 |                 |                 |   with          |
  |                 |                 |                 | | **END MORE**  |
  |                 |                 |                 |   (or END       |
  |                 |                 |                 |   **MOREDATA**) |
  |                 |                 |                 | .               |
  |                 |                 |                 |                 |
  |                 |                 |                 | Use only if     |
  |                 |                 |                 | MORE parameter  |
  |                 |                 |                 | data are to be  |
  |                 |                 |                 | entered;        |
  |                 |                 |                 | otherwise, omit |
  |                 |                 |                 | these data      |
  |                 |                 |                 | entirely. See   |
  |                 |                 |                 | :ref:`7-1-3-8`  |
  |                 |                 |                 |                 |
  +-----------------+-----------------+-----------------+-----------------+
  |                 | d. Optional     | Enter the       | Begin this data |
  |                 | CENTRM          | desired data    | block with      |
  |                 | parameter data  |                 |                 |
  |                 |                 |                 | **CENTRM DATA** |
  |                 |                 |                 | (or             |
  |                 |                 |                 | **CENTRMDATA**) |
  |                 |                 |                 |                 |
  |                 |                 |                 | and terminate   |
  |                 |                 |                 | with            |
  |                 |                 |                 |                 |
  |                 |                 |                 | **END CENTRM**  |
  |                 |                 |                 | (or END         |
  |                 |                 |                 | **CENTRMDATA**) |
  |                 |                 |                 | .               |
  |                 |                 |                 |                 |
  |                 |                 |                 | Use only if     |
  |                 |                 |                 | CENTRM          |
  |                 |                 |                 | parameter data  |
  |                 |                 |                 | are to be       |
  |                 |                 |                 | entered;        |
  |                 |                 |                 | otherwise, omit |
  |                 |                 |                 | these data      |
  |                 |                 |                 | entirely.       |
  +-----------------+-----------------+-----------------+-----------------+
  |                 | e. End of unit  |                 | Terminate with  |
  |                 | cell data       |                 | END CELL (or    |
  |                 |                 |                 | END CELLDATA)   |
  +-----------------+-----------------+-----------------+-----------------+
  | Repeat          |                 |                 |                 |
  | positions 4a–4d |                 |                 |                 |
  | as needed to    |                 |                 |                 |
  | specify all     |                 |                 |                 |
  | unit cells.     |                 |                 |                 |
  | Position 4 data |                 |                 |                 |
  | are applicable  |                 |                 |                 |
  | to the MG       |                 |                 |                 |
  | calculations    |                 |                 |                 |
  | only.           |                 |                 |                 |
  +-----------------+-----------------+-----------------+-----------------+

1.    TITLE. An 80-character maximum title is required. The title is the
      first 80 characters of the XSPROC data.

2.    CROSS SECTION LIBRARY NAME. This item specifies the cross section
      library that is to be used in the calculation. See Table *Standard
      SCALE cross-section libraries* in the XSLIB chapter of the SCALE
      manual for a discussion of the available libraries.

3.    The keywords **READ COMP** followed by the standard compositions
      specifications. These data are used to define mixtures used in the
      problem. See :ref:`7-1-3-3` and :numref:`tab7-1-2` for a description of
      the standard composition specification data. These data are
      required for every problem. After all mixtures have been entered,
      the keywords **END COMP** must be entered.

4.    The keywords **READ CELLDATA** followed by the input describing each
      unit cell as defined below. After all unit cells are described,
      the keywords **END CELLDATA** terminate this input block.

   a.    TYPE OF CALCULATION. The options are **INFHOMMEDIUM**,
         **LATTICECELL**, **MULTIREGION**, **DOUBLEHET**, or nothing. A
         description of these cell types and the associated
         computational methods are provided in :ref:`7-1-2-3`. If all
         input mixtures are to be treated as infinite homogeneous media,
         the **CELLDATA** block can be omitted. In this case the
         self-shielding calculations will not account for any
         geometrical effects, so users should be careful in applying
         this approach. Similarly, mixtures not explicitly assigned to a
         cell are treated as infinite homogeneous media in the manner
         discussed in :ref:`7-1-2-3`.

   b.    CELL GEOMETRY SPECIFICATION. See :ref:`7-1-3-4` and :numref:`tab7-1-3`
         for an explanation of the optional unit cell data associated
         with an **INFHOMMEDIUM** problem. See :ref:`7-1-3-5` for an
         explanation of the data associated with **LATTICECELL**
         problems. :ref:`7-1-3-6` explains the data required for a
         **MULTIREGION** problem. :ref:`7-1-3-7` explains the required
         data for a **DOUBLEHET** problem. The **DOUBLEHET** input may
         be thought of as a combination of **MULTIREGION** input for the
         fuel grains and **LATTICECELL** input for the fuel element.

   c.    OPTIONAL MORE PARAMETER DATA. This option allows certain defaulted
         parameters to be re-specified by the user. This block begins
         with **MORE DATA** and is used by XSDRN. These data apply only
         to the unit cell immediately preceding them. Data placed prior
         to all unit cell data apply to all materials not listed in any
         unit cell and are treated as infinite homogeneous media. Omit
         these data unless they are needed. This block ends with **END
         MORE**. See :ref:`7-1-3-8`.

   d.    OPTIONAL CENTRM PARAMETER DATA. This optional data block begins
         with **CENTRM DATA** and ends with **END CENTRM**. These data
         allow the user to override default data for CENTRM and PMC.
         These data apply only to the unit cell immediately preceding
         them. Data placed prior to all unit cell data apply to all
         materials not listed in any unit cell and are treated as
         infinite homogeneous media.

.. _7-1-3-3:

Standard composition specification data
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Mixtures utilized in the problem are defined using standard composition
specification data. The standard composition input begins with the
keywords **READ COMP**, followed by standard composition specifications
for all mixtures in the problem. When all mixtures have been described,
enter the words **END COMP** to signal the completion of this block of
data. XSProc computes macroscopic cross sections for all mixtures
defined in the **COMP** block.

The required input for the standard composition specification data
varies, depending on the type of standard composition material. However,
every standard composition specification must include the following:

1. a standard composition material name.

2. a mixture number (MX) that contains this material, and

3. a terminator for the standard composition specification data (enter
      the word END).

The types of standard compositions in SCALE are (a) basic mixtures, (b)
fissile solutions, (c) chemical compounds, and (d) alloys. The four
general options for inputting these types of data are shown in :numref:`tab7-1-2`.
For some cases, more than one option could possibly be used to
specify the mixture. The user may select whichever options are most
convenient to define a particular mixture, and these may be entered in
any order.

.. _tab7-1-2:

.. table:: Outline of standard composition specification options (Mixtures can be defined using one or more of these options in any order).
  :align: center

  +-----------------------------------+-----------------------------------+
  | Input data                        | Comments                          |
  |                                   |                                   |
  | name                              |                                   |
  +-----------------------------------+-----------------------------------+
  | **READ COMP**                     |    Enter once for a problem.      |
  |                                   |    Enter the words **READ COMP**  |
  |                                   |    prior to entering any standard |
  |                                   |    composition data.              |
  +-----------------------------------+-----------------------------------+
  | **sc**                            |    This option is used for        |
  |                                   |    defining basic mixtures. Enter |
  |                                   |    one of the alphanumeric        |
  |                                   |    identifiers, symbols, or names |
  |                                   |    from Standard Composition      |
  |                                   |    Library tables *Isotopes in    |
  |                                   |    standard composition library*, |
  |                                   |    *Isotopes and their natural    |
  |                                   |    abundances*, *Elements and     |
  |                                   |    special nuclide symbols*,      |
  |                                   |    *Compounds*, or *Alloys and    |
  |                                   |    mixtures* in place of SC. This |
  |                                   |    indicates the isotope,         |
  |                                   |    nuclide, compound, or alloy    |
  |                                   |    that will make up this         |
  |                                   |    standard composition.          |
  |                                   |    See :numref:`tab7-1-2a` for    |
  |                                   |    additional required and        |
  |                                   |    optional data for each         |
  |                                   |    standard composition.          |
  +-----------------------------------+-----------------------------------+
  | **SOLUTION**                      |    This option is used to specify |
  |                                   |    a fissile solution mixture.    |
  |                                   |    See :numref:`tab7-1-2b` for    |
  |                                   |    additional required and        |
  |                                   |    optional data for each         |
  |                                   |    solution. End the data with an |
  |                                   |    **END**.                       |
  +-----------------------------------+-----------------------------------+
  | **ATOM**                          |    This option creates a chemical |
  |                                   |    compound mixture composed of   |
  |                                   |    the specified nuclide in       |
  |                                   |    the compound. Each nuclide is  |
  |                                   |    entered followed by the        |
  |                                   |    relative number of atoms of    |
  |                                   |    the nuclide in the compound.   |
  |                                   |    All compounds must begin with  |
  |                                   |    the four letters \ **ATOM**    |
  |                                   |    followed by up to eight        |
  |                                   |    additional alphanumeric        |
  |                                   |    characters. :numref:`tab7-1-2c`|
  |                                   |    shows additional required and  |
  |                                   |    optional data for each         |
  |                                   |    compound.                      |
  +-----------------------------------+-----------------------------------+
  | **WTPT**                          |    This option creates a          |
  |                                   |    mixture/alloy composed of the  |
  |                                   |    specified nuclides in          |
  |                                   |    the mixture/alloy. Each        |
  |                                   |    nuclide is entered followed by |
  |                                   |    the weight percent of the      |
  |                                   |    nuclide in the mixture/alloy.  |
  |                                   |    All mixture/alloys must begin  |
  |                                   |    with the four letters **WTPT** |
  |                                   |    followed by up to eight        |
  |                                   |    additional alphanumeric        |
  |                                   |    characters. :numref:`tab7-1-2d`|
  |                                   |    shows additional required and  |
  |                                   |    optional data for each         |
  |                                   |    arbitrary physical mixture or  |
  |                                   |    alloy.                         |
  +-----------------------------------+-----------------------------------+
  | **END COMP**                      |    Enter once for a problem.      |
  |                                   |    Enter the exact words **END    |
  |                                   |    COMP** when all the standard   |
  |                                   |    composition components have    |
  |                                   |    been described. At least two   |
  |                                   |    blanks or a new line must      |
  |                                   |    follow the words **END COMP**  |
  |                                   |    prior to continuing data       |
  |                                   |    entry.                         |
  +-----------------------------------+-----------------------------------+

Names of the standard composition materials (the alphanumeric
identifiers) appearing in the **COMP** block input must be selected from
the tables of elements, compounds, solutions, and alloys given in the
SCALE manual section describing the Standard Composition Library. An
error message will be printed if the user enters an invalid standard
composition material name or if any isotopes in the compound do not
exist in the specified library

Input data to define each of the standard composition types in
:numref:`tab7-1-2` are summarized in :numref:`tab7-1-2a` through :numref:`tab7-1-2d`. Optional input is
indicated by curly brackets { }. *Since some of the input is not keyword
based, the order of entries is important in the standard composition
specification*. The temperature specification is used for Doppler
broadening and/or determination of the proper thermal scattering data.
Input material densities are not modified for temperature effects.
Additional description of the standard composition input for each type
of material is given following all the tables. As in the tables, input
parameters enclosed by curly brackets { } indicate that these are
optional.

.. _tab7-1-2a:
.. list-table:: Standard composition specification for basic mixtures.
  :align: center


  * - .. image:: figs/XSProc/tab2a.svg
        :align: center
        :width: 800

.. _tab7-1-2b:
.. list-table:: Standard composition specification for solutions.
  :align: center

  * - .. image:: figs/XSProc/tab2b.svg
        :width: 800

.. _tab7-1-2c:
.. list-table:: Standard composition specification for chemical compounds.
  :align: center

  * - .. image:: figs/XSProc/tab2c.svg
        :width: 800

.. _tab7-1-2d:
.. list-table:: Input specification for user-specified mixture/alloy data.
  :align: center

  * - .. image:: figs/XSProc/tab2d.svg
        :width: 800

STANDARD COMPOSITION INPUT FOR BASIC MIXTURES (see :numref:`tab7-1-2a`).

Two input syntaxes are available for standard composition specifications
of basic mixtures in the **COMP** block. The first uses information
(e.g., densities, atomic weights, physical constants, etc.) contained in
the Standard Composition Library, along with user specified input, to
automatically compute the number densities for mixture components. In
the second option, the user computes the nuclide number densities, and
inputs these directly for each component of the mixture. XSProc
recognizes syntax 2 if the third entry of the composition specification
is zero, as shown below. It is allowable to use syntax 1 for some
standard composition specifications and syntax 2 for others. The two
syntaxes to define basic mixtures with the standard composition
specifications are shown below.

**syntax 1: Standard Composition Library data used to compute number
densities.**

  **sc** *mx* **DEN**\ =\ *roth* {**VF**\ =}\ *vf* *temp* *iza*\ :sub:`1` *wtp*\ :sub:`1` …
  *iza*\ :sub:`N` *wtp*\ :sub:`N` **END**

**syntax 2: User input number densities**

  **sc** *mx* 0 *aden* *temp* **END**

The definitions for these input parameters are given below.

A1. **sc**

  STANDARD COMPOSITION MATERIAL NAME. This corresponds to one
  of the material names given in the Standard Composition Library for
  isotopes, elements, thermal moderators and activity materials, chemical
  compounds, and alloys/mixtures. Some types of these materials require
  entering certain data such as the volume fraction or theoretical density
  and other engineering-type data. For standard compositions containing
  more than one isotope of an element (such as UO\ :sub:`2`), the user is
  free to specify the weight percent for each isotope, such that they
  total 100%. See the Basic standard composition specifications section
  for examples of basic standard compositions.

A2. *mx*

  MIXTURE ID NUMBER. An arbitrary mixture number is required on
  every standard composition specification for both syntaxes. It defines
  the mixture that contains the material defined by the standard
  composition specification data. The mixture numbers are utilized in the
  CELLDATA block Cell Block for INFHOMMEDIUM, LATTICECELL, MULTIREGION, or
  DOUBLEHET problems and the geometry data.

A3. **DEN**\ =\ *roth*

  MIXTURE DENSITY. The keyword **DEN** is assigned
  a value of *roth,* where *roth* is the specified density of the mixture
  component in g/cm\ :sup:`3`. It should always be entered for materials
  that contain enriched multi-isotopic nuclides. The effective density of
  the material component is equal to the product of *roth* and *vf.* An
  example of this is demonstrated in Appendix A.

A4. {**VF**\ =}\ *vf*

  VOLUME FRACTION. The keyword **VF** is assigned a
  value of *vf*. It is also allowable to omit the keyword **VF=** and just
  enter the value *vf* . The default value of the volume fraction is 1.0.
  The volume fraction can be interpreted as

   a. the volume fraction of this standard composition component in the
   mixture,

   b. the density of the standard composition component in this
   application divided by the theoretical or default density given in
   the Standard Composition Library, or

   c. the product of (a) and (b).

   Appendix A discusses the interaction between *roth* and *vf*. For
   example, assume a homogenized mixture representing the water
   moderator and Zircaloy cladding around a fuel pin is to be described.
   If the volume of the clad is 5.32 cc and the volume of the water
   moderator is 44.68 cc, the mixture can be described using
   H\ :sub:`2`\ O with a volume fraction of 0.8936
   [i.e., 44.68/(44.68+5.32)] and ZIRCALOY with a volume fraction of
   0.1064 [i.e., 5.32/(44.68+5.32)].

A5. *aden*

  NUMBER DENSITY (not used for syntax 1, but required for 2).
  The number density is entered ONLY if 3\ :sup:`rd` entry on the standard
  composition specification is entered as zero. The number density is
  entered in units of atoms per barn-cm.

A6. *temp*

  TEMPERATURE. The default value of the temperature is 300 K.
  The temperature can be omitted if entries A7 and A8 are also omitted.

A7. *iza*

  ISOTOPE ZA NUMBER. Enter a value for each isotope in the
  standard composition component, entry 1. Do not enter a value if the
  volume fraction, **VF**, is zero (A4 above).

   The ZA number of the isotope is entered if the user wishes to specify
   the isotopic distribution. This is done by entering *iza* and *wtp*
   for each isotope until all the desired isotopes have been described.
   In most cases the “ZA” ID number is (A+1000*Z), where A is the atomic
   mass or weight of the isotope, and Z is the atomic number. For
   example, the ZA number for :sup:`235`\ U is 92235.

   Entries A7 and A8 can be skipped if the default values listed in
   :numref:`tab7-1-2` are acceptable.

A8. *wtp*

  WEIGHT PERCENT OF THE ISOTOPE. If entry A7 is entered, a value
  must also be entered for A8. The weight percent of the isotope is the
  percent of this isotope in the element. The weight percent of all
  specified isotopes of the element must sum to 100 (± 0.01).

A9. **END**

  The word **END** is entered to terminate the input data for
  a standard composition component. This **END** can have a label
  associated with it that can be as long as 12 characters. The label is
  optional, and if entered must be preceded from the **END** by a single
  blank. At least two blanks or a new line must separate this item from
  the next data entry.

STANDARD COMPOSITION INPUT FOR FISSILE SOLUTIONS (see :numref:`tab7-1-2b`).

Syntax:

::

  	SOLUTION {MIX=}mx RHO[fuelsalt]=fd  (izai  wtpi)  MOLAR[acid]=aml
  		MASSFRAC[name]=mfrac  MOLEFRAC[name] =molfrac
  		MOLALITY[name]=molal    DENSITY=roth
  		TEMPERATURE=temp VOL_FRAC=vf
  	END SOLUTION

where

   *mx* is the mixture number,

   *fuelsalt* is the Standard Composition Library component name of one
   of the fissile compounds

   *fd* is the fuel density in grams of uranium or plutonium per liter
   of solution

   *acid* is one of the Standard Composition Library acid compounds
   (e.g., HNO3 or HFACID)

   *name* is one of the Standard Composition Library solution components

   *aml* is the acid molarity of the *acid* component (moles of *acid/*
   liter of solution)

   *mfrac* is the mass fraction of *name* in the solution (grams of
   metal in *name*/gram solution)

   *molfrac* is the mole fraction of *name* in the solution (moles of
   *name*/mole solution)

   *molal* is the mass fraction of *name* in the solution (moles of
   *name*/kg water)

   *roth* is the density of the solution,

   *vf* is the density multiplier (ratio of actual to theoretical
   density of the solution),

   *temp* is the temperature in Kelvin,

   *iza* is the isotope ID number from table *Available fissile solution
   components*, and

   *wtp* is the weight percent of the isotope in the material.


Below are the input data for fissile solutions.

1. **SOLUTION**

  Keyword starting a solution specification.
  Solutions require the specification of the mixture and at least one component.
  Current possible components are given in the Standard Composition Library table,
  *Available fissile solution components*. Only the mixture number and one component are required.
  Appendix A contains examples of the input data for solutions.

2. *mx*

  MIXTURE ID NUMBER. A mixture number is required on every standard composition specification.
  It defines the mixture that contains the material defined by the standard composition
  specification data. The mixture numbers are utilized in the Unit Cell Specification for
  INFHOMMEDIUM, LATTICECELL, or MULTIREGION.



| 3. **RHO**\ [*fuelsalt* ]=\ *fd*
| **MOLAR**\ [*acid*]=\ *aml*
| **MASSFRAC**\ [*name*]=\ *mfrac*
| **MOLEFRAC**\ [*name*]=\ *molfrac*
| **MOLALITY**\ [*name*]=\ *molal*

  KEYWORD PARAMETERS TO DEFINE CONCENTRATIONS OF SOLUTION COMPONENTS.
  Each keyword specifies the unit, the component name from the Standard
  Composition Library and the component value, as shown :numref:`tab7-1-2b`. Up
  to three components can be specified for a solution if one is an acid. After
  the value, the isotopic enrichments of the nuclides can be given as pairs of
  isotope IDs and weight percent. **NOTE: the square brackets [ ] containing the
  component name are required.**

4. **DENSITY=**\ *roth*

  Keyword specifying the overall solution density as grams per cubic centimeter
  or as a “?”, meaning it is to be solved for. Solving for the density is the
  default behavior, but the density can be given, and a component value can be
  solved for instead.

5. **TEMPERATURE=**\ *temp*

  Keyword defining temperature of the solution. The default value is 300 K.

6. **VOLFRAC=**\ *vf*

  Keyword defining volume fraction — the default volume fraction is 1.0. This value must be greater than 0.0. The volume fraction can be interpreted as:
  a. 	the volume fraction of this solution specification in the mixture,
  b. 	the density of the solution in this application divided by the calculated density of the solution, or
  c. 	the product of (a) and (b).

7. **END SOLUTION**

STANDARD COMPOSITION INPUT FOR CHEMICAL COMPOUNDS (see :numref:`tab7-1-2c`)

**Syntax:**

**ATOM\ nn** *mx* *roth* *nel* *ncza*\ :sub:`1` *atpm*\ :sub:`1` … *ncza*\ :sub:`nel` *atpm*\ :sub:`nel`
{*vf* {*temp* {*iza*\ :sub:`1` *wtp*\ :sub:`1` …} } } **END**

Below are the data for user-defined chemical compounds.


C1. **ATOM\ nn**

  COMPOUND NAME. User-specified compounds (also defined
  as “arbitrary” in older versions of SCALE) require the user to provide
  all the information normally found in the Standard Composition Library.
  This option allows specifying a compound not available in the Standard
  Composition Library by utilizing nuclides and elements available in the
  library. An user-specified compound name must start with the four
  characters “\ **ATOM**.” A maximum of twelve characters is allowed for
  the compound name, and imbedded blanks are not allowed.

C2. *mx*

  MIXTURE ID NUMBER. A mixture number is required on every
  standard composition specification. It defines the mixture that contains
  the material defined by the compound specification data. The mixture
  numbers are utilized in the Unit Cell Specification for
  **INFHOMMEDIUM**, **LATTICECELL**, or **MULTIREGION** problems and the
  KENO V.a or KENO-VI geometry data.

C3. *roth*

  MIXTURE DENSITY. The density of the arbitrary material is
  entered in units of g/cm\ :sup:`3`. *roth* and *vf* interact to produce
  the density of the mixture used in the problem. Note that this is a
  required entry and does not use “\ **DEN**\ =” keyword.

C4. *nel*

  NUMBER OF ELEMENTS IN THE MATERIAL. Enter the number of
  components from the Standard Composition Library that are to be used to
  define this material.

C5. *ncza*

  ID NUMBER. This is the “ZA” ID number for the element or
  isotope. Usually, *ncza*\ =A+1000*Z, where A is the atomic mass or
  weight of the nuclide, and Z is the atomic number.

C6. *atpm*

  ATOMIC or ELEMENT ABUNDANCE. Enter the number of atoms of
  this element per molecule of compound. Repeat the sequence *ncza* and
  *atpm* (C5 and C6) for every element in the compound before going to
  entry C7.

C7. *vf*

  VOLUME FRACTION. The default value of the volume fraction is
  1.0. This value must be greater than 0.0. The volume fraction can be
  interpreted as

    a. the volume fraction of this compound in the mixture,

    b. the density of the compound in this application divided by the input
       density of the compound, or

    c. the product of (a) and (b).

C8. *temp*

  TEMPERATURE. The default value of the temperature is 300 K.
  The temperature can be omitted if entries C9 and C10 are also omitted.

C9. *iza*

  ISOTOPE ZA NUMBER. Enter a value for each isotope in the
  element in the compound. The ZA number of the isotope is entered if the
  user wishes to specify the isotopic distribution. This is done by
  entering *iza* and *wtp* for each isotope until all the desired isotopes
  have been described. In most cases the “ZA” ID number is (A+1000*Z),
  where A is the atomic mass or weight of the isotope, and Z is the atomic
  number.

  Entries C9 and C10 can be skipped if the default values listed in
  :numref:`tab7-1-2` of :ref:`7-1` are acceptable.

C10. *wtp* WEIGHT PERCENT OF THE ISOTOPE. If entry C9 is entered, a
value must also be entered for C10. The weight percent of the isotope is
the percent of this isotope in the element. The weight percents of all
specified isotopes of the element must sum to 100 (± 0.01).

   Repeat the sequence *iza* *wtp* until the sum of the *wtp*\ s sum to
   100. The sequence *iza* *wtp* is repeated until all of the desired
   isotopes have been specified.

C11. **END**

  The word **END** is entered to terminate the input data for
  compound. This **END** can have a label associated with it that can be
  as long as 12 characters. The label is optional, and if entered must be
  preceded from the **END** by a single blank. At least two blanks or a
  new line must separate item C11 from the next data entry.

STANDARD COMPOSITION INPUT FOR MIXTURES AND ALLOYS (see :numref:`tab7-1-2d`)

**Syntax:**

**WTPTnn** *mx* *roth* *nel* *ncza*\ :sub:`1` *wpct*\ :sub:`1` … *ncza*\ :sub:`nel` *wpct*\ :sub:`nel`
{*vf* {*temp* {*iza*\ :sub:`1` *wtp*\ :sub:`1` …} }} **END**

Below are the input data for arbitrary (i.e., user-defined) physical
mixture or alloy.

D1. **WTPTnn**

  ARBITRARY MIXTURE/ALLOY NAME. The arbitrary
  user-specified mixture/alloy option allows specifying a mixture or an
  alloy not available in the Standard Composition Library by utilizing the
  nuclides and elements available in the library. An arbitrary
  mixture/alloy name must start with the four characters “\ **WTPT**.” A
  maximum of 12 characters is allowed for the arbitrary mixture/alloy
  name. Imbedded blanks are not allowed in an arbitrary mixture/alloy
  name. Appendix A contains input data for arbitrary mixture/alloys.

D2. *mx*

  MIXTURE ID NUMBER. A mixture number is required on every
  standard composition specification. It defines the mixture that contains
  the material defined by the arbitrary compound specification data. The
  mixture numbers are utilized in the Unit Cell Specification for
  **INFHOMMEDIUM**, **LATTICECELL**, **MULTIREGION**, or **DOUBLEHET**
  problems and the KENO V.a or KENO-VI geometry data.

D3. *roth*

  MIXTURE DENSITY. The density of the arbitrary material is
  entered in units of g/cm\ :sup:`3`. *roth* and *vf* interact to produce
  the density of the mixture used in the problem. Note that this is a
  required entry and does not use “\ **DEN**\ =” keyword.

D4. *nel*

  NUMBER OF ELEMENTS IN THE MATERIAL. Enter the number of
  components from the Standard Composition Library that are to be used to
  define this arbitrary material.

D5. *ncza*

  ID NUMBER. This is the “ZA” ID number for the element or
  isotope. Usually, *ncza*\ =A+1000*Z, where A is the atomic mass or
  weight of the nuclide, and Z is the atomic number.

D6. *wpct*

  ATOMIC or ELEMENT ABUNDANCE. Enter the weight percent of this
  element in the arbitrary alloy. The sum of all the weight percents for
  each specified element in the arbitrary alloy MUST be 100.0. Repeat the
  sequence *ncza* and *wpct* (D5 and D6) for every element in the
  arbitrary mixture/alloy before going to entry D7.

D7. *vf*

  VOLUME FRACTION. The default value of the volume fraction is
  1.0. This value must be greater than 0.0. The volume fraction can be
  interpreted as:

     a. the volume fraction of this mixture or alloy in the mixture,

     b. the density of the mixture or alloy in this application divided by
     the input density (*roth*) of the mixture or alloy, or

     c. the product of (a) and (b).

D8. *temp*

  TEMPERATURE. The default value of the temperature is 300 K.
  The temperature can be omitted if entries D9 and D10 are also omitted.

D9. *iza*

  ISOTOPE ZA NUMBER. Enter a value for each isotope in the
  element in the arbitrary alloy. The ZA number of the isotope is entered
  if the user wishes to specify the isotopic distribution. This is done by
  entering *iza* and *wtp* for each isotope until all the desired isotopes
  have been described. In most cases the “ZA” ID number is (A+1000*Z),
  where A is the atomic mass or weight of the isotope, and Z is the atomic
  number.

  Entries D9 and D10 can be skipped if the default values listed in
  :numref:`tab7-1-2` are acceptable.

D10. *wtp*

  WEIGHT PERCENT OF THE ISOTOPE. If entry D9 is entered, a
  value must also be entered for D10. The weight percent of the isotope is
  the percent of this isotope in the element. Weight percents of all
  specified isotopes of the element must sum to 100 (±0.01).

D11. **END**

  The word **END** is entered to terminate the input data for
  an arbitrary compound. This **END** can have a label associated with it
  that can be as long as 12 characters. The label is optional and if
  entered must be preceded from the **END** by a single blank. At least
  two blanks or a new line must separate this item from the next data
  entry.


.. _7-1-3-4:

Unit cell specification for infinite homogeneous problems
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This section describes the unit cell data that can be entered for an
**INFHOMMEDIUM** problem. Additional information is available in
Appendix B.

Syntax:

**INFHOMMEDIUM** *mx* {**CELLMIX**\ {=}*mix*} **END**

The data required to specify the unit cell for an **INFHOMMEDIUM** unit
cell are given in :numref:`tab7-1-3`. The individual entries are explained in
the following text.

1. **celltype**

  **INFHOMMEDIUM**. The keyword **INFHOMMEDIUM** is
  entered to indicate this unit cell contains one mixture with no geometry
  corrections. This data must be entered. The keyword may be truncated to
  any number of characters as long as the characters present are identical
  from the beginning of the keyword (i.e., INF is acceptable). All
  mixtures not in a defined unit cell are by default processed as
  infhommedium.

2. *mx*

  MIXTURE NUMBER. The mixture number defines the mixture to be
  used in the cell. This data must be entered. Be sure the mixture number
  entered is defined in the standard composition data.

3. **CELLMIX**\ =\ *mix*

  CELL-WEIGHTED MIXTURE NUMBER. (the = sign can
  be replaced by a space if desired). Enter ONLY if a cell-weighted
  mixture is to be generated. Enter a unique mixture number to be used by
  XSDRN to create the cell-weighted mixture (:ref:`7-1-2-4`). For
  **INFHOMMEDIUM** cells, cross sections for the cell mixture are equal to
  the shielded values of the original mixture.

4. **END**

  The word **END** is entered to terminate the **INFHOMMEDIUM**
  data. An optional label can be associated with this **END**. The label
  can be as many as 12 characters long and is separated from the **END**
  by a single blank. At least two blanks must follow this entry.

.. _tab7-1-3:
.. table:: Unit cell specifications for INFHOMMEDIUM problems.
  :align: center

  +-----------------+-----------------+-----------------+-----------------+
  | Entry           | Input           | Data            | Comments        |
  |                 |                 |                 |                 |
  | no.             | data            | type            |                 |
  +-----------------+-----------------+-----------------+-----------------+
  | 1               | **INFHOMMEDIUM**| Keyword         | Keyword to      |
  |                 |                 |                 | begin           |
  |                 |                 |                 | infhommedium    |
  |                 |                 |                 | unit cell.      |
  |                 |                 |                 | Enter the       |
  |                 |                 |                 | keyword         |
  |                 |                 |                 | INFHOMMEDIUM.   |
  |                 |                 |                 | This word may   |
  |                 |                 |                 | be truncated to |
  |                 |                 |                 | any number of   |
  |                 |                 |                 | letters as long |
  |                 |                 |                 | as they exactly |
  |                 |                 |                 | replicate the   |
  |                 |                 |                 | beginning part  |
  |                 |                 |                 | of the keyword  |
  |                 |                 |                 | (e.g., INF is   |
  |                 |                 |                 | acceptable).    |
  +-----------------+-----------------+-----------------+-----------------+
  | 2               | *mx*            | Cell mixture    | Specifies the   |
  |                 |                 | number          | mixture number  |
  |                 |                 |                 | to be used in   |
  |                 |                 |                 | the cell.       |
  +-----------------+-----------------+-----------------+-----------------+
  | 3               | **CELLMIX**\ =  | Keyword +       | Enter the       |
  |                 | *mix*           |                 | keyword         |
  |                 |                 | new mixture     | **CELLMIX**\ =  |
  |                 |                 | number          | followed        |
  |                 |                 |                 | immediately by  |
  |                 |                 |                 | a unique        |
  |                 |                 |                 | positive        |
  |                 |                 |                 | integer         |
  |                 |                 |                 | (*mix*). The    |
  |                 |                 |                 | integer will be |
  |                 |                 |                 | a new mixture   |
  |                 |                 |                 | number that has |
  |                 |                 |                 | the neutronic   |
  |                 |                 |                 | properties of   |
  |                 |                 |                 | the             |
  |                 |                 |                 | self-shielded   |
  |                 |                 |                 | unit cell.\     |
  |                 |                 |                 | :sup:`a`        |
  +-----------------+-----------------+-----------------+-----------------+
  | 4               | **END**         |                 | Terminate       |
  |                 |                 |                 | **INFHOMMEDIUM**|
  |                 |                 |                 | data            |
  |                 |                 |                 |                 |
  +-----------------+-----------------+-----------------+-----------------+
  | :sup:`a`\ Note: If CELLMIX is entered for a **INFHOMMEDIUM** cell,    |
  | XSDRNPM is executed to compute k\ :sub:`∞`, but cross sections for the|
  | “homogenized” mixture are identical to the shielded values for the    |
  | original cell.                                                        |
  +-----------------------------------------------------------------------+

.. _7-1-3-5:


Unit cell specification for LATTICECELL problems
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This section describes the unit cell input data for a **LATTICECELL**
problem. The **LATTICECELL** description is especially suited to
self-shield arrays of repeated cells such as a fuel assembly lattice.
The unit cell specification plays a major role in providing accurate
problem-dependent cross sections using the computational procedures
described in :ref:`7-1-2-3`. Unit cells are limited to (a) infinitely
long cylindrical rods in a square or triangular lattice, (b) spheres in
a cubic or triangular lattice, (c) a symmetric array of slabs, or (d) an
asymmetric array of slabs. Both “regular” and “annular” fuel geometries
can be used in **LATTICECELL** problems. “Regular” cells allow a
concentric spherical, cylindrical, or symmetric slab configuration,
where the central region is fuel, surrounded by an optional gap, an
optional clad, and an external moderator. “Annular” cells also allow
concentric spherical, cylindrical, or asymmetric slab configurations,
but the central region corresponds to an inner moderator region which is
surrounded by a fuel region having an optional gap and optional clad on
each side of the fuel. An inner gap may be specified inside the fuel
region, and an outer gap may be specified outside the fuel region.
Similarly an inner clad may be specified inside the fuel region, and an
outer clad may be specified outside the fuel region. For both regular
and annular fuel cells, the outer boundary of the unit cell is
determined from the square or triangular pitch of the array.

Regular cells are **SQUAREPITCH**, **TRIANGPITCH**, **SPHSQUAREP**,
**SPHTRIANGP**, and **SYMMSLABCELL**.

Annular cells are **ASQUAREPITCH** (or **ASQP**), **ATRIANGPITCH** (or
**ATRP**), **ASPHSQUAREP** (or **ASSP**), **ASPHTRIANGP** (or **ASTP**),
and **ASYMSLABCELL**

Syntax:

   **celltype** **ctp PITCH** (or **HPITCH**) *pitch* *mm* **FUELD (or
   FUELR**) *fuel mf*

   **GAPD (or GAPR**) *gap mg* **CLADD (or CLADR**) *clad mc*

   **IMODD (or IMODR**) *imod mim* **IGAPD** (**or IGAPR**) *igap mig*

   **ICLADD** (or **ICLADR**) *iclad mic* {**CELLMIX**\ =\ *mix*}
   **END**

The unit cell geometry data required to specify a LATTICECELL problem
are given in :numref:`tab7-1-4`. The individual entries are explained in the
text below.

1. **celltype**

  **LATTICECELL.** The keyword **LATTICECELL** is entered
  to indicate this unit cell contains mixtures that are positioned in a
  regular array. This data must be entered. The keyword may be truncated
  to any number of characters as long as the characters present are
  identical from the beginning of the keyword (e.g., **LAT** is
  acceptable). This unit cell is normally used for regular arrays of
  materials such as fuel pins in an assembly.

2. **ctp**

  TYPE OF LATTICE. This defines the type of lattice or array
  configuration. Any one of the following alphanumeric descriptions may be
  used. Note that the alphanumeric description must be separated from
  subsequent data entries by one or more blanks. :numref:`fig7-1-1` Mixture and
  position data are entered using keywords. Mixture number 0 may be
  entered for void and may be used multiple times in each and all unit
  cells. For regular cells, the minimum requirement is that a fuel region
  and a moderator region are specified and no other inner components are
  specified. For annular cells, the minimum requirement is the fuel and
  outer moderator and inner moderator regions are specified. Regular and
  annular cell configurations are specified as shown below.

   **Regular Cells**

   **SQUAREPITCH** is used for an array of cylinders arranged in a
   square lattice, as shown in :numref:`fig7-1-1`. The clad and/or gap can be
   omitted.

   **TRIANGPITCH** is used for an array of cylinders arranged in a
   triangular-pitch lattice as shown in :numref:`fig7-1-2`. The clad and/or
   gap can be omitted.

   **SPHSQUAREP** is used for an array of spheres arranged in a
   square-pitch lattice. A cross section view through a cell is
   represented by :numref:`fig7-1-1`. The clad and/or gap can be omitted.

   **SPHTRIANGP** is used for an array of spheres arranged in a
   triangular-pitch (dodecahedral) lattice. A cross section view through
   a cell is represented by :numref:`fig7-1-2`. The clad and/or gap can be
   omitted.

   **SYMMSLABCELL** is used for an infinite array of symmetric slab
   cells, as shown in :numref:`fig7-1-3`. The clad and/or gap can be omitted.

   **Annular Cells**

   **ASQUAREPITCH** or **ASQP** is used for annular cylindrical rods in
   a square-pitch lattice as shown in :numref:`fig7-1-4`. The inner and outer
   clad and gap are independently entered so they must be different
   materials and dimensions. Note that each mixture in the problem can
   be used only once and in only one zone of a cell.

   **ATRIANGPITCH** or **ATRP** is used for annular cylindrical rods in
   a triangular-pitch lattice as shown in :numref:`fig7-1-5`. The inner and
   outer clad and gap are independently entered, so they must be
   different materials and dimensions.

   **ASPHSQUAREP** or **ASSP** is used for spherical shells in a
   square-pitch lattice as shown in :numref:`fig7-1-4`. The inner and outer
   clad and gap are independently entered, so they must be different
   materials and dimensions.

   **ASPHTRIANGP** or **ASTP** is used for spherical shells in a
   triangular-pitch (dodecahedral) lattice as shown in :numref:`fig7-1-5`. The
   inner and outer clad and gap are independently entered, so they must
   be different materials and dimensions.

   **ASYMSLABCELL** is used for a periodic, but asymmetric, array of
   slabs as shown in :numref:`fig7-1-6`. The inner and outer clad and gap are
   independently entered, so they may be different materials and
   dimensions.

3. **PITCH** or **HPITCH**

  ARRAY PITCH. This is the center-to-center spacing
  or half-spacing between the fuel lumps (rods, pellets, or slabs), *pitch*, in
  cm followed by the outer moderator material number, mm, as shown in
  :numref:`fig7-1-1` through :numref:`fig7-1-6`.

4. **FUELD** or **FUELR**

  OUTSIDE DIMENSION OF FUEL. This is the outside diameter or radius of the
  fuel, fuel, in cm followed by the fuel mixture number, *mf*, as shown in
  :numref:`fig7-1-1` through :numref:`fig7-1-6`.

5. **GAPD** or **GAPR**

  OUTSIDE DIMENSION OF OUTER GAP. Enter only if outer gap is present.
  This is the outside diameter or radius of the outer gap, *gap*, in cm
  followed by the gap mixture number, mg, as shown in :numref:`fig7-1-1` through
  :numref:`fig7-1-6`.

6. **CLADD** or **CLADR**

  OUTSIDE DIMENSION OF OUTER CLAD. Enter ONLY if a clad is present.
  This is the outside diameter or radius of the outer clad, *clad*, in cm
  followed by the clad mixture number, mc, as shown in :numref:`fig7-1-1` through
  :numref:`fig7-1-6`.

7. **IMODD** or **IMODR**

  DIMENSION OF INNER MODERATOR. Enter ONLY if an annular cell is specified.
  This is the outside diameter or radius of the inner moderator, *imod*, in cm
  followed by the inner moderator mixture number, *mim*, as shown
  in :numref:`fig7-1-4` through :numref:`fig7-1-6`.

8. **IGAPD** or **IGAPR**

  OUTSIDE DIMENSION OF INNER GAP. Enter ONLY if an annular cell is specified and
  inner gap is present. This is the outside diame*ter or radius of the inner gap,
  *igap*, in cm followed by the inner gap mixture number, *mig*, as shown in
  :numref:`fig7-1-4` through :numref:`fig7-1-6`.

9. **ICLADD** or **ICLADR**

  OUTSIDE DIMENSION OF INNER CLAD. Enter ONLY if an annular cell is
  specified and inner clad is present. This is the outside diameter or
  radius of the inner clad, *iclad*, in cm followed by the inner clad mixture
  number, *mic*, as shown in :numref:`fig7-1-4` through :numref:`fig7-1-6`.

10. {**CELLMIX\ =}\ mix**

  CELL-WEIGHTED MIXTURE NUMBER. [the = sign can be replaced by a space if desired).
  Enter ONLY if a cell-weighted mixture is to be generated. Enter a unique mixture
  number to be used by XSDRN to create the cell-weighted mixture (:ref:`7-1-2-4`).

11.	END

  The word **END** is entered to terminate the **LATTICECELL** data.
  An optional label can be associated with this **END**. The label can be as many
  as 12 characters long and is separated from the **END** by a single blank. At least
  two blanks must follow this entry. Must not start in column 1.

.. _tab7-1-4:
.. list-table:: Unit cell specification for LATTICECELL problems.
  :align: center

  * - .. image:: figs/XSProc/tab4.svg
        :width: 1000

.. _fig7-1-1:
.. figure:: figs/XSProc/fig1.png
  :align: center
  :width: 400

  Arrangement of materials in a SQUAREPITCH and SPHSQUAREP unit cell.

.. _fig7-1-2:
.. figure:: figs/XSProc/fig2.png
  :align: center
  :width: 400

  Arrangement of materials in a TRIANGPITCH and SPHTRIANGP unit cell.

.. _fig7-1-3:
.. figure:: figs/XSProc/fig3.png
  :align: center
  :width: 600

  Arrangement of materials in a SYMMSLABCELL unit cell having reflected
  left and right boundary conditions.

.. _fig7-1-4:
.. figure:: figs/XSProc/fig4.png
  :align: center
  :width: 400

  Arrangement of materials in an ASQUAREPITCH and ASPHSQUAREP unit cell.

.. _fig7-1-5:
.. figure:: figs/XSProc/fig5.png
  :align: center
  :width: 400

  Arrangement of materials in an ATRIANGPITCH and ASPHTRIANGP unit cell.

.. _fig7-1-6:
.. figure:: figs/XSProc/fig6.png
  :align: center
  :width: 600

  Arrangement of materials in an ASYMSLABCELL unit cell having reflected
  left and right boundary conditions.

.. _7-1-3-6:

Unit cell specification for MULTIREGION cells
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A **MULTIREGION** cell can be used to define a 1-D geometric arrangement
that is more general than allowed by a **LATTICECELL**. It can also be
used for large geometric regions where the geometry effects for the
cross sections are small. For CENTRM/PMC self-shielding, lattice effects
can be approximated by applying reflected, periodic, or white external
boundary conditions to a MULTIREGION cell. HOWEVER, MULTIREGION CELLS
SHOULD NOT BE USED FOR BONAMI-ONLY SELF-SHIELDING OF AN ARRAY UNIT CELL.
In this case a LATTICECELL should always be used for BONAMI
self-shielding in order to incorporate the proper Dancoff effects.

The data required for a MULTIREGION cell are given in :numref:`tab7-1-5` and
explained in the following text.

1. **celltype**

  **MULTIREGION**. The keyword **MULTIREGION** is used to
  represent arbitrary 1‑D geometries, with no restrictions the on number
  or placement of mixtures in the cell. The keyword may be truncated to
  any number of characters as long as the characters presented are
  identical from the beginning of the keyword (i.e., M is acceptable).

2. **cs**

  TYPE OF GEOMETRY. The type of geometry must always be
  specified for a **MULTIREGION** cell. The available geometry options are
  listed below.

     **SLAB**. This is used to describe a slab geometry.

     **CYLINDRICAL**. This is used to describe cylindrical geometry.

     **SPHERICAL**. This is used to describe spherical geometry.

     **BUCKLEDSLAB**. This is used for slab geometry with a buckling
     correction for the two transverse directions.

     **BUCKLEDCYL**. This is used for cylindrical geometry with a buckling
     correction in the axial direction.

3. **RIGHT_BDY**

  RIGHT BOUNDARY CONDITION. This is defaulted to
  **VACUUM**. The available options and their qualifications are listed
  below.

     **VACUUM**. This imposes a vacuum at the boundary of the system.

     **REFLECTED**. This imposes mirror image reflection at the boundary.
     Do not use for **CYLINDRICAL** or **SPHERICAL**.

     **PERIODIC**. This imposes periodic reflection at the boundary. Do
     not use for **CYLINDRICAL** or **SPHERICAL**.

     **WHITE**. This imposes isotropic return at the boundary.

4. **LEFT_BDY**

  LEFT BOUNDARY CONDITION. This is defaulted to
  **REFLECTED**. The available options and their qualifications are listed
  below.

     **VACUUM**. This imposes a vacuum at the boundary of the system.

     **REFLECTED**. This imposes mirror image reflection at the boundary.
     For **CYLINDRICAL** or **SPHERICAL**, this is the only valid boundary
     condition because the left boundary corresponds to the centerline of
     the cylinder or the center of the sphere.

     **PERIODIC**. This imposes periodic reflection at the boundary.

     **WHITE**. This imposes isotropic return at the boundary.

5. **ORIGIN**

  LOCATION OF LEFT BOUNDARY ON THE ORIGIN. The default value
  of **ORIGIN** is 0.0. This is the only value allowed for **CYLINDRICAL**
  or **SPHERICAL** geometry. For **SLAB**\ s, enter the location of the
  left boundary on the X-axis perpendicular to the slab (in cm).

6. **DY**

  BUCKLING HEIGHT. This is the buckling height in cm. It
  corresponds to one of the transverse dimensions of an actual 3-D slab
  assembly or the length of a finite cylinder.

7. **DZ**

  BUCKLING DEPTH. This is the buckling width in cm.
  It corresponds to the second transverse dimension of an actual 3-D slab
  assembly.

8. **CELLMIX**

  CELL-WEIGHTED MIXTURE NUMBER. Enter ONLY if a
  cell-weighted mixture is required. Enter a unique mixture number used to
  create a cell-weighted homogeneous mixture (:ref:`7-1-2-4`).

9. **END**

  The word **END** is entered to terminate these data before
  entering the zone description data. It must not be entered in columns 1
  through 3, and at least two blanks must separate it from the zone
  description. A label can be associated with this **END**. The label can
  be a maximum of 12 characters and is separated from the **END** by a
  single blank. At least two blanks must follow this entry.

  The zone description data are entered at this point. Entries 10 and
  11 are entered for each zone, and the sequence is repeated until all
  the desired zones have been described. To terminate the data, enter
  the words END ZONE. Zone dimensions must be in increasing order.

10. **mxz**

  MIXTURE NUMBER IN THE ZONE. Enter the mixture number of the
  material that is present in the zone. Enter a zero for a void. Repeat
  the sequence of entries 10 and 11 for each zone. Mixtures other than
  zero must not be used more than once in a cell and may be used in no
  more than one cell.

11. **rz**

  OUTSIDE RADIUS OF THE ZONE. Enter the outside dimension of
  the zone in cm.

  In **SLAB** geometry, **rz** is the location of the zone’s right
  boundary on the X-axis. Repeat the sequence of entries 10 and 11 for
  each zone.

12. **END ZONE**

  Is used to terminate the **MULTIREGION** zone data.
  Enter the words **END** **ZONE** when all the zones have been described.
  Note that **ZONE** is a label associated with this **END**. This label
  can be as long as 12 characters, but the first four characters must be
  **ZONE**. At least two blanks must follow this entry.

.. _tab7-1-5:
.. list-table:: Unit cell specification for MULTIREGION problems.
  :align: center

  * - .. image:: figs/XSProc/tab5.svg
        :width: 1000

.. _7-1-3-7:

Unit cell specification for doubly heterogeneous (DOUBLEHET) cells
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The data required for a **DOUBLEHET** cell are given in :numref:`tab7-1-6` and
explained in the following text.

Details about the computation procedures for **DOUBLEHET** cells can be
found in :ref:`7-1-2-3`.

“Grain” refers to a spherical fuel particle surrounded by one or more
coating zones and does not include the matrix material the grains are
in. “Grain type” refers to a grain that has specified dimensions and
mixtures such as a 0.025-cm-radius UO\ :sub:`2` fuel kernel with a
0.01-cm-thick carbon coating. Another grain type could be a
0.012-cm-radius PuO\ :sub:`2` fuel kernel with a 0.01-cm-thick carbon
coating. The user must first define all grain types in a fuel element.
Next, all fuel element–related data must be entered.

Since all grains and the matrix material are homogenized into a single
uniform mixture for the fuel element, there are restrictions on how each
grain type must be defined so that the volume fraction of each grain
type within the homogenized fuel mixture can be determined. Related
entries are **PITCH**, **NUMPAR** (number of particles), and **VF**
(volume fraction). If there is only one grain type for a fuel element,
the code needs the pitch and will directly use the input value if
entered. If **PITCH** is not given, then the **VF** (if given) is used
to calculate the pitch. If neither **PITCH** nor **VF** is given, then
**NUMPAR** is used to calculate the pitch and the volume fraction. The
user should only enter one of these items.

If more than one grain type is present, additional information is needed
since all grain types are homogenized into a single mixture. Similar to
the one grain type case, the pitch is needed to perform the CENTRM
spherical cell calculations. However, the pitch by itself is not
sufficient to perform the homogenization. Therefore, the user needs to
input **VF** or **NUMPAR** for each grain type. Since each grain’s
volume is known (grain dimensions must always be entered), entering
**NUMPAR** or **VF** for each grain type essentially provides the total
volume of each grain type and therefore enables the calculation of the
other unknowns (**VF** or **NUMPAR**, and **PITCH**). In this case,
since pitch is not given, the available matrix material is distributed
around the grains of each grain type proportional to the grain volume to
calculate the corresponding pitch.

Syntax:

**DOUBLEHET** *fuelmix* **END**

**GF**\ (**D**\ \|\ **R**)=\ *fuel mg*
(**COAT**\ (**D**\ \|\ **R**)=\ *coat mc*)|(\ **COATT**\ =\ *coat mc*)
{**H**}\ **PITCH**\ =\ *mod* **MATRIX**\ =\ *mm* **NUMPAR**\ =\ *npar*
**VF**\ =\ *vf* **END GRAIN**

**mct** **ctp** **FUEL**\ (**D**\ \|\ **R**)=\ *mfuel*
{**FUELH**\ =\ *hfuel*} {**FUELW**\ =wfuel}
{**GAP**\ (**D**\ \|\ **R**)=\ *mgap mmg*}
{**CLAD**\ (**D**\ \|\ **R**)=\ *mclad* *mmc*}
{**H**}\ **PITCH**\ =\ *mpitch* *mmm* {**CELLMIX**\ =\ *mcmx*} **END**


1. **celltype**

  DOUBLEHET. The keyword DOUBLEHET is used to represent a doubly heterogeneous
  problem such as fuel units that are composed of grains of fuel.

2. *fuelmix*

  HOMOGENIZED MIXTURE NUMBER. Enter a unique mixture number to be
  used for the homogenized grains and matrix material.

3. **END**

  The word **END** is entered to terminate these data before entering the grain and
  fuel element description data. It must not be entered in columns 1 through 3,
  and at least two blanks must separate it from the zone description.
  A label can be associated with this **END**. The label can be a maximum of
  12 characters and is separated from the **END** by a single blank. At least
  two blanks must follow this entry.


The grain description data are entered at this point. Entries 5 through
12 are entered for each grain, and the sequence is repeated until all
the grains have been described. To terminate the data, enter the words
**END GRAIN**. Data may be entered in any order.

4. **PITCH** or **HPITCH**

  EQUIVALENT CELL DIMENSION. This is the equivalent spherical diameter (or radius),
  in cm, of the "average" unit cell for this grain, as shown in :numref:`fig7-1-7`.
  Physically, the volume of the average unit cell is equal to the volume of the
  fuel element divided by the total number of all grain types.

5. **GFD** or **GFR**

  OUTSIDE DIMENSION OF FUEL. This is the outside diameter or radius of the fuel
  zone in a grain, *fuel*, in cm followed by the fuel mixture number, *mg*, as shown in
  :numref:`fig7-1-7`.

6. **COATD** or **COATR**

  OUTSIDE DIMENSION OF COATING. This is the outside diameter or radius of a
  coating zone, *coat*, in cm followed by the coating mixture number, *mc*, as shown in
  :numref:`fig7-1-7`. As many coating-mixture pairs as desired may be entered.
  If the coating dimensions are entered using COATD or COATR, then the COATT keyword should not be used.

7. **COATT**

  THICKNESS OF COATING. This is the thickness of a coating zone, *coat*,
  in cm followed by the coating mixture number, *mc*, as shown in :numref`fig7-1-7`.
  As many coating-mixture pairs as desired may be entered. If the coating
  dimensions are entered using COATT, then the COATD or COATR keyword should not be used.

8. **MATRIX**

  MIXTURE NUMBER OF THE MATRIX MATERIAL. This is the mixture number, *mm*, of the matrix material that encloses the grains.

9. **NUMPAR**

  NUMBER OF PARTICLES. This is the number of grains, *npar*, of this type in each fuel element.

10.	**VF**

  VOLUME FRACTION. This is the volume fraction, *vf*, of grains of this type in each
  fuel element’s fuel zone. A fuel element’s fuel zone is entered using the entry
  number 16—\ **FUELD** (or **FUELR**).

11.	**END GRAIN**

  This is used to terminate the grain zone data for this grain type. At least two blanks must follow this entry.

REPEAT ENTRIES 4-11 FOR EACH GRAIN TYPE IN A FUEL ELEMENT.

12. **mct**

  TYPE OF FUEL ELEMENT (macro cell type). One of the keywords **PEBBLE** or **ROD**
  or SLAB is entered to indicate the type of the fuel element, i.e., the second
  layer of heterogeneity. This data must be entered. The keyword may NOT be
  truncated. **PEBBLE** is used for spherical fuel elements; **ROD** is used for
  cylindrical fuel elements; and SLAB for plate fuel elements.

13. **ctp**

  TYPE OF LATTICE. This defines the type of lattice or array configuration.
  Any one of the following alphanumeric descriptions may be used. Note that the
  alphanumeric description must be separated from subsequent data entries by one
  or more blanks. :numref:`fig7-1-1` Mixture and position data are entered using keywords.
  Mixture number 0 may be entered for void and may be used multiple times
  in each and all unit cells. For regular cells, the minimum requirement is that
  a fuel region and a moderator region are specified and no inner components are
  specified. For annular cells, the minimum requirement is the fuel and outer
  moderator and inner moderator regions are specified. Regular and annular cell
  configurations are specified as shown below.

**Regular Cells**

   **SQUAREPITCH** is used for an array of cylinders arranged in a
   square lattice, as shown in :numref:`fig7-1-1`. The clad and/or gap can be
   omitted.

   **TRIANGPITCH** is used for an array of cylinders arranged in a
   triangular-pitch lattice as shown in :numref:`fig7-1-2`. The clad and/or
   gap can be omitted.

   **SPHSQUAREP** is used for an array of spheres arranged in a
   square-pitch lattice. A cross section view through a cell is
   represented by :numref:`fig7-1-1`. The clad and/or gap can be omitted.

   **SPHTRIANGP** is used for an array of spheres arranged in a
   triangular-pitch (dodecahedral) lattice. A cross section view through
   a cell is represented by :numref:`fig7-1-2`. The clad and/or gap can be
   omitted.

   **SYMMSLABCELL** is used for an infinite array of symmetric slab
   cells, as shown in :numref:`fig7-1-3`. The clad and/or gap can be omitted.

   **Annular Cells**

   **ASQUAREPITCH** or **ASQP** is used for annular cylindrical rods in
   a square-pitch lattice as shown in :numref:`fig7-1-4`. The inner and outer
   clad and gap are independently entered so they may be different
   materials and dimensions.

   **ATRIANGPITCH** or **ATRP** is used for annular cylindrical rods in
   a triangular-pitch lattice as shown in :numref:`fig7-1-5`. The inner and
   outer clad and gap are independently entered, so they may be
   different materials and dimensions.

   **ASPHSQUAREP** or **ASSP** is used for spherical shells in a
   square-pitch lattice as shown in :numref:`fig7-1-4`. The inner and outer
   clad and gap are independently entered, so they may be different
   materials and dimensions.

   **ASPHTRIANGP** or **ASTP** is used for spherical shells in a
   triangular-pitch (dodecahedral) lattice as shown in :numref:`fig7-1-5`. The
   inner and outer clad and gap are independently entered, so they may
   be different materials and dimensions.

   **ASYMSLABCELL** is used for a periodic, but asymmetric, array of
   slabs as shown in :numref:`fig7-1-6`. The inner and outer clad and gap are
   independently entered, so they may be different materials and
   dimensions.

14.	**PITCH** or **HPITCH**

  ARRAY PITCH. This is the center-to-center spacing or half-spacing between the
  fuel lumps (pebbles or rods or slabs), *mpitch*, in cm followed by the outer
  moderator material number, *mmm*, as shown in :numref:`fig7-1-1` and :numref:`fig7-1-2`.

15.	**FUELD** or **FUELR**

  OUTSIDE DIMENSION OF FUEL. This is the outside dimension (diameter or radius
  for sphere/cylinder or x-thickness for slab) of the fuel region, *mfuel*, in cm,
  as shown in :numref:`fig7-1-1` and :numref:`fig7-1-2`.

16.	**FUELH**

  HEIGHT OF FUEL ROD OR SLAB. This is the height (z-dimension) of the fuel plate,
  *hfuel*, in cm. (only used to compute volume of fuel plate).

17.	**FUELW**

  WIDTH OF FUEL ROD or slab. This is the width/depth (y-dimension) of the fuel
  plate, *wfuel*, in cm. (only used to compute volume of fuel plate).

18.	**GAPD** or **GAPR**

  OUTSIDE DIMENSION OF GAP. Enter only if outer gap is present. This is the
  outside diameter or radius of the outer gap, *mgap*, in cm followed by the gap
  mixture number, *mmg*, as shown in :numref:`fig7-1-1` and :numref:`fig7-1-2`.

19.	**CLADD** or **CLADR**

  OUTSIDE DIMENSION OF CLAD. Enter ONLY if a clad is present. This is the
  outside diameter or radius of the outer clad, *mclad*, in cm followed by the
  clad mixture number, *mmc*, as shown in :numref:`fig7-1-1` and :numref:`fig7-1-2`.

20.	**CELLMIX**

  CELL-WEIGHTED MIXTURE NUMBER. Enter ONLY if cell-weighted mixture, *mcmx*, is to be created.

21.	**IMODD** or **IMODR**

  DIMENSION OF INNER MODERATOR. Enter ONLY if an annular cell is specified.
  This is the outside diameter or radius of the inner moderator, *imod*, in
  cm followed by the inner moderator mixture number, *mim*, as shown in
  :numref:`fig7-1-4` through :numref:`fig7-1-6`.

22.	**IGAPD** or **IGAPR**

  OUTSIDE DIMENSION OF INNER GAP. Enter ONLY if an annular cell is specified and
  inner gap is present. This is the outside diameter or radius of the inner gap,
  *igap*, in cm followed by the inner gap mixture number, *mig*, as shown in
  :numref:`fig7-1-4` through :numref:`fig7-1-6`.

23.	**ICLADD** or **ICLADR**

  OUTSIDE DIMENSION OF INNER CLAD. Enter ONLY if an annular cell is specified
  and inner clad is present. This is the outside diameter or radius of the inner
  clad, *iclad*, in cm followed by the inner clad mixture number, *mic*, as shown
  in :numref:`fig7-1-4` through :numref:`fig7-1-6`.

24.	**END**

  The word **END** is entered to terminate the **DOUBLEHET** data.
  An optional label can be associated with this **END**. The label can be
  as many as 12 characters long and is separated from the **END** by a single
  blank. At least two blanks must follow this entry.

.. _fig7-1-7:
.. figure:: figs/XSProc/fig7.png
  :align: center
  :width: 500

  Arrangement of materials in a grain (first level cell) in a DOUBLEHET unit cell.

.. _tab7-1-6:
.. list-table:: Unit cell specification for DOUBLEHET problems
  :align: center

  * - .. image:: figs/XSProc/tab6.svg
        :width: 1000

.. list-table:: Unit cell specification for DOUBLEHET problems (continued).
  :align: center

  * - .. image:: figs/XSProc/tab6cont.svg
        :width: 1000

.. list-table:: Unit cell specification for DOUBLEHET problems (continued).
  :align: center

  * - .. image:: figs/XSProc/tab6cont2.svg
        :width: 1000

.. _7-1-3-8:

Optional MORE DATA parameter data
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**MORE DATA** is an optional sub-block of the **READ CELL** block.
**MORE DATA** parameters allow certain default options in BONAMI and
XSDRNPM to be modified for individual cell calculations. Each **MORE
DATA** sub-block applies only to the unit cell immediately preceding it.
However a **MORE DATA** sub-block placed prior to all unit cell
definitions applies to all mixtures not assigned to a unit cell, which
are treated as infinite homogeneous media. If the default parameters are
acceptable, this section of input data should be omitted in its
entirety. Non-default values for one or more of the parameters can be
specified by entering the words **MORE DATA** followed by the desired
keyword parameters and their associated values. One or more of the
parameters can be entered in any order. Default values are used for
parameters that are not entered. Each parameter is entered by spelling
its name, followed immediately by an equal sign and the value to be
entered. There should not be a blank between the parameter name and the
equal sign. Each parameter specification must be separated from the rest
by at least one blank. For example, if an XSDRNPM calculation is
performed for particular unit cell (e.g., *cellmix=* is specified),

**MORE DATA ISN**\ =16 **EPS**\ =0.00008 **END MORE**

would result in using an S16 angular quadrature set and tightening the
convergence criteria to 0.00008 in the XSDRNPM calculation.

A description of each entry is given. (Also see sections on BONAMI and XSDRNPM input description.)

1.  **MORE DATA** These words, followed by one or more blanks, are
    entered ONLY if optional parameter data are to be entered. Entries 2
    through 42 can be entered in any order.

2.  **NSENSX** This is the XSDRNPM sensitivity output file for TSUNAMI
    sequences.

3.  **CROSSEDT** BONAMI CROSS SECTION EDIT. Cross section print option
    for BONAMI 0/1 –no/yes (default is 0).

4.  **FFACTEDT** BONDARENKO FACTOR EDIT. Bondarenko factor (f-factor)
    print option 0/1 –no/yes (default is 0).

5.  **ISSOPT** BONAMI BACKGROUND XSEC OPTIONS. BONAMI background cross
    section selection option if > 1000 potential; otherwise, total cross
    section is used (default is –1).

6.  **IROPT** BONAMI IR/NR CALCULATION OPTION. BONAMI uses intermediate
    resonance (IR) if iropt=1 and narrow resonance (NR) approximation
    for iropt=0 (default is 0).

7.  **BELLOPT** BELL FACTOR OPTION. Optional user-defined bell factor
    calculation option (default is -1).

8.  **BELLFACT** BELL FACTOR. Optional user-defined bell factor for
    BONAMI (default is 0.0).

9.  **ESCXSOPT** ESCAPE CROSS SECTION CALC OPTION. Escape cross section
    calculation for IR calculations. 0/1 =consistent/inconsis tent
    (default is 0).

10. **BONAMIEPS** BONAMI CONVERGENCE CRITERIA. BONAMI Bondarenko
    iteration convergence criteria (default is 0.001).

11. **LBARIN** INPUT MEAN CORD LENGTH. Mean cord length for each zone
    (default is 0.00).

12. **ADJTHERM** ADJUST 1D THERMAL CROSS SECTIONS TO MATCH SUM OF 2D
    CROSS SECTIONS. Flag determining whether 1-D cross sections are
    scaled to match the 2-D cross sections or the 2-D cross sections are
    scaled to match the 1-D cross sections.

13. **EXSIG** ESCAPE CROSS SECTION. External escape cross section for
    BONAMI (default is 0.00).

14. **IEVT** XSDRNPM CALCULATION TYPE. The type of calculation to be
    performed— fixed source, eigenvalue, alpha, zone width search, outer
    radius search, buckling search, direct buckling search (default is
    1).

15. **ICLC** THEORY OPTION. Number of outer iterations to use an
    alternative theory (diffusion, infinite medium, or B\ :sub:`N`)
    before using discrete ordinates. Negative values indicate
    alternative theory (default is 0).

16. **IPVT** PARAMETRIC EIGENVALUE SEARCH. 0 – none; 1 – search for
    eigenvalue equal PV; 2 – alpha search (default is 0).

17. **IPP** WEIGHTED CROSS SECTION PRINT. 2 -> No print; -1 -> 1-D edit;
    0-N – edit through PN cross section arrays (default is 2).

18. **IFLU** GENERALIZED ADJOINT CALCULATION. 0 is a standard
    calculation; 1 is a generalized adjoint calculation (default is 0).

19. **IFSN** FISSION SOURCE SUPPRESSION. Non-zero suppresses the fission
    source in a fixed source calculation (default is 0).

20. **IQM** VOLUMETRIC FIXED SOURCES. The number of volumetric sources
    in a fixed source problem (default is 0).

21. **IPM** BOUNDARY FIXED SOURCES. The number of boundary sources in a
    fixed source problem (default is 0).

22. **XNF** SOURCE NORMALIZATION FACTOR. The value used to normalize the
    problem source (default is 1.0).

23. **VSC** VOID STREAMING CORRECTION. The height of a void streaming
    path in a cylinder or slab in centimeters (default is 0.0).

24. **EV** EIGENVALUE GUESS. Starting eigenvalue guess for a search
    calculation (default is 0.0).

25. **EQL** INITIAL SEARCH CONVERGENCE. Initial eigenvalue search
    convergence (default is 0.0001).

26. **XNPM** DAMPING FACTOR. Damping factor used in search calculations
    (default is 0.75).

27. **ISN** ORDER OF ANGULAR QUADRATURE FOR XSDRNPM. Quadrature sets are
    geometry-dependent quantities that are defaulted to order 8 by the
    XSProc for **LATTICECELL** and cylindrical **MULTIREGION**. The
    default is 32 for **MULTIREGION** slabs and spheres. See the
    automatic quadrature generator and Appendix B for a more detailed
    explanation.

28. **SZF** SPATIAL MESH SIZE FACTOR FOR XSDRNPM. The size of the mesh
    intervals can be adjusted by entering a value for **SZF**, which is
    a multiplier of the mesh size. The default value is 1.0. A value
    between zero and 1.0 yields a finer mesh; a value greater than 1.0
    yields a coarser mesh. If **SZF** ≤ 0, the user specifies the number
    of mesh intervals in each zone immediately following the **MORE
    DATA** block. If **SZF** = 0, the interval spacing is automatically
    generated, while if **SZF** < 0 the intervals are equally spaced
    intervals in each zone.

29. **IIM** MAXIMUM NUMBER OF INNER ITERATIONS FOR XSDRNPM. This is the
    maximum number of inner iterations to be used in the XSDRNPM
    calculation. The default value is 20. See Appendix B for a more
    detailed explanation.

30. **ICM** MAXIMUM NUMBER OF OUTER ITERATIONS FOR XSDRNPM. This is the
    maximum number of outer iterations to be used in the XSDRNPM
    calculation. The default value is 25. If the calculation reaches the
    outer iteration limit, a larger value should be used. See Appendix B
    for a more detailed explanation.

31. **EPS** OVERALL CONVERGENCE CRITERIA FOR XSDRNPM. This is used by
    XSDRNPM after each outer iteration to determine if the problem has
    converged. The default value of **EPS** is 0.00001. A value less
    than 0.00001 tightens the convergence criteria; a larger value
    loosens the convergence criteria.

32. **PTC** POINTWISE CONVERGENCE CRITERIA FOR XSDRNPM. This is the
    point flux convergence criteria used by XSDRNPM to determine if
    convergence has been achieved after an inner iteration. The default
    value for PTC is 0.000001. A smaller value tightens convergence; a
    larger value loosens it.

33. **BKL** BUCKLING FACTOR FOR XSDRNPM. A buckling factor should be
    used ONLY for a **MULTIREGION** **BUCKLEDSLAB** or **BUCKLEDCYL**
    problem. Because cylinders are assumed to be infinitely long and
    slabs are assumed to be infinite in both transverse directions, the
    analytic sequence may tend to overestimate the total flux for a
    finite system. A buckling correction can be used to approximate the
    leakage from the system in the transverse direction(s). The
    extrapolation distance factor, **BKL**, is defaulted to 1.420892.

34. **IUS** UPSCATTER SCALING FLAG for XSDRNPM. This option allows the
    use of upscatter scaling to accelerate the solution or force
    convergence. The default value is zero, in which case upscatter
    scaling is not used. **IUS**\ =1 facilitates upscatter scaling.
    Guidelines are not available to indicate when upscatter scaling is
    needed. Some problems will not converge with it, and some will not
    converge without it. See Appendix B for a more detailed explanation.

35. **DAN**\ (mm) DANCOFF FACTOR for the specified mixtures used in
    BONAMI and in the CENTRM 2REGION option. This value overrides the
    internally computed Dancoff factor used in the resonance correction
    for the specified mixture *mm*. The Dancoff data are entered in the
    form **DAN**\ (mm) = Dancoff factor. Note that the parentheses must
    be entered as part of the data, and the mixture number, mm, must be
    enclosed in the parentheses. See Appendix B for additional details.
    (Note: this is not to be confused with the DAN2PITCH parameter in
    CENTRMDATA)

36. **BAL** BALANCE TABLE PRINT FLAG for XSDRNPM. This allows control of
    the balance table print from **XSDRNPM**. The default value is
    **FINE**. **BAL**\ =\ **NONE** suppresses the balance table print.
    **BAL**\ =\ **ALL** prints all of the balance tables.
    **BAL**\ =\ **FINE** prints only the fine-group balance tables. See
    Appendix B for additional details.

37. **DY** FIRST TRANSVERSE DIMENSION for XSDRNPM. This is the first
    transverse dimension, in cm, used in a buckling correction to
    calculate the leakage normal to the principal calculation direction
    (the height of a slab or cylinder). It should only be entered if
    XSDRNPM is to create cell-weighted cross sections and/or calculate
    the eigenvalue of a cylinder or slab system of finite height for a
    **LATTICECELL** problem. **DY**\ = is defaulted to an infinite
    height, or is set to **DY** for a buckled **MULTIREGION** cell
    description. A value entered here overrides any buckling height
    value entered in the **MULTIREGION** data.

38. **DZ** SECOND TRANSVERSE DIMENSION for XSDRNPM. This is the second
    transverse dimension, in cm, used for a buckling correction for a
    slab of finite width. It should only be entered if XSDRNPM is to
    create cell-weighted cross sections and/or calculate the eigenvalue
    of a **LATTICECELL** slab of finite width. **DZ**\ = is defaulted to
    an infinite width, or is set to **DZ** for a buckled **MULTIREGION**
    slab cell of finite width. A value entered here overrides any
    buckling depth value entered in the **MULTIREGION** data.

39. **COF** DIFFUSION COEFFICIENT FOR TRANSVERSE LEAKAGE CORRECTIONS IN
    XSDRNPM. The default value is 3. The available options are as
    follows.

    **COF**\ =0 sets a transport-corrected cross section for each zone

    **COF**\ =1 use a spatially averaged diffusion coefficient for each
    zone

    **COF**\ =2 use a diffusion coefficient for all zones that is
    one-third of the diffusion coefficient determined from the spatially
    averaged transport cross section for all zones

    **COF**\ =3 use a flux and volume weighting across all zones

    See Appendix B or XSDRNPM Input/Output Assignments in the XSDRNPM
    chapter, 3$ array, variable **IPN** for more details.

40. **NT3** UNIT WHERE XSDRNPM WRITES THE WEIGHTED LIBRARY. If XSDRN
    does a weighting calculation, this is the unit number it uses to
    write the weighted library on (default is 3).

41. **NT4** UNIT WHERE XSDRNPM WRITES THE ANGULAR FLUXES. XSDRN writes
    the angular fluxes on this unit if it is non-zero (default is 16).

42. **ADJ** Adjoint mode flag for XSDRNPM. Set to 1 to cause XSDRNPM to
    solve the adjoint problem (default is 0).

43. **NTA** UNIT WHERE XSDRNPM WRITES THE ACTIVITIES. XSDRN writes the
    calculated activities on this unit if it is non-zero (default is
    75).

44. **NBU** UNIT WHERE XSDRNPM WRITES BALANCE TABLES. If the balance
    tables file is to be saved, enter the unit number where it is to be
    written (default is 76).

45. **NTC** UNIT WHERE XSDRNPM WRITES THE DERIVED DATA. XSDRN writes the
    derived input data on this unit if it is non-zero (default is 73).

46. **NTD** UNIT WHERE XSDRNPM WRITES THE DATA FOR A SENSITIVITY
    ANALYSIS. XSDRN writes the data for a sensitivity analysis on this
    unit if it is non-zero (default is 0).

47. **FRD** UNIT WHERE XSDRNPM READS INPUT FLUX GUESS. If greater than
    0, a flux guess will be read from this unit.

48. **FWR** UNIT WHERE XSDRNPM WRITES OUPUT FLUX. If greater than 0, the
    space-dependent multigroup scalar flux is written in binary format
    to this unit.

49. **WGT** CROSS SECTION WEIGHTING FLAG for XSDRNPM. The default is 0,
    not to perform cross section weighting. To turn on cross section
    weighting, a positive value should be entered. A value of 1 will
    weight the cross sections by nuclide; 2 will weight by mixture.

50. **ZMD**\ (iz) ZONE WIDTH MODIFIERs for an XSDRNPM search problem.
    This allows entering a zone width modifier for zone iz in the
    XSDRNPM problem description. The zone width data are entered in the
    following form:

    **ZMD(iz)=modifier**

    Note that the parentheses must be entered as part of the keyword.
    The zone number iz, to which the modifier is applied, must be
    enclosed in the parentheses. The modifier is entered after the equal
    sign. See the “Dimension Search Calculations” description in the
    XSDRNPM chapter for more information.

51. **INT**\ (iz) NUMBER OF MESH INTERVALS FOR ZONE IZ in XSDRNPM. The
    default is 0, which causes the number to be calculated. The data are
    entered in the following form:

..

   **INT(iz)=number**

     Note that the parentheses must be entered as part of the keyword. The
     zone number iz, for which the number of intervals is specified, must
     be enclosed in the parentheses. The number of intervals is entered
     after the equal sign.

52. **KEF** DESIRED VALUE OF *k*\ :sub:`EFF` for an XSDRNPM zone width search.
    The default value is 1.0. If it is desired to search for some other
    value, such as 0.9, then input it here.

53. **KFM** The first eigenvalue modifier used in an XSDRNPM search.
    This value is used to make the first change in the XSDRNPM search.
    The default value is −0.1. A user may sometimes need to change this
    to make the search converge.

54. **ID1** SCALAR FLUX PRINT CONTROL. The default value is −1, which
    suppresses printing the scalar fluxes in XSDRNPM. See the XSDRNPM
    Input/Output Assignments section in the XSDRNPM chapter, 2$ array,
    variable **ID1** for allowed values and corresponding actions.

55. **ISCT** ORDER OF SCATTERING for XSDRMPM. The default is 5 for all
    libraries.

56. **ICON** TYPE OF WEIGHTING (see Cross-Section Weighting section in
    the XSDRNPM chapter).

..

   **INNERCELL** − followed by integer N (zones in the cell). Cell
   weighting is performed over the N innermost regions in the problem.
   Nuclides outside these regions are not weighted.

   **CELL** − cell weighting

   **ZONE** − zone weighting

   **REGION** − region weighting

58. **ITP** COLLAPSED OUTPUT FORMAT. The default is 0.

..

   0−19 − cross sections are written only in the AMPX weighted library
   formats on logical 3. A weighted library is always written when IFG=
   1.

   The various values of ITP (modulo 10) are used to select the
   different transport cross section weighting options mentioned
   earlier. The options are as follows:

   ITP = 0, 10, ... :math:`\sqrt{(\psi^{g}_{1} + (DG\psi))^{2}}`

   ITP = 1 ,11, ... absolute value of current

   ITP = 2, 12, ... :math:`DB^{2}\psi_{g}` + outside leakage

   ITP = 3, 13, ... :math:`\frac{\psi}{\Sigma^{g}_{t}}`

   ITP = 4, 14, ... :math:`DB\psi_{g}`

   ITP = Other values are reserved for future development and should not be used.

59. **GAMMA_MT_LIST** LIST OF GAMMA 1D REACTIONS ASSOCIATED WITH INPUT.
    A list of 1-D gamma reactions to be included on a condensed library
    for later use gamma_mt_list= numberEntries mt1 mt2 ...
    mt_numberEntries.

60. **NEUTRON_MT_LIST** LIST OF NEUTRON 1D REACTIONS ASSOCIATED WITH
    INPUT. A list of 1-D neutron reactions to be included on a condensed
    library for later use neutron_mt_list= numberEntries mt1 mt2 ...
    mt_numberEntries.

61. **NEUTRON_2D_LIST** LIST OF NEUTRON 2D ARRAYS FOR THE MICRO LIBRARY.
    This list flags the finalizer to place 2-D arrays (currently MT 2,
    4, 16) on the micro library for use in SAMS.

62. **ACTIVITY** Enter:

    IAZ (number of activities)

    IAI (calculate activities by zone or interval)

    0 – zone

    1 – interval

    LACFX (unit number to which activities are written)

    LAZ (IAZ sets of numbers consisting of the nuclide and process
    numbers for each activity)

63. **BAND** NUMBER OF REBALANCE BANDS for XSDRNPM (default is 1).

64. **IPRT** CROSS SECTION PRINT CONTROL. The default value is −2, which
    suppresses printing the cross sections in XSDRNPM. See XSDRNPM
    chapter, 2$ array, variable IPRT for allowed value, and
    corresponding actions.

65. **GRAIN_K** Flag to control execution of XSDRNPM after each grain
    calculation for a **DOUBLEHET** cell.

66. **SOURCE**\ (iz) ZONE SOURCE for an XSDRNPM fixed source problem.
    This allows entering a source spectrum for zone iz in the XSDRNPM
    problem description. The source spectrum data are entered in the
    following form:

    **SOURCE(iz)= numEntries spectrum_grp_1 … spectrum_grp_numEntries**

    Note that the parentheses must be entered as part of the keyword. The
    zone number, iz, to which the spectrum is applied, must be enclosed by
    the parentheses. The numEntries follows the equal sign and must be less
    than or equal to the number of energy groups for the problem. It is
    followed by numEntries numbers defining the spectrum for the first
    numEntries groups for zone iz. Groups not defined are set to zero. The
    spectrum applies uniformly to zone iz. A different spectrum may be
    entered for different zones.


67. **END MORE**	Terminate the optional parameter data.

.. _7-1-3-9:

Optional CENTRM DATA parameter data
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The CENTRM DATA block defines input parameter values for the CENTRM, PMC
and CRAWDAD modules. XSProc defines default values for these parameters
which are adequate for most applications. If all default values are
acceptable, this section of input data can be omitted. The CENTRM DATA
block applies only to the unit cell immediately preceding it. CENTRM
DATA placed prior to all unit cell data applies to all materials not
listed in any unit cell. Parameter values are assigned by entering the
words **CENTRM DATA** followed by the desired keyword parameters and
their associated values. One or more parameters can be entered in any
order. There should not be a blank between the parameter name and the
equal sign. Each parameter specification must be separated from the rest
by at least one blank. For example,

::

  **CENTRM DATA ISN**\ =16 **PTC**\ =0.0008 **N1D**\ =1 **END CENTRM
  DATA**

A description of CENTRM DATA parameters is given below.

1.  **CENTRM DATA** These words, followed by one or more blanks, are
    entered ONLY if optional parameter data are to be entered. They must
    precede all other optional parameter data. Entries 2 through 42 can
    be entered in any order.

2.  **ISN** ORDER OF SN ANGULAR QUADRATURE FOR CENTRM. SN Quadrature
    sets are geometry-dependent quantities. Default value for **ISN** is
    6 (only used for **NFST** and **NTHR**\ =0; and **NPXS**\ =1).

3.  **ISCT** LEGENDRE POLYNOMIAL P\ :sub:`N` ORDER OF SCATTERING. These
    are used to determine the number of moments calculated for the
    scattering cross sections. Default value is 0 for 2-D MoC option and
    1 for 1-D S\ :sub:`n`, which have been found adequate for nearly all
    cases.

4.  **IIM** MAXIMUM NUMBER OF INNER ITERATIONS. This is the maximum
    number of inner iterations for Sn transport calculations in CENTRM.
    Default value is 10.

5.  **IUP** MAXIMUM NUMBER OF OUTER ITERATIONS IN THERMAL RANGE. This is
    the maximum number of outer iterations used to converge PW flux
    changes caused by upscattering in the thermal range. Default value
    is 3. More iterations (~ 15) may be required for higher accuracy in
    some cases.

6.  **NFST** FAST RANGE MULTIGROUP CALCULATION OPTION, E > \ **DEMAX**.
    This determines what type of calculation is done above **DEMAX**.
    The options are (0) S:sub:`N`, (1) diffusion theory, (2) homogenized
    infinite medium, (3) zonewise infinite medium, or (6) 2D MoC lattice
    cell [NOTE: NFST=4,5 are deprecated]. Default value is 0
    (S\ :sub:`N`).

7.  **NTHR** THERMAL RANGE MULTIGROUP CALCULATION OPTION,
    E < \ **DEMIN**. This determines what type of calculation is done
    below **DEMIN**. The options include (0) S:sub:`N`, (1) diffusion,
    (2) homogenized infinite medium, (3) zonewise infinite medium, or
    (6) 2-D MoC lattice cell [NOTE: NTHR=4,5 are deprecated]. Default
    value is 0 (S\ :sub:`N` ).

8.  **NPXS** POINTWISE RANGE MULTIGROUP CALCULATION OPTION,
    **DEMIN** < E < **DEMAX**. This determines what type of calculation
    is done between **DEMIN** and **DEMAX**. The options include (0) MG
    calculation, (1) 1-D S\ :sub:`N`, (2) collision probability,
    (3) homogenized infinite medium, (4) zonewise infinite medium,
    (5) two-region, or (6) 2-D MoC lattice cell. Default value
    is 1 (S\ :sub:`N`), except for square-pitch LATTICECELL where the
    default is 6 (2D MoC).

9.  **ISVAR** LINEARIZATION OPTION. This determines if the MG source
    and/or the cross sections are linearized in CENTRM calculations.
    Options for linearizing are (0) neither, (1) source, (2) cross
    section, or (3) both. Default value is 3.

10. **ISCTI** LEGENDRE POLYNOMIAL P\ :sub:`N` ORDER OF SCATTERING IN THE
    INELASTIC RANGE. These are used to determine the number of moments
    calculated for the inelastic scattering cross sections. Default
    value is 0, isotropic.

11. **NMF6** INELASTIC FLAG. This determines if inelastic data are used.
    The options are to include (−1) no inelastic data, (0) discrete
    inelastic data, and (1) discrete inelastic and continuum. Default
    value is −1. Use of **NMF6**\ =1 is not recommended due to long
    running times.

12. **IPRT** MIXTURE CROSS-SECTION OUTPUT OPTION. This determines the
    output of cross section. The options include (−3) none, (−2) output
    macro PW cross sections to file “_­centrm.pw.macroxs”, (−1) 1-D MG
    cross sections, (N) P\ :sub:`0` to P\ :sub:`N` MG 2-D matrices.
    Default value is −3, none.

13. **ID1** FLUX EDIT OPTION. This option determines the output of flux
    energy spectra. The options are (−1) none, (0) print MG fluxes,
    (1) also print MG flux moments, (2) save CE fluxes on output file,
    “_centrm.pw_flux”. Default value is −1.

14. **KERNEL** BOUND KERNELS. This indicates use of CENTRM PW thermal
    kernel data [S(α,β)] for bound nuclides if **KERNEL**\ =1. If
    **KERNEL**\ =0, all thermal kernels are treated as free gas; Default
    is 1, use bound scattering kernels if available.

15. **IPBT** PRINT GROUP SUMMARY TABLES. Group summary tables for each
    zone are printed in CENTRM if greater than 0. Default is 0. Balance
    ratios are not computed in thermal groups or for MoC option.

16. **IPN** GROUP DIFFUSION COEFFICENT. Used for DB\ :sup:`2` loss term.
    See XSDRNPM chapter for more information. Default is 2.

17. **IXPRT** PRINT OPTION FOR CENTRM. This value is >0 if more
    information is printed to output. Default value is 0, minimum
    output.

18. **MLIM** MASS VALUE RESTRICTION ON ORDER OF SCATTERING. Nuclides
    with mass ratios greater than **MLIM** are limited to a **NLIM**
    order of scattering. Default value is 100.

19. **NLIM** ORDER OF SCATTERING RESTRICTION. This is the limiting order
    of scattering for all nuclides with mass ratios greater than
    **MLIM**. Default value is 0.

20. **EPS** INTEGRAL CONVERGENCE CRITERIA. This is used by CENTRM after
    each outer iteration to determine if the problem has converged.
    Default value is 0.001. A value less than 0.0001 tightens the
    convergence criteria; a larger value loosens the convergence
    criteria.

21. **PTC** POINTWISE CONVERGENCE CRITERIA. This is the point flux
    convergence criteria used by CENTRM to determine if convergence has
    been achieved after an inner iteration. Default value is 0.0001. A
    smaller value tightens convergence; a larger value loosens it.

22. **B2** MATERIAL BUCKLING FACTOR (cm\ :sup:`-2`). This is used with a
    buckled system. If a buckled system is specified for a unit cell,
    the code will use this value. Default value is 0.0.

23. **DEMIN** LOWEST ENERGY OF POINTWISE FLUX CALCULATION. This value is
    the lowest energy (eV) for which CENTRM calculates PW fluxes.
    Default is 0.001 eV.

24. **DEMAX** HIGHEST ENERGY OF POINTWISE FLUX CALCULATION. This value
    is the highest energy (eV) for which CENTRM calculates PW fluxes.
    Default is 20,000.0 eV, which encompasses the resolved resonance
    range of all actinides. It is recommended that DEMAX be <500 keV.

25. **TOLE** CENTRM PW THINNING TOLERANCE. This is the tolerance used to
    thin the PW material cross sections after they are mixed. Default
    value is 0.001.

26. **FLET** FRACTIONAL LETHARGY CONSTRAINT. This is the maximum
    lethargy difference between points in the flux solution energy mesh.
    Smaller values increase the number of energy points. Default value
    is 0.1.

27. **DAN2PITCH** CENTRM DANCOFF FACTOR SEARCH. Fuel Dancoff factor to
    search for a Dancoff-equivalent pitch used in the CENTRM cell
    calculation. Only applicable in LATTICECELL cases with fuel in
    center region, with SN or MoC transport solvers. Default is 0, which
    indicates no pitch modification. NOTE! This option should not be
    used to enter Dancoff factors for the CENTRM *2REGION* transport
    option—use EDAN(m) array in **MOREDATA** for these values.

28. **MRANGE** PMC GROUP CROSS-SECTION PROCESSING RANGE. This option
    determines the range over which the group cross sections will be
    processed. The options are (0) compute new group cross section over
    the PW range, (1) over the resolved resonance range of each nuclide,
    or (2) over the PW flux range (**DEMAX** to **DEMIN**). Default
    value is 2.

29. **N2D** PMC ELASTIC MATRIX PROCESSING FLAG. This option determines
    how MG P\ :sub:`N` elastic scattering matrices are obtained. Options
    are (-2) perform operations in both (-1) and (2); (−1) compute P0
    self-scatter, then renormalize matrix to shielded 1-D elastic
    values; (0) normalize original scatter matrix to shielded 1-D
    elastic values; (1) compute new P\ :sub:`N` moments of elastic
    matrix using scalar flux and S‑wave kinematics; or (2)  use
    flux-moments to compute “consistent PN” correction for diagonal
    elements of elastic P\ :sub:`N` components. Default value is −1. For
    unit cell calculations in reactor lattices, option -2 may improve
    results. NOTE: option 0 is always used in thermal range

30. **IXTR3** PMC P\ :sub:`N` ORDER FLAG. This option determines the
    maximum order of Legendre moments to be retained on output MG
    library. The default is 5; i.e., retain scattering moments up to
    P\ :sub:`5` if available on the input MG library. If (−1) is
    entered, all elastic moments on the MG library are included.

31. **NPRT** PMC PRINT FLAG. This option determines what is printed to
    output. The options include (−1) minimum output, (0) standard
    output, (1) print 1-D cross sections, (2) print both 1-D and 2-D
    cross sections. Default value is −1, minimum output.

32. **NWT** PMC MULTIGROUP SPATIAL-WEIGHTING FLAG. This option
    determines if the MG data are (0) zone-weighted or
    (1) cell-weighted. Default value is 0.

33. **MTT** PMC MT PROCESSING FLAG. This option determines if reaction
    MTs are processed individually or treat dependencies explicitly. If
    **MTT**\ =0 all MTs are processed independently; if **MTT**\ =1, all
    MTs are processed except 1, 27, and 101. These are then computed as
    follows: MT101 = sum MT102 − 114, MT27 = MT18 + MT101, MT1 = MT2 +
    MT4 + MT16 + MT17 + MT27. Default value is 1.

34. **N1D** PMC WEIGHTING FUNCTION FLAG. This is used to determine if
    (0) flux weighting or (1) current weighting is used to collapse the
    cross sections. Default value is 0, flux weighting.

35. **PMC_DILUTE** PMC INFINITELY DILUTE BACKGROUND. The background
    cross section :math:`\sigma_{0}` value above which materials are considered
    to be infinitely dilute in PMC. No resonance shielding corrections
    are performed for materials with background cross sections greater
    than *pmc_dilute*. Higher values of *pmc_dilute* result in more
    nuclides being processed. The default value is 1.0E10.

36. **MTOUT** PW REACTION TYPES. Reactions included by CRAWDAD on PW
    library for MG processing in PMC: (0) all; (1) output only MTs 1, 2,
    4, 102, 18, 452, 455, 456 (and 107 for :sup:`10`\ B or
    :sup:`7`\ Li); (2) all from option (1) and all inelastic MTs and 16.
    Default is **MTOUT**\ =1 for **NMF6**\ =-1 and **MTOUT**\ =2 for
    **NMF6**>-1.

37. **IBR** CENTRM RIGHT BOUNDARY TYPE. Type of boundary condition on
    right boundary of unit cell for CENTRM **LATTICECELL** calculations.
    See allowable IBR values in CENTRM. Default is white (**IBR** = 3)
    for 1D SN; 2D MoC transport option always uses reflected.

38. **IBL** CENTRM LEFT BOUNDARY TYPE. Same as **IBR**, but for left
    boundary. Default is reflected (**IBL** = 1).

39. **ALUMP** MASS LUMPING FRACTION. A value in range [0.0, 1.0]
    indicates fractional mass lumping criterion for CENTRM. Value of 0
    indicates no lumping applied. For example, **ALUMP**\ =0.3 means
    that materials are combined into one or more lumps such that their
    masses are within +/‑30% of the effective lump mass, while
    preserving the slowing-down power. This approximation reduces
    execution time. Default value is 0.2.

40. **PMC_OMIT** PMC NUCLIDES SKIPPED. PMC normally processes
    problem-dependent (e.g., self-shielded) MG cross sections for all
    materials. If **PMC_OMIT**\ =1, processing is only performed for
    materials contained in fuel mixtures. Default value is 0 (all
    materials processed).

41. **PXSMEM** CENTRM PW DATA STORAGE. Option to store PW data in memory
    or in external file during centrm execution. If **PXSMEM**\ =1, PW
    cross section data are stored by group in external scratch file
    during CENTRM calculation; if **PXSMEM**\ =0 (default value), all PW
    cross sections are kept in memory.

42. **MOCMESH** CENTRM MOC MESH OPTION. Pre-defined space mesh intervals
    for CENTRM MoC calculation: 0=>coarse mesh (1 interval per zone);
    1=>regular mesh (4 intervals in fuel, 2 in moderator, 1 in others);
    2=> fine mesh (8 in fuel, 4 in moderator, 1 in others). Default=0.

43. **MOCRAY** CENTRM MOC RAY SPACING. Distance between characteristic
    rays in CENTRM MoC calculation. Default=0.02.

44. **MOCPOL** CENTRM NUMBER OF MOC POLAR ANGLES. Allowable values are
    2, 3, 4. Default=3 (only used for **NPXS**\ =6).

45. **MOCAZI** CENTRM NUMBER OF MOC AZIMUTHAL ANGLES. Allowable values
    are 2–16. Default=8 (only used for **NPXS**\ =6).

46. **MOCZONE_INT** CENTRM MOC MESH BY ZONE. User-defined mesh intervals
    by zone; e.g., moczone_int(1)=5 defines five intervals for zone 1;
    zero value means not used. This overrides the predefined meshs
    described by **MOCMESH**

47. **ISRC** CENTRM SOURCE TYPE. CENTRM can use a fission-spectrum
    source (isrc=1), an input source spectrum (isrc=0), or a
    combination(isrc=3) for transport. Default=1.

48. **XNF** CENTRM SOURCE NORMALIZATION. The integrated source
    (fission-spectrum and/or fixed source spectrum) is normalized to
    this value. Default=1.0.

49. **ITERP** CRAWDAD TEMPERATURE INTERPOLATION METHOD. Method to use
    for CE cross section interpolation 0=>combination of square-root(T)
    and finite-difference; 1=>only square-root(T); 2=> only
    finite-difference. Default is 0.

50. **END CENTRM** The word **END** is entered to terminate the optional
    parameter data. A label can be associated with this **END**. The
    label can be as long as 12 characters but must be preceded by a
    single blank. If this **END** is entered without a label, it must
    not begin in column 1. At least two blanks must follow this entry.