From 5e8fd2f2fb39c4a3ddb6b12a5f6de873e93e9a53 Mon Sep 17 00:00:00 2001
From: Brown <2mx@ornl.gov>
Date: Mon, 3 Jan 2022 17:38:16 -0500
Subject: [PATCH] Added all chapters and sections
and addressed Goran's comment to clarify
how the phase shift was handled at the
reaction threshold
---
docs/tex/appendices.tex | 7 +
docs/tex/auxiliary-programs.tex | 82 +++
docs/tex/computer-code.tex | 33 ++
docs/tex/evaluation-connection.tex | 11 +
docs/tex/examples.tex | 19 +
docs/tex/{multScat.tex => exp-conditions.tex} | 506 +++++++++---------
docs/tex/fitting-procedure.tex | 27 +
docs/tex/helpful-hints.tex | 20 +
docs/tex/input.tex | 32 ++
docs/tex/introduction.tex | 24 +-
docs/tex/miscellaneous.tex | 32 ++
docs/tex/output.tex | 35 ++
docs/tex/sammy_main.pdf | 4 +-
docs/tex/sammy_main.tex | 13 +-
docs/tex/scattering-theory.tex | 97 ++--
docs/tex/urr.tex | 6 +-
16 files changed, 652 insertions(+), 296 deletions(-)
create mode 100644 docs/tex/appendices.tex
create mode 100644 docs/tex/auxiliary-programs.tex
create mode 100644 docs/tex/computer-code.tex
create mode 100644 docs/tex/evaluation-connection.tex
create mode 100644 docs/tex/examples.tex
rename docs/tex/{multScat.tex => exp-conditions.tex} (75%)
create mode 100644 docs/tex/fitting-procedure.tex
create mode 100644 docs/tex/helpful-hints.tex
create mode 100644 docs/tex/input.tex
create mode 100644 docs/tex/miscellaneous.tex
create mode 100644 docs/tex/output.tex
diff --git a/docs/tex/appendices.tex b/docs/tex/appendices.tex
new file mode 100644
index 000000000..42f537816
--- /dev/null
+++ b/docs/tex/appendices.tex
@@ -0,0 +1,7 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Appendices %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Appendices}\label{ch:appendices}
\ No newline at end of file
diff --git a/docs/tex/auxiliary-programs.tex b/docs/tex/auxiliary-programs.tex
new file mode 100644
index 000000000..0736b32a3
--- /dev/null
+++ b/docs/tex/auxiliary-programs.tex
@@ -0,0 +1,82 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Auxiliary Programs %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Auxiliary Programs}\label{ch:auxiliary-programs}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{angodf: Convert From Energy/Angle To Angle/Energy} \label{sec:angodf}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{convrt: Convert From Refit Input to Sammy or Vice Versa} \label{sec:convrt}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samamr: Add, Mix, or Recover Variables} \label{sec:samamr}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samamx: Modify a Single Value} \label{sec:samamx}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samcpr: Compare Results} \label{sec:samcpr}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samdis: Statistical Distributions} \label{sec:samdis}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samftz: Fix TZERO ($t_0$)} \label{sec:samftz}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samort: Plot The Oak Ridge Resolution Function} \label{sec:samort}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samplt: Alternative Form For Plot Files} \label{sec:samplt}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samqua: Resonance Quantum Numbers} \label{sec:samqua}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samrpt: Plot RPI Resolution Function} \label{sec:samrpt}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samrst: Plot Resolution Function} \label{sec:samrst}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samsmc: Monte Carlo Multiple Scattering} \label{sec:samsmc_monte_carlo}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samsta: Staircase Plots} \label{sec:samsta}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samthn: Thinning Data} \label{sec:samthn}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{suggel: Estimating L and J} \label{sec:suggel}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samrml: Calculate Cross Sections From Endf File 2} \label{sec:samrml}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{samgy2: Smooth The Tabulated Y2 Function} \label{sec:samgy2}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
diff --git a/docs/tex/computer-code.tex b/docs/tex/computer-code.tex
new file mode 100644
index 000000000..c0e29c3cb
--- /dev/null
+++ b/docs/tex/computer-code.tex
@@ -0,0 +1,33 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Computer Code %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Computer Code}\label{ch:computer-code}
+
+\textcolor{red}{Use of the more modern CMake system should remove most of computer dependence now.}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Dynamic Allocation Of Array Storage} \label{sec:dynamic-arrays}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Use Of Temporary Data Files To Store Intermediate Results} \label{sec:temporary-files}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Division Of The Program Into Autonomous Segments} \label{sec:modularity}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Computer-specific Features} \label{sec:computer-specific-feat}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{ORELA Data Format} \label{sec:odf}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Configuration And Distribution System} \label{sec:config-and-dist}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ No newline at end of file
diff --git a/docs/tex/evaluation-connection.tex b/docs/tex/evaluation-connection.tex
new file mode 100644
index 000000000..7f98a6ae9
--- /dev/null
+++ b/docs/tex/evaluation-connection.tex
@@ -0,0 +1,11 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Evaluation Connection %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Evaluation Connection}\label{ch:eval-connection}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{CSEWG Constants} \label{sec:csewg-constants}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ No newline at end of file
diff --git a/docs/tex/examples.tex b/docs/tex/examples.tex
new file mode 100644
index 000000000..2b23f7538
--- /dev/null
+++ b/docs/tex/examples.tex
@@ -0,0 +1,19 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Examples %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Examples}\label{ch:examples}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Tutorial} \label{sec:tutorial}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Test Cases} \label{sec:test-cases}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Monte Carlo Simulations of Multiple-scattering Corrections} \label{sec:mc-test-cases}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ No newline at end of file
diff --git a/docs/tex/multScat.tex b/docs/tex/exp-conditions.tex
similarity index 75%
rename from docs/tex/multScat.tex
rename to docs/tex/exp-conditions.tex
index 1a97e5af4..25ca9383e 100644
--- a/docs/tex/multScat.tex
+++ b/docs/tex/exp-conditions.tex
@@ -1,243 +1,263 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% %
-% CHAPTER THREE %
-% %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\chapter{Self-shielding And Multiple-scattering Corrections To Capture Or Fission Yields}\label{ch:multScat}
-
-The theoretical capture, fission, and other cross sections may be calculated directly from the equations in Sec. \ref{theory} using the Reich-Moore (or other) approximation to the multilevel R-matrix. However, in order to compare with experimental results, corrections must often be made for the finite (non\-infinitesimal) size of the sample.
-
-Both ``self-shielding'' and ``multiple-scattering'' effects must be included in the calculation. These corrections are most often needed for capture experiments; however, they may also be needed for fission, absorption, or other partial cross sections. For the rest of this section, ``capture'' will be taken to indicate whichever type of cross section is under investigation; the corrections described here apply in any case.
-
-Derivation of the appropriate expressions for self-shielding and multiple-scattering corrections, including details of the methods of calculation, is non\-trivial and will not be presented here. Results of comparison tests with Monte Carlo calculations indicate good agreement between Monte Carlo results and results obtained via SAMMY, as reported in \cite{larson_multscat_2002}. See Section \ref{samsmc_monte_carlo} for a description of the Monte Carlo code used for such comparisons.
-
-The capture yield Y (E)can be written as the sum of four components, each of which is described separately below; that is,
-
-\begin{equation} \label{total_yield}
- Y(E) = Y_0(E) + Y_1(E) + Y_2(E) + Y_n(E) .
-\end{equation}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Self-Shielding} \label{self_shielding}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-Self-shielding is the reduction in the observed capture cross section due to interactions of incident neutrons with other nuclei in front of the current position. The probability that capture will occur at depth $z$ (within $dz$) can be written as
-
-\begin{equation} \label{eq_prob_capture_dz}
- \frac{n}{D}e^{-n\sigma_tz/D}\sigma_c dz ,
-\end{equation}
-
-\noindent
-where $n$ is the sample thickness in atoms/barn and $D$ is the sample thickness in the same units as $z$. Subscripts $t$ and $c$ denote total and capture cross sections, respectively. Integrating over $z$ (from 0 to $D$) gives the self-shielded capture yield
-
-\begin{equation} \label{eq_self_shield_cap_yield}
- Y_0 = \frac{\sigma_c}{\sigma_t}\left(1-e^{-n\sigma_t}\right) .
-\end{equation}
-
-\noindent
-(See the end of this section for a discussion of the normalization options for capture yields.)
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Single Scattering} \label{single_scattering}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-The scattering correction is the increase in the observed capture cross section due to capture of neutrons that have been scattered out of the original beam path. Calculation of the scattering effect is more complicated than the self-shielding because it involves the product of (1) the probability of reaching a position ($x,y,z$) inside the sample, (2) the probability of scattering from that position into solid angle $\Omega$ within $d\Omega$, (3) the probability of those scattered nuclei reaching position $q$ within $dq$ along that direction, and (4) the probability of being captured at that location. This product is then integrated over the position $q$, over solid angle $\Omega$, and over the sample volume, giving the single-scattering result. If the $z$ axis is defined by the beam line, this expression can be reduced to the form
-
-\begin{equation} \label{eq_single_scatter_integration}
- Y_1(E) = \frac{1}{S}\int dx\int dy\frac{n}{D}\int dz\; e^{-(\frac{n}{D}\sigma_t z)}\int d\Omega\frac{d\sigma}{d\Omega}\sigma^{'}_c\frac{n}{D}\int dq\;e^{-(\frac{n}{D}\sigma_t^{'}q)} ,
-\end{equation}
-
-\noindent
-in which primes indicate the evaluation at the scattered energy, rather than at the incident energy of the neutron. The scattered energy is given by
-
-\begin{equation} \label{eq_energy_loss}
- E^{'} = E\left[\frac{cos(\theta)}{1+r}+\sqrt{\frac{1}{(1+1/r)^2}}-\frac{sin^2(\theta)}{(1+r)^2}\right]^2 ,
-\end{equation}
-
-where $r$ is the ratio of the mass of the target nuclide\footnote{There may, of course, be several different types of target nuclide, each with a different mass. While the equations in this section assume only one nuclide, the implementation in the SAMMY code includes summations over all nuclides in the sample.} to the mass of the neutron. (See Section II.C.2 and especially Eq. (II C2 b.3) for a derivation of this equation.)
-
-Explicit evaluation of the expression in Eq. \ref{eq_single_scatter_integration} requires detailed knowledge of the geometry of the sample and its positioning relative to the neutron beam, as shown in the sketch in Figure III D.1. In the case where the sample is a round disk, with a flat surface perpendicular to the beam, the expression can be reduced to
-
-\begin{equation} \label{eq_single_scatter_reduction}
- Y_1(E) = Y_{1\infty f} + Y_{1\infty b} + Y_{1cf} + Y_{1cb} ,
-\end{equation}
-
-where the subscripts $f$ and $b$ refer to forward and backward scattering, respectively. The subscript $\infty$ indicates that this term assumes the sample extends to infinity in the dimensions perpendicular to the beam; subscript $c$ indicates that this term is the correction for finite size.
-
-The ``infinite'' terms in Eq. \ref{eq_single_scatter_reduction} are one-dimensional integrals,
-
-\begin{equation} \label{eq_single_scatter_reduction_inf_forward}
- Y_{1\infty f}(E) = \frac{1}{2}\int_0^1d\mu\frac{d\sigma}{d\Omega}\frac{\sigma_c^{'}}{\sigma_{t}^{'}}\left(\frac{1-e^{-n\sigma_t}}{\sigma_t} + \frac{e^{-n\sigma_t}-e^{-n\sigma_t^{'}/\mu}}{\sigma_t-\sigma_t^{'}/\mu}\right) ,
-\end{equation}
-
-\noindent
-and
-
-\begin{equation} \label{eq_single_scatter_reduction_inf_backward}
- Y_{1\infty b}(E) = \frac{1}{2}\int_{-1}^0d\mu\frac{d\sigma}{d\Omega}\frac{\sigma_c^{'}}{\sigma_{t}^{'}}\left(\frac{1-e^{-n\sigma_t}}{\sigma_t} + \frac{1-e^{-n(\sigma_t-\sigma_t^{'}/\mu)}}{\sigma_t-\sigma_t^{'}/\mu}\right) ,
-\end{equation}
-
-\noindent
-in which $\mu = cos(\theta)$. The ``finite'' corrections involve four-dimensional integrals of the form
-
-\begin{equation} \label{eq_single_scatter_reduction_fin_forward}
- Y_{1cf}(E) = \frac{1}{2}\int_{0}^1d\mu\frac{d\sigma}{d\Omega}\frac{\sigma_c^{'}}{\sigma_{t}^{'}}Q_{\textcolor{blue}f}(\mu,\sigma_t,\sigma_t^{'})
-\end{equation}
-
-\noindent
-and
-
-\begin{equation} \label{eq_single_scatter_reduction_fin_backward}
- Y_{1cb}(E) = \frac{1}{2}\int_{-1}^0d\mu\frac{d\sigma}{d\Omega}\frac{\sigma_c^{'}}{\sigma_{t}^{'}}Q_{\textcolor{blue}b}(\mu,\sigma_t,\sigma_t^{'}) .
-\end{equation}
-
-\noindent
-Here the three-dimensional integral $Q_f$ is given by
-
-% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
-\begin{equation} \label{eq_qf}
- Q_f(\mu,\sigma_t,\sigma_t^{'}) = \int dz\;e^{-n\sigma_t^{'}D/z} \int d^2S\left(e^{-n\sigma_t(D-z)/(D\mu)}-e^{-n\sigma_tL/D}\right)
-\end{equation}
-
-\noindent
-and $Q_b$ by
-
-% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
-\begin{equation} \label{eq_qb}
- Q_b(\mu,\sigma_t,\sigma_t^{'}) = \int dz\;e^{-n\sigma_t^{'}(D-z)/z} \int d^2S\left(e^{-n\sigma_t(D-z)/(D\mu)}-e^{-n\sigma_tL/D}\right),
-\end{equation}
-
-\noindent
-where $L$ is the actual path length, within the sample, available for travel by the scattered neutron; note that $L$ is geometry dependent. The integration over $d^2S$ in this expression for $Q_{f,b}$ is over the beam cross section; the integration over $z$ is over the thickness of the sample. SAMMY evaluates $Q$ on a separate grid and interpolates to produce the required values for Eqs. \ref{eq_single_scatter_reduction_fin_forward} and \ref{eq_single_scatter_reduction_fin_backward}.
-
-Values for Q are generated in advance (in segment SAMPAR) and stored in a file named SAMMY.SSM. This file may be renamed and reused for subsequent runs, as long as the geometry remains the same.
-
-\begin{figure}
- \centering
- \includegraphics[width=10.5cm, height=7.5cm]{figures/multScat_cylinder.pdf}
- \caption{Geometry for the single-scattering correction to capture or fission yield, for a neutron incident on the flat surface of a cylindrical sample.}
- \label{multScat_cylinder}
-\end{figure}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{More than one scatter} \label{multiple_scattering}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-Derivation of the effect of two or more scatters followed by capture is accomplished in a similar manner to the derivation of the single-scattering effect. The exact expression for $k$ scatters involves $(3k + 3)$ embedded integrations; it is therefore necessary to make severe approximations in order to derive an expression that can be calculated in a finite amount of time. The approximation currently employed by SAMMY is borrowed from Moxon \cite{moxon_refit_1989}, based on a derivation by Case et al. \cite{case_1953}; an independent derivation was developed in preparation for implementation into the SAMMY code. The approximation assumes that after two scatterings, neutrons are uniformly distributed both in direction of motion and in position within the sample\footnote{This approximation has the effect of decoupling 2k of the embedded integrals, so that they can be performed separately from the others.}. To quantify this approximation, we assume that the escape probability for a neutron after $k$ scatterings (i.e., at energy $E (k)$ ) depends only on the energy; specifically, the escape probability is given by the formula
-
-% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
-\begin{equation} \label{eq_escape_probability}
- p_{escape}\left(E^{(k)}\right) = \frac{1}{n\sigma_t^{(k)}}\left[\frac{1}{2}-\int_1^\infty\mu^{-3}e^{-n\sigma_t^{(k)}\mu}d\mu\right]\frac{1+2n\sigma_t^{(k)}}{1+\frac{2n\sigma_t^{(k)}}{1+Z/R}},
-\end{equation}
-
-\noindent
-where $R$ is the radius of the sample. With this approximation, one can recursively define a function
-$y$ via
-
-% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
-\begin{equation} \label{eq_yj_function}
- y_{j-1} = \int d\Omega_j \frac{d\sigma_t^{(j-1)}}{d\Omega_j}\left(\sigma_c^{(j)}+y_j\right)\left(1-p_{escape}\left(E^{(j)}\right)\right) ,
-\end{equation}
-
-\noindent
-in which the superscript denotes the energy at which the cross section is to be calculated. The initial estimate for a neutron scattered k times is
-
-% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
-\begin{equation} \label{eq_yk_function}
- y_{k-1} \approx 2\pi\int d\mu_k \frac{d\sigma_t^{(k-1)}}{d\Omega_k}\sigma_c^{(k)}\left(1-p_{escape}\left(E^{(k)}\right)\right) .
-\end{equation}
-
-\noindent
-This function y can then be used to estimate the capture yield for two or more scatterings:
-
-% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
-\begin{equation} \label{eq_multiple_scatter_integration}
- Y_2(E) = \frac{1}{S}\int dx\int dy\frac{n}{E}\int dz\;e^{-\frac{n}{D}\sigma_tz}\int d\Omega\frac{d\sigma_t}{d\Omega}y_l\frac{n}{D}\int dq\;e^{-\frac{n}{D}\sigma_t^{'}q} \;.
-\end{equation}
-
-\noindent
-In this form the multiple-scattering capture yield has the same mathematical properties as the single- scattering capture yield of Eq. \ref{eq_single_scatter_integration}. Similar computational techniques can therefore be used to evaluate both quantities.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Alternative for more than one scatter} \label{multiple_scattering_alternative}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-For very thick samples and/or very strong resonances, the crude approximation described above for double-plus scattering may be woefully inadequate. For those situations, tabulated values can be use for $Y_2$. The tabulated values are generated with a series of three runs, first SAMMY with the command
-
-\texttt{PREPARE INPUT FOR MOnte carlo simulation}, or simply
-
-\texttt{MONTE CARLO}
-
-\noindent
-Next, the SAMSMC code is run to perform the Monte Carlo calculation. Then SAMGY2 reads the output from SAMSMC, smooths the $Y_2$ curve, and creates a file named SAMY2.DAT that contains the tabulated $Y_2$ values for use in the next SAMMY run. For that run, the command
-
-\texttt{Y2 VALUES ARE TABULAted}
-
-\noindent
-is inserted into the INPut file, and the name of the file must be included in the input stream.
-
-Only the values of $Y_2$ are given in this manner; derivatives are still generated as though the original form were used. \textcolor{red}{Caution must be exercised when using this option}, especially when varying resonance parameters, since (1) the tabulated values of $Y_2$ do not change unless the entire process is repeated and (2) derivatives are inaccurate.
-
-Simulation sim009 makes use of this option.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Neutron sensitivity} \label{neutron_sensitivity}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-In capture experiments, not only gamma rays but also scattered neutrons reach the detector. The detector is not always able to distinguish between the two; hence, it may be necessary to make corrections for the neutron sensitivity of the detector. These corrections are temporarily unavailable in SAMMY, pending further study.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Normalization and input options} \label{norm_mult_scat_input_options}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-Capture yield data may be normalized in a variety of ways; therefore, SAMMY allows the user to choose which normalization is to be taken. The normalization generally referred to as capture ``yield'' is the one shown in the equations in this section; this choice has the property that values are in the range from 0 to 1. Another commonly used normalization requires dividing by thickness $n$; in this case, the value approaches the capture cross section in the limit of zero thickness. Finally, the data may be normalized as $\left(1-e^{-n\sigma_t}\right)\sigma_t$, that is, by multiplying the yield by the total cross section. To use these options, the appropriate phrase must be included in the alphanumeric section of the INPut file:
-
-\texttt{NORMALIZE AS YIELD Rather than cross section}
-
-\texttt{NORMALIZE AS CROSS Section rather than yield}
-
-\texttt{NORMALIZE AS (1-E)SIgma}
-
-\noindent
-No default is assumed for normalization; instead, SAMMY requires that one of the above options be specified by the user.
-
-The default mode in SAMMY is to not include self-shielding and multiple-scattering corrections; therefore, to invoke these corrections, users will need to include one or more of the following phrases in their INPut file.
-
-\noindent
-For self-shielding but no multiple-scattering correction:
-
-\texttt{USE SELF SHIELDING Only, no scattering}, or
-
-\texttt{SELF SHIELD}
-
-\noindent
-For self-shielding, single-scattering (with edge-effects), and no double-scattering correction:
-
-\texttt{USE SINGLE SCATTERINg plus self shielding}, or
-\texttt{SINGLE}
-
-\noindent
-For self-shielding, single-scattering (infinite slab approximation), and no double-scattering corrections, two commands are required:
-
-\texttt{SINGLE} and
-\texttt{INFINITE SLAB}
-
-\noindent
-For self-shielding, single-scattering (with edge-effects correction), and multiple-scattering corrections:
-
-\texttt{INCLUDE DOUBLE SCATTering plus single scattering}, or
-\texttt{MULTIPLE SCATTERING} or
-\texttt{DOUBLE}
-
-\noindent
-For self-shielding, single-scattering (infinite-slab approximation), and multiple-scattering corrections, two commands are needed:
-
-\texttt{DOUBLE} and
-\texttt{INFINITE SLAB}
-
-When finite-size corrections (for single scattering) are wanted, additional input is needed to express the geometric properties of the beam and of the sample. These include the dimensions of the sample, the cross-sectional dimensions of the beam if smaller than the sample, and integers that determine the accuracy to which the functions $Q_{f,b}$ will be calculated. Details are given in Table VI A.1, card set 11.
-
-Examples using multiple-scattering corrections can be found in test cases tr039, tr052, tr064, tr099, and others.
-
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Experimental Conditions %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Experimental Conditions}\label{ch:exp-conditions}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Theoretical Foundation For Numerical Broadening} \label{sec:numerical-broadening}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Doppler Broadening} \label{sec:doppler-broadening}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Resolution Broadening} \label{sec:resolution-broadening}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Self-shielding And Multiple-scattering Corrections To Capture Or Fission Yields}\label{sec:multiple-scattering}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+The theoretical capture, fission, and other cross sections may be calculated directly from the equations in Sec. \ref{ch:scattering-theory} using the Reich-Moore (or other) approximation to the multilevel R-matrix. However, in order to compare with experimental results, corrections must often be made for the finite (non\-infinitesimal) size of the sample.
+
+Both ``self-shielding'' and ``multiple-scattering'' effects must be included in the calculation. These corrections are most often needed for capture experiments; however, they may also be needed for fission, absorption, or other partial cross sections. For the rest of this section, ``capture'' will be taken to indicate whichever type of cross section is under investigation; the corrections described here apply in any case.
+
+Derivation of the appropriate expressions for self-shielding and multiple-scattering corrections, including details of the methods of calculation, is non\-trivial and will not be presented here. Results of comparison tests with Monte Carlo calculations indicate good agreement between Monte Carlo results and results obtained via SAMMY, as reported in \cite{larson_multscat_2002}. See Section \ref{sec:samsmc_monte_carlo} for a description of the Monte Carlo code used for such comparisons.
+
+The capture yield Y (E)can be written as the sum of four components, each of which is described separately below; that is,
+
+\begin{equation} \label{total_yield}
+ Y(E) = Y_0(E) + Y_1(E) + Y_2(E) + Y_n(E) .
+\end{equation}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Self-Shielding} \label{self_shielding}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Self-shielding is the reduction in the observed capture cross section due to interactions of incident neutrons with other nuclei in front of the current position. The probability that capture will occur at depth $z$ (within $dz$) can be written as
+
+\begin{equation} \label{eq_prob_capture_dz}
+ \frac{n}{D}e^{-n\sigma_tz/D}\sigma_c dz ,
+\end{equation}
+
+\noindent
+where $n$ is the sample thickness in atoms/barn and $D$ is the sample thickness in the same units as $z$. Subscripts $t$ and $c$ denote total and capture cross sections, respectively. Integrating over $z$ (from 0 to $D$) gives the self-shielded capture yield
+
+\begin{equation} \label{eq_self_shield_cap_yield}
+ Y_0 = \frac{\sigma_c}{\sigma_t}\left(1-e^{-n\sigma_t}\right) .
+\end{equation}
+
+\noindent
+(See the end of this section for a discussion of the normalization options for capture yields.)
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Single Scattering} \label{single_scattering}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+The scattering correction is the increase in the observed capture cross section due to capture of neutrons that have been scattered out of the original beam path. Calculation of the scattering effect is more complicated than the self-shielding because it involves the product of (1) the probability of reaching a position ($x,y,z$) inside the sample, (2) the probability of scattering from that position into solid angle $\Omega$ within $d\Omega$, (3) the probability of those scattered nuclei reaching position $q$ within $dq$ along that direction, and (4) the probability of being captured at that location. This product is then integrated over the position $q$, over solid angle $\Omega$, and over the sample volume, giving the single-scattering result. If the $z$ axis is defined by the beam line, this expression can be reduced to the form
+
+\begin{equation} \label{eq_single_scatter_integration}
+ Y_1(E) = \frac{1}{S}\int dx\int dy\frac{n}{D}\int dz\; e^{-(\frac{n}{D}\sigma_t z)}\int d\Omega\frac{d\sigma}{d\Omega}\sigma^{'}_c\frac{n}{D}\int dq\;e^{-(\frac{n}{D}\sigma_t^{'}q)} ,
+\end{equation}
+
+\noindent
+in which primes indicate the evaluation at the scattered energy, rather than at the incident energy of the neutron. The scattered energy is given by
+
+\begin{equation} \label{eq_energy_loss}
+ E^{'} = E\left[\frac{cos(\theta)}{1+r}+\sqrt{\frac{1}{(1+1/r)^2}}-\frac{sin^2(\theta)}{(1+r)^2}\right]^2 ,
+\end{equation}
+
+where $r$ is the ratio of the mass of the target nuclide\footnote{There may, of course, be several different types of target nuclide, each with a different mass. While the equations in this section assume only one nuclide, the implementation in the SAMMY code includes summations over all nuclides in the sample.} to the mass of the neutron. (See Section II.C.2 and especially Eq. (II C2 b.3) for a derivation of this equation.)
+
+Explicit evaluation of the expression in Eq. \ref{eq_single_scatter_integration} requires detailed knowledge of the geometry of the sample and its positioning relative to the neutron beam, as shown in the sketch in Figure III D.1. In the case where the sample is a round disk, with a flat surface perpendicular to the beam, the expression can be reduced to
+
+\begin{equation} \label{eq_single_scatter_reduction}
+ Y_1(E) = Y_{1\infty f} + Y_{1\infty b} + Y_{1cf} + Y_{1cb} ,
+\end{equation}
+
+where the subscripts $f$ and $b$ refer to forward and backward scattering, respectively. The subscript $\infty$ indicates that this term assumes the sample extends to infinity in the dimensions perpendicular to the beam; subscript $c$ indicates that this term is the correction for finite size.
+
+The ``infinite'' terms in Eq. \ref{eq_single_scatter_reduction} are one-dimensional integrals,
+
+\begin{equation} \label{eq_single_scatter_reduction_inf_forward}
+ Y_{1\infty f}(E) = \frac{1}{2}\int_0^1d\mu\frac{d\sigma}{d\Omega}\frac{\sigma_c^{'}}{\sigma_{t}^{'}}\left(\frac{1-e^{-n\sigma_t}}{\sigma_t} + \frac{e^{-n\sigma_t}-e^{-n\sigma_t^{'}/\mu}}{\sigma_t-\sigma_t^{'}/\mu}\right) ,
+\end{equation}
+
+\noindent
+and
+
+\begin{equation} \label{eq_single_scatter_reduction_inf_backward}
+ Y_{1\infty b}(E) = \frac{1}{2}\int_{-1}^0d\mu\frac{d\sigma}{d\Omega}\frac{\sigma_c^{'}}{\sigma_{t}^{'}}\left(\frac{1-e^{-n\sigma_t}}{\sigma_t} + \frac{1-e^{-n(\sigma_t-\sigma_t^{'}/\mu)}}{\sigma_t-\sigma_t^{'}/\mu}\right) ,
+\end{equation}
+
+\noindent
+in which $\mu = cos(\theta)$. The ``finite'' corrections involve four-dimensional integrals of the form
+
+\begin{equation} \label{eq_single_scatter_reduction_fin_forward}
+ Y_{1cf}(E) = \frac{1}{2}\int_{0}^1d\mu\frac{d\sigma}{d\Omega}\frac{\sigma_c^{'}}{\sigma_{t}^{'}}Q_{\textcolor{blue}f}(\mu,\sigma_t,\sigma_t^{'})
+\end{equation}
+
+\noindent
+and
+
+\begin{equation} \label{eq_single_scatter_reduction_fin_backward}
+ Y_{1cb}(E) = \frac{1}{2}\int_{-1}^0d\mu\frac{d\sigma}{d\Omega}\frac{\sigma_c^{'}}{\sigma_{t}^{'}}Q_{\textcolor{blue}b}(\mu,\sigma_t,\sigma_t^{'}) .
+\end{equation}
+
+\noindent
+Here the three-dimensional integral $Q_f$ is given by
+
+% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
+\begin{equation} \label{eq_qf}
+ Q_f(\mu,\sigma_t,\sigma_t^{'}) = \int dz\;e^{-n\sigma_t^{'}D/z} \int d^2S\left(e^{-n\sigma_t(D-z)/(D\mu)}-e^{-n\sigma_tL/D}\right)
+\end{equation}
+
+\noindent
+and $Q_b$ by
+
+% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
+\begin{equation} \label{eq_qb}
+ Q_b(\mu,\sigma_t,\sigma_t^{'}) = \int dz\;e^{-n\sigma_t^{'}(D-z)/z} \int d^2S\left(e^{-n\sigma_t(D-z)/(D\mu)}-e^{-n\sigma_tL/D}\right),
+\end{equation}
+
+\noindent
+where $L$ is the actual path length, within the sample, available for travel by the scattered neutron; note that $L$ is geometry dependent. The integration over $d^2S$ in this expression for $Q_{f,b}$ is over the beam cross section; the integration over $z$ is over the thickness of the sample. SAMMY evaluates $Q$ on a separate grid and interpolates to produce the required values for Eqs. \ref{eq_single_scatter_reduction_fin_forward} and \ref{eq_single_scatter_reduction_fin_backward}.
+
+Values for Q are generated in advance (in segment SAMPAR) and stored in a file named SAMMY.SSM. This file may be renamed and reused for subsequent runs, as long as the geometry remains the same.
+
+\begin{figure}
+ \centering
+ \includegraphics[width=10.5cm, height=7.5cm]{figures/multScat_cylinder.pdf}
+ \caption{Geometry for the single-scattering correction to capture or fission yield, for a neutron incident on the flat surface of a cylindrical sample.}
+ \label{multScat_cylinder}
+\end{figure}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{More than one scatter} \label{multiple_scattering}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Derivation of the effect of two or more scatters followed by capture is accomplished in a similar manner to the derivation of the single-scattering effect. The exact expression for $k$ scatters involves $(3k + 3)$ embedded integrations; it is therefore necessary to make severe approximations in order to derive an expression that can be calculated in a finite amount of time. The approximation currently employed by SAMMY is borrowed from Moxon \cite{moxon_refit_1989}, based on a derivation by Case et al. \cite{case_1953}; an independent derivation was developed in preparation for implementation into the SAMMY code. The approximation assumes that after two scatterings, neutrons are uniformly distributed both in direction of motion and in position within the sample\footnote{This approximation has the effect of decoupling 2k of the embedded integrals, so that they can be performed separately from the others.}. To quantify this approximation, we assume that the escape probability for a neutron after $k$ scatterings (i.e., at energy $E (k)$ ) depends only on the energy; specifically, the escape probability is given by the formula
+
+% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
+\begin{equation} \label{eq_escape_probability}
+ p_{escape}\left(E^{(k)}\right) = \frac{1}{n\sigma_t^{(k)}}\left[\frac{1}{2}-\int_1^\infty\mu^{-3}e^{-n\sigma_t^{(k)}\mu}d\mu\right]\frac{1+2n\sigma_t^{(k)}}{1+\frac{2n\sigma_t^{(k)}}{1+Z/R}},
+\end{equation}
+
+\noindent
+where $R$ is the radius of the sample. With this approximation, one can recursively define a function
+$y$ via
+
+% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
+\begin{equation} \label{eq_yj_function}
+ y_{j-1} = \int d\Omega_j \frac{d\sigma_t^{(j-1)}}{d\Omega_j}\left(\sigma_c^{(j)}+y_j\right)\left(1-p_{escape}\left(E^{(j)}\right)\right) ,
+\end{equation}
+
+\noindent
+in which the superscript denotes the energy at which the cross section is to be calculated. The initial estimate for a neutron scattered k times is
+
+% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
+\begin{equation} \label{eq_yk_function}
+ y_{k-1} \approx 2\pi\int d\mu_k \frac{d\sigma_t^{(k-1)}}{d\Omega_k}\sigma_c^{(k)}\left(1-p_{escape}\left(E^{(k)}\right)\right) .
+\end{equation}
+
+\noindent
+This function y can then be used to estimate the capture yield for two or more scatterings:
+
+% !!!!!! Changing equation from Larson: I think she meant for these to be sig total, but she has no subscript !!!!!!!!
+\begin{equation} \label{eq_multiple_scatter_integration}
+ Y_2(E) = \frac{1}{S}\int dx\int dy\frac{n}{E}\int dz\;e^{-\frac{n}{D}\sigma_tz}\int d\Omega\frac{d\sigma_t}{d\Omega}y_l\frac{n}{D}\int dq\;e^{-\frac{n}{D}\sigma_t^{'}q} \;.
+\end{equation}
+
+\noindent
+In this form the multiple-scattering capture yield has the same mathematical properties as the single- scattering capture yield of Eq. \ref{eq_single_scatter_integration}. Similar computational techniques can therefore be used to evaluate both quantities.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Alternative for more than one scatter} \label{multiple_scattering_alternative}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+For very thick samples and/or very strong resonances, the crude approximation described above for double-plus scattering may be woefully inadequate. For those situations, tabulated values can be use for $Y_2$. The tabulated values are generated with a series of three runs, first SAMMY with the command
+
+\texttt{PREPARE INPUT FOR MOnte carlo simulation}, or simply
+
+\texttt{MONTE CARLO}
+
+\noindent
+Next, the SAMSMC code is run to perform the Monte Carlo calculation. Then SAMGY2 reads the output from SAMSMC, smooths the $Y_2$ curve, and creates a file named SAMY2.DAT that contains the tabulated $Y_2$ values for use in the next SAMMY run. For that run, the command
+
+\texttt{Y2 VALUES ARE TABULAted}
+
+\noindent
+is inserted into the INPut file, and the name of the file must be included in the input stream.
+
+Only the values of $Y_2$ are given in this manner; derivatives are still generated as though the original form were used. \textcolor{red}{Caution must be exercised when using this option}, especially when varying resonance parameters, since (1) the tabulated values of $Y_2$ do not change unless the entire process is repeated and (2) derivatives are inaccurate.
+
+Simulation sim009 makes use of this option.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Neutron sensitivity} \label{neutron_sensitivity}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+In capture experiments, not only gamma rays but also scattered neutrons reach the detector. The detector is not always able to distinguish between the two; hence, it may be necessary to make corrections for the neutron sensitivity of the detector. These corrections are temporarily unavailable in SAMMY, pending further study.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Normalization and input options} \label{norm_mult_scat_input_options}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Capture yield data may be normalized in a variety of ways; therefore, SAMMY allows the user to choose which normalization is to be taken. The normalization generally referred to as capture ``yield'' is the one shown in the equations in this section; this choice has the property that values are in the range from 0 to 1. Another commonly used normalization requires dividing by thickness $n$; in this case, the value approaches the capture cross section in the limit of zero thickness. Finally, the data may be normalized as $\left(1-e^{-n\sigma_t}\right)\sigma_t$, that is, by multiplying the yield by the total cross section. To use these options, the appropriate phrase must be included in the alphanumeric section of the INPut file:
+
+\texttt{NORMALIZE AS YIELD Rather than cross section}
+
+\texttt{NORMALIZE AS CROSS Section rather than yield}
+
+\texttt{NORMALIZE AS (1-E)SIgma}
+
+\noindent
+No default is assumed for normalization; instead, SAMMY requires that one of the above options be specified by the user.
+
+The default mode in SAMMY is to not include self-shielding and multiple-scattering corrections; therefore, to invoke these corrections, users will need to include one or more of the following phrases in their INPut file.
+
+\noindent
+For self-shielding but no multiple-scattering correction:
+
+\texttt{USE SELF SHIELDING Only, no scattering}, or
+
+\texttt{SELF SHIELD}
+
+\noindent
+For self-shielding, single-scattering (with edge-effects), and no double-scattering correction:
+
+\texttt{USE SINGLE SCATTERINg plus self shielding}, or
+\texttt{SINGLE}
+
+\noindent
+For self-shielding, single-scattering (infinite slab approximation), and no double-scattering corrections, two commands are required:
+
+\texttt{SINGLE} and
+\texttt{INFINITE SLAB}
+
+\noindent
+For self-shielding, single-scattering (with edge-effects correction), and multiple-scattering corrections:
+
+\texttt{INCLUDE DOUBLE SCATTering plus single scattering}, or
+\texttt{MULTIPLE SCATTERING} or
+\texttt{DOUBLE}
+
+\noindent
+For self-shielding, single-scattering (infinite-slab approximation), and multiple-scattering corrections, two commands are needed:
+
+\texttt{DOUBLE} and
+\texttt{INFINITE SLAB}
+
+When finite-size corrections (for single scattering) are wanted, additional input is needed to express the geometric properties of the beam and of the sample. These include the dimensions of the sample, the cross-sectional dimensions of the beam if smaller than the sample, and integers that determine the accuracy to which the functions $Q_{f,b}$ will be calculated. Details are given in Table VI A.1, card set 11.
+
+Examples using multiple-scattering corrections can be found in test cases tr039, tr052, tr064, tr099, and others.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Other Experimental Corrections} \label{sec:other-exp-corrections}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
diff --git a/docs/tex/fitting-procedure.tex b/docs/tex/fitting-procedure.tex
new file mode 100644
index 000000000..ad740ff08
--- /dev/null
+++ b/docs/tex/fitting-procedure.tex
@@ -0,0 +1,27 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Fitting Procedure %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Fitting Procedure}\label{ch:fitting-procedure}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Derivation Of Bayes' Equations} \label{sec:derivation-bayes-eqs}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Implementation Of Bayes' Equations} \label{sec:implementation-bayes-eqs}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Constructing The Parameter Set} \label{sec:construct-par-set}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Treatment Of Data Covariance Matrices} \label{sec:data-cov-matrices}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Miscellaneous Topics Related To Covariances} \label{sec:miscellaneous-cov}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/docs/tex/helpful-hints.tex b/docs/tex/helpful-hints.tex
new file mode 100644
index 000000000..dc6cf144f
--- /dev/null
+++ b/docs/tex/helpful-hints.tex
@@ -0,0 +1,20 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Helpful Hints %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Helpful Hints}\label{ch:helpful-hints}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Strategy For Data Evaluation With Sammy} \label{sec:eval-strategy}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Procedures To Follow When You Have Problems} \label{sec:problem-procedure}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Miscellaneous Comments And Suggestions} \label{sec:miscel-suggestions}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ No newline at end of file
diff --git a/docs/tex/input.tex b/docs/tex/input.tex
new file mode 100644
index 000000000..4b55ac6d6
--- /dev/null
+++ b/docs/tex/input.tex
@@ -0,0 +1,32 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Input %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Input}\label{ch:input}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{The INPut File} \label{sec:input-file}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{The PARameter File} \label{sec:par-file}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{The DATa and Data CoVariance Files} \label{sec:dat-dcv-files}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Integral Data File} \label{sec:int-data-file}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Interactive Input To Sammy} \label{sec:interactive-inp}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Other Input Files For Sammy} \label{sec:other-inp-files}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
diff --git a/docs/tex/introduction.tex b/docs/tex/introduction.tex
index f5d3f9115..6d760656d 100644
--- a/docs/tex/introduction.tex
+++ b/docs/tex/introduction.tex
@@ -8,31 +8,31 @@
This document serves as a users' guide to the multilevel multichannel R-matrix code SAMMY. Beginning with Revision 6, the organization of this manual has been redesigned in an effort to make it more legible, logical, and useful. A summary of the structure of this document is given here.
-Introductions for the original version of this manual through the previous revision are available in Appendix A. An introduction specifically for the current revision, describing recent modifications and additions to the code and the manual, is found immediately following this general introduction. All SAMMY users are encouraged to read Section I.A for an overview of recent developments.
+Introductions for the original version of this manual through the previous revision are available in Appendix A. An introduction specifically for the current revision, describing recent modifications and additions to the code and the manual, is found immediately following this general introduction. All SAMMY users are encouraged to read \S I.A for an overview of recent developments.
-Analysis of neutron cross-section data in the resolved resonance region (RRR) has three distinct aspects, each of which must be included in any analysis code: First, an appropriate formalism is needed for generating theoretical cross sections. Second, a plausible mathematical description must be provided for every experimental condition that affects the values of the quantities being measured. Third, a fitting procedure must be available to determine the parameter values which provide the ``best'' fit of theoretical to experimental numbers. These three aspects of the SAMMY code are described in Sections II\ref{ch:scattering_theory}, III\ref{}, and IV\ref{} of this manual, respectively.
+Analysis of neutron cross-section data in the resolved resonance region (RRR) has three distinct aspects, each of which must be included in any analysis code: First, an appropriate formalism is needed for generating theoretical cross sections. Second, a plausible mathematical description must be provided for every experimental condition that affects the values of the quantities being measured. Third, a fitting procedure must be available to determine the parameter values which provide the ``best'' fit of theoretical to experimental numbers. These three aspects of the SAMMY code are described in \S II (\ref{ch:scattering_theory}), III (\ref{ch:exp-conditions}), and IV (\ref{ch:fitting-procedure}) of this manual, respectively.
-Calculation of the cross sections in the RRR is described in Section II\ref{}, with emphasis on the Reich-Moore approximation to R-matrix theory. Explicit equations are given for the various types of energy-differential cross sections (total, elastic, capture, fission, other reaction) and for the angle and energy-differential cross sections (elastic, reaction). Both Coulomb and non-Coulomb (neutron) formulae are shown.
+Calculation of the cross sections in the RRR is described in \S II (\ref{ch:scattering_theory}), with emphasis on the Reich-Moore approximation to R-matrix theory. Explicit equations are given for the various types of energy-differential cross sections (total, elastic, capture, fission, other reaction) and for the angle and energy-differential cross sections (elastic, reaction). Both Coulomb and non-Coulomb (neutron) formulae are shown.
-Experimental modifications to the theoretical cross sections in the RRR are described in Section III\ref{}. Included here are such effects as Doppler and resolution broadening, normalization and backgrounds, finite-size corrections, and treatment of more than one nuclide in the target sample. SAMMY's fitting procedure is described in Section IV\ref{}. Bayes' equations are derived from Bayes' theorem plus assumptions about normality and linearity. The relationship between Bayes' equations and the more familiar least-squares equations is described. Emphasis is placed on methodologies for properly including all measurement uncertainty in the analysis process, including the many SAMMY options for inclusion of data covariance information.
+Experimental modifications to the theoretical cross sections in the RRR are described in \S III(\ref{ch:exp-conditions}). Included here are such effects as Doppler and resolution broadening, normalization and backgrounds, finite-size corrections, and treatment of more than one nuclide in the target sample. SAMMY's fitting procedure is described in \S IV(\ref{ch:fitting-procedure}). Bayes' equations are derived from Bayes' theorem plus assumptions about normality and linearity. The relationship between Bayes' equations and the more familiar least-squares equations is described. Emphasis is placed on methodologies for properly including all measurement uncertainty in the analysis process, including the many SAMMY options for inclusion of data covariance information.
-Section V\ref{} describes such topics as post-processor options (calculating multigroup cross sections or other averages) and other miscellaneous features.
+\S V(\ref{ch:miscellaneous}) describes such topics as post-processor options (calculating multigroup cross sections or other averages) and other miscellaneous features.
-The input to SAMMY is detailed in Section VI\ref{}. Output is described in Section VII\ref{}.
+The input to SAMMY is detailed in \S VI(\ref{ch:input}). Output is described in \S VII(\ref{ch:output}).
-SAMMY's treatment of the unresolved resonance region (URR) is discussed in Section VIII\ref{}.
+SAMMY's treatment of the unresolved resonance region (URR) is discussed in \S VIII(\ref{ch:urr}).
The theoretical treatment was borrowed directly from Fritz Fr\"{o}hner's FITACS program; subsequently, input/output and certain details of the calculation have been augmented to increase the functionality of this code.
-Section IX\ref{} describes the relationship of SAMMY to the Evaluated Nuclear Data Files (ENDF). Certain types of ENDF files can be used to provide resonance parameters, parameter covariance matrices, or experimental data as input to SAMMY. Likewise, SAMMY can produce ENDF files containing resonance parameters, point-wise cross sections, or uncertainty information.
+\S IX(\ref{ch:eval-connection}) describes the relationship of SAMMY to the Evaluated Nuclear Data Files (ENDF). Certain types of ENDF files can be used to provide resonance parameters, parameter covariance matrices, or experimental data as input to SAMMY. Likewise, SAMMY can produce ENDF files containing resonance parameters, point-wise cross sections, or uncertainty information.
-A number of auxiliary programs are available for use with SAMMY input or output. Section X\ref{} contains a brief description of those for which the SAMMY author has maintenance responsibility.
+A number of auxiliary programs are available for use with SAMMY input or output. \S X(\ref{ch:auxiliary-programs}) contains a brief description of those for which the SAMMY author has maintenance responsibility.
-Advice for running SAMMY is presented in Section XI\ref{}. Even experienced SAMMY users are encouraged to read this section, as it contains information about recent developments that may be unfamiliar (but potentially useful) to long-time users. Novices are likely to find valuable suggestions in this section. Anyone requesting the author's help is expected to have read and followed the procedures outlined in Section XI.B\ref{}.
+Advice for running SAMMY is presented in \S XI(\ref{ch:helpful-hints}). Even experienced SAMMY users are encouraged to read this section, as it contains information about recent developments that may be unfamiliar (but potentially useful) to long-time users. Novices are likely to find valuable suggestions in this section. Anyone requesting the author's help is expected to have read and followed the procedures outlined in \S XI.B(\ref{sec:problem-procedure}).
-Sample runs are described in Section XII\ref{}. These include (1) tutorial exercises (designed to familiarize a novice user with running the code), (2) test cases (designed for quality control, to ensure that the code gives consistent answers from one platform to another and from one version to another, but also useful as examples of input for specific features of the code), and (3) simulations (Monte Carlo simulations of multiple-scattering corrections, designed to test the accuracy of the SAMMY treatment for those corrections).
+Sample runs are described in \S XII(\ref{ch:examples}). These include (1) tutorial exercises (designed to familiarize a novice user with running the code), (2) test cases (designed for quality control, to ensure that the code gives consistent answers from one platform to another and from one version to another, but also useful as examples of input for specific features of the code), and (3) simulations (Monte Carlo simulations of multiple-scattering corrections, designed to test the accuracy of the SAMMY treatment for those corrections).
-Section XIII\ref{} provides an introduction to the computer code itself, for the benefit of the code managers at various sites. The casual user will probably not need the information from this section.
+\S XIII(\ref{ch:computer-code}) provides an introduction to the computer code itself, for the benefit of the code managers at various sites. The casual user will probably not need the information from this section.
diff --git a/docs/tex/miscellaneous.tex b/docs/tex/miscellaneous.tex
new file mode 100644
index 000000000..d93a5993f
--- /dev/null
+++ b/docs/tex/miscellaneous.tex
@@ -0,0 +1,32 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Miscellaneous %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Miscellaneous}\label{ch:miscellaneous}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Reconstructing Point-wise Cross Sections} \label{sec:pointwise-xs}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Integral Quantities} \label{sec:integral-quantities}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Averaging The Cross Sections} \label{sec:average-xs-out}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Stellar-averaged Capture Cross Sections} \label{sec:stellar-avg-xs}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Pseudo Cross Sections For Testing} \label{sec:pseudo-xs-for-tests}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Summed Strength Function} \label{sec:sum-strength-function}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
diff --git a/docs/tex/output.tex b/docs/tex/output.tex
new file mode 100644
index 000000000..ce47e05cf
--- /dev/null
+++ b/docs/tex/output.tex
@@ -0,0 +1,35 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% Output %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Output}\label{ch:output}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Line-printer Output} \label{sec:lpt-out}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Output To Be Used As Input} \label{sec:out-as-inp}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Plot Output} \label{sec:plot-out}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Complete Set Of Partial Derivatives For Resonance Parameters} \label{sec:derivs-out}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Compact Format For Parameter Covariance Information} \label{sec:compact-cov-out}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Publication Aids} \label{sec:pub-out}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Other Output Files} \label{sec:other-out}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ No newline at end of file
diff --git a/docs/tex/sammy_main.pdf b/docs/tex/sammy_main.pdf
index c5665c693..2cd063cd9 100644
--- a/docs/tex/sammy_main.pdf
+++ b/docs/tex/sammy_main.pdf
@@ -1,3 +1,3 @@
version https://git-lfs.github.com/spec/v1
-oid sha256:5c20e643d710f8b1e991b154513aca20d5a2b0760f3c85366a2dee1c3e1feb07
-size 474945
+oid sha256:b6ba33edffdd850a1dcc40d4e5b62dae7fc1fa144aa53ee0ea14b8dde21160f9
+size 491445
diff --git a/docs/tex/sammy_main.tex b/docs/tex/sammy_main.tex
index 93fa5efa7..349b936aa 100644
--- a/docs/tex/sammy_main.tex
+++ b/docs/tex/sammy_main.tex
@@ -87,10 +87,19 @@
\include{abstract} % abstract
\include{introduction}
\include{scattering-theory}
- \include{multScat} % Section
+ \include{exp-conditions}
+ \include{fitting-procedure}
+ \include{miscellaneous}
+ \include{input}
+ \include{output}
\include{urr}
+ \include{evaluation-connection}
+ \include{auxiliary-programs}
+ \include{helpful-hints}
+ \include{examples}
+ \include{computer-code}
\include{sammybib} % bibliography
% \bibliography{sammy_refs}
% \renewcommand*\thetable{\Alph{chapter}.\arabic{table}} % to get the tables to use chapter letters
- % \include{} % appendix
+ \include{appendices}
\end{document}
diff --git a/docs/tex/scattering-theory.tex b/docs/tex/scattering-theory.tex
index a38956587..4b775307e 100644
--- a/docs/tex/scattering-theory.tex
+++ b/docs/tex/scattering-theory.tex
@@ -33,27 +33,19 @@ R-matrix theory is expressed in terms of channels, where a channel is defined as
\label{scattering-theory_rmatrix_channel_diagram}
\end{figure}
-In Section \ref{sec:equations-for-scattering-theory}, general equations of scattering theory are presented and their derivations discussed. The fundamental R-matrix equations are presented. Section II.A.1\ref{} gives a detailed derivation of the equations for a simple case. Section II.A.2\ref{} shows the relationship between the R-matrix and the A-matrix, which is another common representation of scattering theory.
+In Section \ref{sec:equations-for-scattering-theory}, general equations of scattering theory are presented and their derivations discussed. The fundamental R-matrix equations are presented. Section II.A.1\ref{subsec:r-matrix-a-matrix} gives a detailed derivation of the equations for a simple case. Section II.A.2\ref{subsec:derivation-of-scat-theory} shows the relationship between the R-matrix and the A-matrix, which is another common representation of scattering theory.
-The approximations to R-matrix theory available in the SAMMY code are detailed in Section II.B\ref{}. The recommended choice for most applications is the Reich-Moore approximation, described in Section II.B.1\ref{}. For some applications, the Reich-Moore approximation is inadequate; for those cases, a method for using SAMMY's Reich-Moore approximation to mimic the full (exact) R-matrix is presented Section II.B.2\ref{}. Two historically useful but now obsolete approximations are single-level and multilevel Breit Wigner (SLBW and MLBW), discussed in Section II.B.3\ref{}. Provisions for including non-compound (direct) effects are discussed in Section II.B.4\ref{}.
+The approximations to R-matrix theory available in the SAMMY code are detailed in Section II.B\ref{sec:versions-of-r-matrix}. The recommended choice for most applications is the Reich-Moore approximation, described in Section II.B.1\ref{subsec:r-matrix-RM}. For some applications, the Reich-Moore approximation is inadequate; for those cases, a method for using SAMMY's Reich-Moore approximation to mimic the full (exact) R-matrix is presented Section II.B.2\ref{subsec:r-matrix-full}. Two historically useful but now obsolete approximations are single-level and multilevel Breit Wigner (SLBW and MLBW), discussed in Section II.B.3\ref{subsec:r-matrix-BW}. Provisions for including non-compound (direct) effects are discussed in Section II.B.4\ref{subsec:direct-capture}.
-In Section II.C\ref{}, details are given for the SAMMY nomenclature and other conventions,
-for transformations to the center-of-momentum system, and for the calculation of penetrability,
-shift factors, and hard-sphere phase shifts in both Coulomb and non-Coulomb cases.
+In Section II.C\ref{sec:details-and-conventions}, details are given for the SAMMY nomenclature and other conventions, for transformations to the center-of-momentum system, and for the calculation of penetrability, shift factors, and hard-sphere phase shifts in both Coulomb and non-Coulomb cases.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Equations For Scattering theory} \label{sec:equations-for-scattering-theory}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-In this section, equations for scattering theory are presented but not derived. Specifics for
-the R-matrix formulation of scattering theory are presented in Section II.A.1\ref{}, which provides a
-discussion of an alternative formulation (the A-matrix). Readers interested in the derivation of
-the equations for scattering theory are referred to the Lane and Thomas article \cite{lane_thomas_1958} for a
-detailed derivation in the general case, or to Section II.A.2\ref{} of this document for a simplified
-version.
+In this section, equations for scattering theory are presented but not derived. Specifics for the R-matrix formulation of scattering theory are presented in Section II.A.1\ref{subsec:r-matrix-a-matrix}, which provides a discussion of an alternative formulation (the A-matrix). Readers interested in the derivation of the equations for scattering theory are referred to the Lane and Thomas article \cite{lane_thomas_1958} for a detailed derivation in the general case, or to Section II.A.2\ref{subsec:derivation-of-scat-theory} of this document for a simplified version.
-In scattering theory, a channel may be defined by $c = (\alpha, l, s, J)$, where the following
-definitions apply:
+In scattering theory, a channel may be defined by $c = (\alpha, l, s, J)$, where the following definitions apply:
\begin{itemize}
\item $\alpha$ represents the two particles making up the channel; $\alpha$ includes mass ($m$ and $M$), charge ($z$ and $Z$), spin ($i$ and $I$ ) with associated parities, and all other quantum numbers for each of the two particles, plus the Q-value (equivalent to the negative of the threshold energy in the
@@ -77,7 +69,7 @@ Let the angle-integrated cross sections from entrance channel $c$ to exit channe
\end{equation}
\noindent
-where $k_\alpha$ is the wave number (and $K_\alpha = \hbar k_\alpha =$ center-of-mass momentum) associated with incident particle pair $\alpha$, $g_{J\alpha}$ is the spin statistical factor, and $w_c$ is the Coulomb phase-shift difference. Note that $w_c$ is zero for non-Coulomb channels. (Details for the charged-particle case are presented in Section II.C.4.\ref{}) The spin statistical factor $g_{J\alpha}$ is given by
+where $k_\alpha$ is the wave number (and $K_\alpha = \hbar k_\alpha =$ center-of-mass momentum) associated with incident particle pair $\alpha$, $g_{J\alpha}$ is the spin statistical factor, and $w_c$ is the Coulomb phase-shift difference. Note that $w_c$ is zero for non-Coulomb channels. (Details for the charged-particle case are presented in Section II.C.4.\ref{subsec:charged-particle-conventions}) The spin statistical factor $g_{J\alpha}$ is given by
\begin{equation}\label{eq:spin-stat-factor}
g_{J\alpha} = \frac{2J+1}{(2i+1)(2I+1)} \:,
@@ -91,7 +83,7 @@ and center-of-mass momentum $K_\alpha$ by
\end{equation}
\noindent
-Here $E$ is the \textbf{laboratory} kinetic energy of the incident (moving) particle. A derivation of this value for $K_\alpha$ is given in Section II.C.2\ref{}.
+Here $E$ is the \textbf{laboratory} kinetic energy of the incident (moving) particle. A derivation of this value for $K_\alpha$ is given in Section II.C.2\ref{subsec:kinematic-conventions}.
The scattering matrix $U$ can be written in terms of matrix $W$ as
@@ -107,14 +99,14 @@ where $\Omega$ is given by
\end{equation}
\noindent
-Here again, $w_c$ is zero for non-Coulomb channels, and the potential scattering phase shifts for non-Coulomb interactions $\phi_c$ are defined in many references (e.g., \cite{lane_thomas_1958}) and shown in Table \ref{}. The matrix $W$ in Eq. \ref{eq:scat-matrix} is related to the R-matrix (in matrix notation with indices suppressed) via
+Here again, $w_c$ is zero for non-Coulomb channels, and the potential scattering phase shifts for non-Coulomb interactions $\phi_c$ are defined in many references (e.g., \cite{lane_thomas_1958}) and shown in Table \ref{tab:penetrabilities}. The matrix $W$ in Eq. \ref{eq:scat-matrix} is related to the R-matrix (in matrix notation with indices suppressed) via
\begin{equation}\label{eq:W-matrix}
W = P^{1/2}\left(I-RL\right)^{-1}\left(I-RL^*\right)P^{-1/2} \:.
\end{equation}
\noindent
-The quantity $I$ in this equation represents the identity matrix, and superscript $*$ indicates a complex conjugate. The form of the R-matrix is given in Section IIA.1\ref{} in general Section II.B\ref{} for the versions used in SAMMY. The quantity $L$ in Eq. \ref{eq:W-matrix} is given by
+The quantity $I$ in this equation represents the identity matrix, and superscript $*$ indicates a complex conjugate. The form of the R-matrix is given in Section II.A.1\ref{subsec:r-matrix-a-matrix} in general Section II.B\ref{sec:versions-of-r-matrix} for the versions used in SAMMY. The quantity $L$ in Eq. \ref{eq:W-matrix} is given by
\begin{equation}\label{eq:L-matrix}
L = (S-B) + iP \:,
@@ -137,40 +129,40 @@ where $\rho$ is related to the center-of-mass momentum which in turn is related
\end{equation}
\noindent
-as shown in Section II.C.2\ref{}. Here $\Xi_\alpha$ is the energy threshold for the particle pair $\alpha$, $m_\alpha$ and $M_\alpha$ are the masses of the two particles of particle pair $\alpha$, and $m$ and $M$ are the masses of the incident particle and target nuclide, respectively.
+as shown in Section II.C.2 \ref{subsec:kinematic-conventions}. Here $\Xi_\alpha$ is the energy threshold for the particle pair $\alpha$, $m_\alpha$ and $M_\alpha$ are the masses of the two particles of particle pair $\alpha$, and $m$ and $M$ are the masses of the incident particle and target nuclide, respectively.
-Appropriate formulae for $P$, $S$, and $\phi$ in the non-Coulomb case are shown in Table IIA.1. For two charged particles, formulae for the penetrabilities are given in Section II.C.4\ref{tab:penetrabilities}. The energy dependence of fission and capture widths is negligible over the energy range of these calculations. Therefore, a penetrability of unity may be used.
+Appropriate formulae\footnote{To avoid ambiguity, it should be stated that below the channel threshold, that is, for $(E-\Xi_\alpha)<0$, SAMMY uses the convention of Lane-Thomas, namely setting $P_c=0$ and $S_c=\text{Re}(L_c)=L_c$, instead of using an analytical continuation of the shift and penetrability function in the complex plane by computing the expressions in Table \ref{tab:penetrabilities} as a function of an imaginary $\rho$ for which $iP_c(\rho)$ becomes real-valued, but separate from $S_c(\rho)$.} for $P$, $S$, and $\phi$ in the non-Coulomb case are shown in Table II.A.1 \ref{tab:penetrabilities}. For two charged particles, formulae for the penetrabilities are given in Section II.C.4 \ref{subsec:charged-particle-conventions}. The energy dependence of fission and capture widths is negligible over the energy range of these calculations. Therefore, a penetrability of unity may be used.
% multiline cell: \begin{tabular}{@{}c@{}} line1 \\ line2 \end{tabular}
\begin{threeparttable}
\centering
-\caption{Hard-sphere penetrability (penetration factor) $P$, level shift factor $S$, and potential-scattering phase shift $\phi$ for orbital angular momentum $l$, wave number $k$, and channel radius $a_c$, with $\rho=ka_c$} \label{tab:penetrabilities}
+\caption{Hard-sphere penetrability (penetration factor) $P$, level shift factor $S$, and potential-scattering phase shift $\phi$ for orbital angular momentum $l$, wave number $k$, and channel radius $a_c$, with $\rho=ka_c$.} \label{tab:penetrabilities}
\begin{tabular}{ l c c c }
\hline\hline
$\mathbf{l}$ & $\mathbf{P_l}$ & $\mathbf{S_l}$ & $\mathbf{\phi_l}$ \cr
\hline\hline
0 & $\rho$ & 0 & $\rho$ \cr
- 1 & $\rho^3/(1+\rho^2)$ & $-1/(1+\rho^2)$ & $\rho-tan^{-1}\rho$ \cr
- 2 & $\rho^5/(9+3\rho^2+\rho^4)$ & $-(18+3\rho^2)/(9+3\rho^2+\rho^4)$ & $\rho-tan^{-1}\left[3\rho/(3-\rho^2)\right]$ \cr
- 3 & \begin{tabular}{@{}c@{}}$\rho^7/$ \\ $(225+45\rho^2+6\rho^4+\rho^6)$\end{tabular} & \begin{tabular}{@{}c@{}} $-(675+90\rho^2+6\rho^4)/$ \\ $(225+45\rho^2+6\rho^4+\rho^6)$ \end{tabular} & $\rho-tan^{-1}\left[\rho(15-\rho^2)/(15-6\rho^2)\right]$ \cr
+ 1 & $\rho^3/(1+\rho^2)$ & $-1/(1+\rho^2)$ & $\rho-\tan^{-1}\rho$ \cr
+ 2 & $\rho^5/(9+3\rho^2+\rho^4)$ & $-(18+3\rho^2)/(9+3\rho^2+\rho^4)$ & $\rho-\tan^{-1}\left[3\rho/(3-\rho^2)\right]$ \cr
+ 3 & \begin{tabular}{@{}c@{}}$\rho^7/$ \\ $(225+45\rho^2+6\rho^4+\rho^6)$\end{tabular} & \begin{tabular}{@{}c@{}} $-(675+90\rho^2+6\rho^4)/$ \\ $(225+45\rho^2+6\rho^4+\rho^6)$ \end{tabular} & $\rho-\tan^{-1}\left[\rho(15-\rho^2)/(15-6\rho^2)\right]$ \cr
\hline
- $l$ & $\frac{\rho^2P_{l-1}}{(1-S_{l-1})^2+P_{l-1}^2}$ & $\frac{\rho^2(l-S_{l-1})}{(1-S_{l-1})^2+P_{l-1}^2}-l$ & $\phi_{l-1} - tan^{-1}\left(P_{l-1}/(l-S_{l-1})\right)$\tnote{\textdagger} \cr
+ $l$ & $\frac{\rho^2P_{l-1}}{(1-S_{l-1})^2+P_{l-1}^2}$ & $\frac{\rho^2(l-S_{l-1})}{(1-S_{l-1})^2+P_{l-1}^2}-l$ & $\phi_{l-1} - \tan^{-1}\left(P_{l-1}/(l-S_{l-1})\right)$\tnote{\textdagger} \cr
\hline\hline
\end{tabular}
\begin{tablenotes}
- \item[\textdagger] \footnotesize{The iterative formula for $\phi_l$ could also be defined by $B_l = (B_{l-1}+X_l)/(1-B_{l-1}X_l)$ where $B_l=tan(\rho-\phi_l)$ and $X_l=P_{l-1}/(l-S_{l-1})$}
+ \item[\textdagger] \footnotesize{The iterative formula for $\phi_l$ could also be defined by $B_l = (B_{l-1}+X_l)/(1-B_{l-1}X_l)$ where $B_l=\tan(\rho-\phi_l)$ and $X_l=P_{l-1}/(l-S_{l-1})$}
\end{tablenotes}
-\end{threeparttable}
+\end{threeparttable}\\
Formulae for a particular cross section type can be derived by summing over the terms in Eq. (II A.1)\ref{eq:sigma-ccprime}. For the total cross section, the sum over all possible exit channels and all spin groups gives
\begin{equation}\label{eq:sigma-tot}
\begin{aligned}
- \sigma^{total} & = \sum_{\substack{incident \\ channels \\ c }} \sum_{\substack{all \\ channels \\ c' }} \sum_J \frac{\pi}{k_\alpha^2}g_\alpha|\delta_{cc'}-U_{cc'}|^2 \\
- & = \frac{\pi}{k_\alpha^2} \sum_{J}g_J \sum_{\substack{incident \\ channels \\ c }} \sum_{\substack{all \\ channels \\ c' }} \left( \delta_{cc'}-U_{cc'}\delta_{cc'}-U^*_{cc'}\delta_{cc'}+\left|U_{cc'}\right|^2 \right) \\
- & = \frac{2\pi}{k_\alpha^2} \sum_J g_J \sum_{\substack{incident \\ channels \\ c }} \left( 1-\text{Re}\left(U_{cc}\right) \right).
+ \sigma^{total} & = \sum_{\substack{\text{incident} \\ \text{channels} \\ c }} \sum_{\substack{\text{all} \\ \text{channels} \\ c' }} \sum_J \frac{\pi}{k_\alpha^2}g_\alpha|\delta_{cc'}-U_{cc'}|^2 \\
+ & = \frac{\pi}{k_\alpha^2} \sum_{J}g_J \sum_{\substack{\text{incident} \\ \text{channels} \\ c }} \sum_{\substack{\text{all} \\ \text{channels} \\ c' }} \left( \delta_{cc'}-U_{cc'}\delta_{cc'}-U^*_{cc'}\delta_{cc'}+\left|U_{cc'}\right|^2 \right) \\
+ & = \frac{2\pi}{k_\alpha^2} \sum_J g_J \sum_{\substack{\text{incident} \\ \text{channels} \\ c }} \left( 1-\text{Re}\left(U_{cc}\right) \right).
\end{aligned}
\end{equation}
@@ -178,14 +170,14 @@ Formulae for a particular cross section type can be derived by summing over the
For non-charged incident particles, the elastic (or scattering) cross section is given by
\begin{equation}\label{eq:sigma-scat}
- \sigma_{\alpha\alpha} = \frac{\pi}{k_\alpha^2} \sum_J g_J \sum_{\substack{ c=incident \\ channel }} \left( 1-2\text{Re}\left(U_{cc}\right) + \sum_{\substack{c'=incident \\ channel }} \left|U_{cc'}\right|^2 \right).
+ \sigma_{\alpha\alpha} = \frac{\pi}{k_\alpha^2} \sum_J g_J \sum_{\substack{ c=\text{incident} \\ \text{channel} }} \left( 1-2\text{Re}\left(U_{cc}\right) + \sum_{\substack{c'=\text{incident} \\ \text{channel} }} \left|U_{cc'}\right|^2 \right).
\end{equation}
\noindent
Similarly, the cross section for any non-elastic reaction can be written
\begin{equation}\label{eq:sigma-reaction}
- \sigma_\alpha^{reaction} = \frac{\pi}{k_\alpha^2} \sum_J g_J \sum_{\substack{ c=incident \\ channel }} \sum_{\substack{ c'=reaction \\ channel }} \left| U_{cc'} \right|^2.
+ \sigma_\alpha^{reaction} = \frac{\pi}{k_\alpha^2} \sum_J g_J \sum_{\substack{ c=\text{incident} \\ \text{channel} }} \sum_{\substack{ c'=\text{reaction} \\ \text{channel} }} \left| U_{cc'} \right|^2.
\end{equation}
\noindent
@@ -193,7 +185,7 @@ In particular, the capture cross section could be written as the difference betw
other cross sections,
\begin{equation}\label{eq:sigma-capture}
- \sigma_\alpha^{reaction} = \frac{\pi}{k_\alpha^2} \sum_J g_J \sum_{\substack{ c=incident \\ channel }} \left( 1 - \sum_{\substack{ c'=all\: channels \\ except\: capture }} \left| U_{cc'} \right|^2 \right).
+ \sigma_\alpha^{reaction} = \frac{\pi}{k_\alpha^2} \sum_J g_J \sum_{\substack{ c=\text{incident} \\ \text{channel} }} \left( 1 - \sum_{\substack{ c'=\text{all channels} \\ \text{except capture} }} \left| U_{cc'} \right|^2 \right).
\end{equation}
\noindent
@@ -318,7 +310,7 @@ These equations are exact; no approximations have been made.
One common approximation should be discussed here: the ``eliminated channel'' approximation, for which one particular type of channel is treated in aggregate and assumed to not interfere from level to level. This is most easily understood in the A-matrix definition, Eq. (II A1.4)\ref{eq:a-matrix}; assuming no level-level interference for the gamma channels (for example), this equation can be approximated as
\begin{equation}\label{eq:a-matrix-rm-approx}
- A_{\mu\lambda}^{-1} \approx (E_\lambda-E)\delta_{\mu\lambda} - \left[\sum_{\substack{\gamma=gamma \\ channels}} \gamma_{\mu\gamma}L_{\gamma}\gamma_{\lambda\gamma}\right]\delta_{\mu\lambda} - \sum_{\substack{c=particle \\channels}} \gamma_{\mu c}L_c\gamma_{\lambda c} .
+ A_{\mu\lambda}^{-1} \approx (E_\lambda-E)\delta_{\mu\lambda} - \left[\sum_{\substack{\gamma=\text{gamma} \\ \text{channels}}} \gamma_{\mu\gamma}L_{\gamma}\gamma_{\lambda\gamma}\right]\delta_{\mu\lambda} - \sum_{\substack{c=\text{particle} \\\text{channels}}} \gamma_{\mu c}L_c\gamma_{\lambda c} .
\end{equation}
\noindent
@@ -327,7 +319,7 @@ interference is to be neglected; that is, only the interactions within one level
gamma channels, $L=S+iP$ reduces to $L=i$, so Eq. (II A1.13)\ref{eq:a-matrix-rm-approx} becomes
\begin{equation}\label{eq:a-matrix-rm-reduced}
- A_{\mu\lambda}^{-1} \approx \left(E_\lambda-E-i\overline{\Gamma}_{\lambda\gamma}/2\right)\delta_{\mu\lambda} - \sum_{\substack{c=particle \\ channels}} \gamma_{\mu c}L_c\gamma_{\lambda c} .
+ A_{\mu\lambda}^{-1} \approx \left(E_\lambda-E-i\overline{\Gamma}_{\lambda\gamma}/2\right)\delta_{\mu\lambda} - \sum_{\substack{c=\text{particle} \\ \text{channels}}} \gamma_{\mu c}L_c\gamma_{\lambda c} .
\end{equation}
\noindent
@@ -757,14 +749,51 @@ Finally, it should be noted that SAMMY's implementation of MLBW does not corresp
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Details and Conventions Used In Sammy} \label{sec:details-and-conventions}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\textbf{Note: Subject to change with inclusion of AMPX R-matrix engine!!!}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Spin and Angular Momentum Conventions} \label{subsec:spin-conventions}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Kinematics} \label{subsec:kinematic-conventions}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Evaluation of Hard-Sphere Phase Shift} \label{subsec:phase-shift-conventions}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Modifications for Charged Particles} \label{subsec:charged-particle-conventions}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Inverse Reactions (Reciprocity)} \label{subsec:inverse-reactions-conventions}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Derivatives} \label{sec:derivatives}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+In order to make use of sophisticated fitting procedures such as Bayes' equations (Section IV \ref{} of this manual), it is necessary to know the partial derivatives of the theory with respect to the parameters to be fitted (the ``varied parameters''). The easiest method for calculating derivatives of cross sections with respect to resonance parameters is to use a numerical difference approximation, of the form
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Derivatives for Reich-Moore Approximation} \label{subsec:derivs-RM}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Derivatives for MLBW and SLBW Approximations} \label{subsec:derivs-BW}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Details Involving Derivatives} \label{subsec:derivs-details}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
diff --git a/docs/tex/urr.tex b/docs/tex/urr.tex
index 093cedef2..8cbe6c546 100644
--- a/docs/tex/urr.tex
+++ b/docs/tex/urr.tex
@@ -4,7 +4,7 @@
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\chapter{Unresolved Resonance Region}\label{ch:unresolved-res-region}
+\chapter{Unresolved Resonance Region}\label{ch:urr}
As a first step towards expansion into the unresolved resonance region, Fritz Fr\"{o}hner's code
FITACS \cite{frohner1989evaluation} has been obtained and inserted into SAMMY. FITACS uses Hauser-Feshbach
@@ -682,7 +682,7 @@ As with the resolved resonance region, each SAMMY/URR run may produce several ou
\begin{enumerate}
\item The SAMMY.LPT file contains details of the calculations.
- \item For runs which involve the solution of Bayes' equations and hence the generation of updated parameter values (a ``Bayes run'' as opposed to a ``no-Bayes run'' which simply calculates cross sections), an output file SAMMY.PAR is provided in the annotated form described in Table \ref{annotated-urr-par-input}. (This file, of course, is quite different from the file by the same name produced in a resolved resonance region run.)
+ \item For runs which involve the solution of Bayes' equations and hence the generation of updated parameter values (a ``Bayes run'' as opposed to a ``no-Bayes run'' which simply calculates cross sections), an output file SAMMY.PAR is provided in the annotated form described in Table \ref{table:annotated-urr-par-input}. (This file, of course, is quite different from the file by the same name produced in a resolved resonance region run.)
\item For Bayes runs, a COVariance file SAMMY.COV is produced, which contains (among other things) the final parameter covariance matrix; see below for more detail.
\item Files SAMMY.NDF and SAMMY.N32 contain the URR portion of ENDF File 2 and 32, respectively; these files are produced when the appropriate command is in the INPut file.
\item Files SAMMY.NDX and SAMMY.N3X contain the same information as in SAMMY.NDF and SAMMY.N32 respectively, but also include comment lines defining the parameters whose values are given. Only the uncertainty values are given in SAMMY.N3X; correlations are printed only in SAMMY.N32.
@@ -695,7 +695,7 @@ similar fashion to sequential runs in the RRR. There are slight differences, how
this COVariance file; no auxiliary program comparable to SAMAMR is required here, as there is
only one type of data-reduction parameter (the normalizations). The user must simply rename and
modify the SAMMY.PAR file to contain the appropriate normalization parameters for the data sets
-about to be analyzed. The output PARameter file will contain card set 10a of Table \ref{annotated-urr-par-input};
+about to be analyzed. The output PARameter file will contain card set 10a of Table \ref{table:annotated-urr-par-input};
PARameter files to be used as input will use either card set 10 (for new data sets for which the
normalizations have not yet been defined) or card set 10a (to re-use normalizations already defined
for the current data sets). See test case tr145 for examples.
--
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