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Fix URR bug

If fitting > 15 datasets, a hard-coded set of
odf file names got overwritten causing an issue

change LST to lst
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......@@ -85,6 +85,7 @@
\include{introduction}
\include{scattering-theory}
\include{multScat} % Section
\include{urr}
\include{sammybib} % bibliography
% \bibliography{sammy_refs}
% \renewcommand*\thetable{\Alph{chapter}.\arabic{table}} % to get the tables to use chapter letters
......
......@@ -1198,4 +1198,37 @@ abstract = "The response of the RPI 16-segment NaI(Tl) multiplicity detector sys
publisher={Clarendon Press, Oxford}
}
@article{frohner1989evaluation,
title={{Evaluation of the unresolved resonance range of $^{238}$U}},
author={Fr{\"o}hner, Friedrich H},
journal={Nuclear Science and Engineering},
volume={103},
number={2},
pages={119--128},
year={1989},
publisher={Taylor \& Francis}
}
@techreport{derrien2000neutron,
title={{Neutron Total Cross Sections of $^{235}$U From Transmission Measurements in the Energy Range 2 keV to 300 keV and Statistical Model Analysis of the Data}},
author={Derrien, Herve and Harvey, John A and Larson, NM and Leal, Luiz C and Wright, Richard Q},
year={2000},
month={August},
institution={Oak Ridge National Laboratory},
number={ORNL/TM-2000/129},
}
@article{hill1953nuclear,
title={Nuclear constitution and the interpretation of fission phenomena},
author={Hill, David Lawrence and Wheeler, John Archibald},
journal={Physical Review},
volume={89},
number={5},
pages={1102},
year={1953},
publisher={APS}
}
@Comment{jabref-meta: databaseType:bibtex;}
......@@ -113,7 +113,7 @@ 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 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 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
\begin{equation}\label{eq:L-matrix}
L = (S-B) + iP \:,
......
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% Unresolved Resonance Region %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Unresolved Resonance Region}\label{ch:unresolved-res-region}
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
theory with width fluctuations. The adjustable parameters are neutron strength functions,
distant-level parameters, average radiation widths (at $E = 0$), and average fission widths (at $E = 0$).
The energy dependence of the radiation widths is specified via the giant dipole model, of the fission
widths via Hill-Wheeler fission barrier transmission coefficients, and of the mean level spacing for
s-waves via the Gilbert-Cameron composite formula. Mean spacings for $l > 0$ are given via the
Bethe formula. Moldauer's prescription is used for partial cross sections. Details of the theory are
presented in Section \ref{sec:equations-for-urr}.
Initially (for release M2 of the code), FITACS was incorporated into SAMMY (as segments
SAMFFF and SAMACS) in a limited fashion only. Internal changes were made, to be consistent
with SAMMY notation and to use dynamic dimensioning of arrays. The M + W version of Bayes'
method has replaced the fitting procedure used in FITACS. Calculation of penetrabilities was
extended to all $l$ values (FITACS had used only s, p, d, and f-waves). The output included files from
which plots can be made. Results were reported in SAMMY.PAR in the same format as is used in
the input file (as well as in more human-legible fashion in SAMMY.LPT).
Subsequently, additional modifications, improvements, and new features have been made in
the SAMMY URR treatment:
\begin{itemize}
\item Partial derivatives with respect to varied parameters are calculated exactly rather than approximately.
\item A more efficient integration routine has been written for the Dresner integral, Eq. (VIII A.5) \ref{}.
\item It is possible to include (and vary, if desired) a normalization for each data set.
\item Elastic cross section data may be fitted.
\item There is no limit on the number or type of experimental data sets. Data may be kept in separate files rather than appended to the parameter file.
\item The output has been modified to conform more closely to SAMMY conventions.
\item An ``annotated'' PARameter file, including key-word-based input, is the default input option, and the only option available for output. (Files in the original format can still be used for input, but options are limited with that format.)
\item Different sets of average resonance parameters can be used in different energy ranges.
\item Output can be produced in ENDF/B format, for both File 2 (resonance parameters) and File 32 (covariance matrices). ENDF files cannot be used for input, because the ENDF format requires a more limited theoretical description than does FITACS/SAMMY.
\item The fitting procedure can be performed sequentially, in similar fashion as in the resolved resonance region. That is, output PARameter and COVariance files from the fit to one data set may be used as input to another run which fits another data set. [Initially, only simultaneous fitting of all data sets was permitted.]
\item ``No-Bayes'' runs can be made: cross sections will be calculated from the resonance parameters, but no fitting will be done.
\end{itemize}
\noindent
Additions being considered for future revisions of the code include the following:
\begin{itemize}
\item Multiple nuclides in the sample
\item An option to calculate multigroup cross sections and covariances
\item An option to include integral quantities in the fit
\item Extensions to the theory
\item Additional ENDF capability (requiring ENDF format changes)
\item A link between the resolved resonance parameters and those for the unresolved region, in order to provide more consistent evaluated cross sections
\item Methodologies for retroactive generation of covariance matrices, similar to that used in the resolved resonance region
\end{itemize}
Input for analysis of data in the unresolved resonance region is described in Section VIII.B\ref{}.
Output is described in Section VIII.C\ref{}. The relationship between ENDF parameters and
SAMMY/URR parameters is discussed in Section VIII.D\ref{}. For an example of the use of SAMMY/URR, see \cite{derrien2000neutron} and test cases 73, 88, 127, 133, 134, 142, and 145.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Equations For Unresolved Resonance Region} \label{sec:equations-for-urr}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The formulae for cross sections in the unresolved resonance region, as implemented in
SAMMY, are presented in this section. The implementation is a modified form of that provided by
Fritz Fr\"{o}hner in his FITACS code \cite{frohner1989evaluation}. (Please note that any mistakes in these formulae are
attributable only to the author of this manual, not to Fr\"{o}hner. The author is indebted to Herve
Derrien for significant contributions both to the development of the code and to the composition of
this section of the manual.)
\vspace{0.5cm}
\noindent
\textbf{Elastic cross section}
The elastic cross section is given as the difference between the total cross section and the
sum of all the non-elastic partial cross sections. The total cross section is given by Eqs. (VIII A.1)
through (VIII A.4), and the non-elastic partial cross sections by Eqs. (VIII A.5) through (VIII A.20).
\vspace{0.5cm}
\noindent
\textbf{Total cross section}
The average total cross section, for a given spin and parity and incident channel $c$, may be
written in the form
\begin{equation} \label{eq:urr-tot-xs}
\langle \sigma_c \rangle = \frac{2\pi g_c}{k_c^2}\left(1-\text{Re}\left\langle S_{cc} \right\rangle\right) \:,
\end{equation}
\noindent
where, as usual, $g_c$ is the spin factor and $k_c$ is the center-of-mass momentum. The average scattering matrix $\left\langle S_{cc}\right\rangle$ is given by
\begin{equation} \label{eq:avg-scattering-matrix}
\left\langle S_{cc} \right\rangle = e^{-2i\phi_c}\frac{1-\langle R_{cc}\rangle L_{c}^{0*}}{1-\langle R_{cc}\rangle L_{c}^{0}} \:,
\end{equation}
\noindent
and the average R-matrix can be written in the form
\begin{equation} \label{eq:avg-r-matrix}
\left\langle R_{cc} \right\rangle = R_c^\infty + i\pi s_c \:,
\end{equation}
\noindent
with parameters defined as follows:
\vspace{0.5cm}
\noindent
$R_c^\infty = $ distant-level parameter (in input quantity);
\vspace{0.2cm}
\noindent
$\phi_c = $ hard-sphere phase shift, generated using matching radius $a$ (an input quantity);
\vspace{0.2cm}
\noindent
$L_c^0 = (S_c-B_c)+iP_c$ (see Section \ref{sec:equations-for-scattering-theory}) with boundary condition $B_c$ chosen such that $S_c - B_c = 0$;
\vspace{0.2cm}
\noindent
$s_c = $ pole strength.
\vspace{0.5cm}
\noindent
The pole strength is defined in terms of input quantities $\tilde{S}_c$ (the strength function, for which we have introduced the tilde to avoid confusion with the shift factor used in the definition of $L_c^0$) and $a_c$ (the R-matrix matching radius) as
\begin{equation} \label{eq:pole-strength-definition}
s_c = \tilde{S}_c\sqrt{E}/2\rho
\end{equation}
\noindent
where $\rho$ is the center-of-mass momentum $k_c$ multiplied by the channel radius $a_c$.
\vspace{0.5cm}
\noindent
\textbf{Non-elastic partial cross sections}
The non-elastic partial cross sections may be written in terms of transmission coefficients $T_x$ as
\begin{equation} \label{eq:urr-partial-xs}
\langle \sigma_{ab} \rangle = \frac{\pi g_a}{k_a^2}\frac{T_aT_b}{T} \int_0^\infty dt\; e^{-T_\gamma/T}\; \Pi\left(1+\frac{2}{\nu_c}\frac{T_c}{T}t\right)^{-\nu_c/2-\delta_{ac}-\delta_{bc}} \;,
\end{equation}
\noindent
where the quantities to the left of the integral sign are the Hauser-Feshbach expression, and the integrand is the Moldauer prescription \cite{moldauer_1980} for the width fluctuation correction factor. (A derivation of this expression, including the assumptions under which it is derived, is provided in Section \ref{}.) Here $a$ represents the incident channel and $b$ the exit channel; $\nu_c$ and $T_c$ represent the number of degrees of freedom (multiplicity) and transmission coefficient, respectively, for channel $c$. Subscript $\gamma$ refers to photon channels. $T$ is defined as the sum over all channels:
\begin{equation} \label{eq:urr-tot-trans-coeff}
T = \sum_c T_c \;.
\end{equation}
The transmission coefficient for neutron channels is given by
\begin{equation} \label{eq:urr-chan-trans-coeff}
T_c = 1-|\langle S_{cc}\rangle|^2 = \frac{4\pi P_cs_c}{\left|1-\langle R_{cc}\rangle L_c\right|^2} \;,
\end{equation}
\noindent
where $c$ is an incident channel, $P$ and $L$ are as defined in Section \ref{sec:equations-for-scattering-theory}, and the other quantities are given above. For photon and fission channels, the transmission coefficients for spin $J$ are
\begin{equation} \label{eq:urr-gam-fiss-trans-coeff}
T_\gamma = 2\pi \langle \Gamma_\gamma\rangle/D_J \qquad \text{and} \qquad T_f = 2\pi \langle \Gamma_f\rangle/D_J \;,
\end{equation}
\noindent
in which $D_J$ is the mean level spacing for levels with this spin.
The $J$-dependence of the mean level spacing is set in SAMMY/FITACS via the Bethe formula (e.g., \cite{frohner_1978}):
\begin{equation} \label{eq:urr-J-dep-level-spacing}
(D_J(E))^{-1} = (d(E))^{-1}\left\{e^{\frac{-J^2}{2(\sigma(E))^2}}-e^{\frac{-(J+1)^2}{2(\sigma(E))^2}}\right\} \;,
\end{equation}
\noindent
where $d(E)$ is independent of $J$, and $\sigma$ is the spin cutoff parameter. The spin cutoff parameter is related to the level density parameter $a$ and the energy $E$ by the formula
\begin{equation} \label{eq:urr-spin-cutoff-parameter}
\sigma^2 = (0.14592)(A+1)^{2/3}\sqrt{a(E+BE-PE)} \;,
\end{equation}
\noindent
in which $BE$ represents the neutron binding energy (an input parameter) and $PE$ the pairing energy (also an input parameter). The value for $a$ is determined from the input quantity $D$, which is the mean level spacing of the $l=0$ resonances at $E=0$; note that $D$ includes both $J=I-i$ and $J=I+i$, where $I$ is the spin of the target nucleus and $i=1/2$ is the spin of the neutron. An expression for the inverse of $D$ can be found from Eq. \ref{eq:urr-J-dep-level-spacing} to be
\begin{equation} \label{eq:urr-level-spacing-at-zero}
\begin{split}
D^{-1} &= \sum_J(D_J(E=0))^{-1} \\
&= (d(0))^{-1}\left\{e^{\frac{-(I-\frac{1}{2})^2}{2\sigma^2}}-e^{\frac{-(I+\frac{3}{2})^2}{2\sigma^2}}\right\} \;;
\end{split}
\end{equation}
\noindent
this expression is used to determine the value of $\sigma^2$ and hence the value of the level density parameter $a$.
The energy dependence of the mean level spacing is calculated with the Gilbert-Cameron
composite formula \cite{gilbert_cameron}. Let $E_x$ represent the excitation energy of the compound nucleus; this
energy is equal to the sum of the incident neutron kinetic energy $E$ and the neutron binding energy
$BE$ (which is an input quantity). That is to say,
\begin{equation} \label{eq:urr-excitation-energy}
E_x = E+BE \;.
\end{equation}
The energy dependence for low excitation energies $E_x < E_0$ , where $E_0$ is a matching
energy, is given by the constant-temperature formula
\begin{equation} \label{eq:urr-constant-temperature-formula}
D^{-1} \sim C_3\frac{\text{exp}\left[{C_2\sqrt{E_0-PE}}\right]}{(E_0-PE)^{3/2}} \; \text{exp}\left[\frac{E_x-E_0}{2}\left(\frac{C_2}{\sqrt{E_0-PE}}-\frac{3}{E_0-PE}\right)\right] \;.
\end{equation}
\noindent
In the code, the matching energy $E_0$ is set at
\begin{equation} \label{eq:urr-matching-energy}
E_0 = \left[\frac{5}{2}+\frac{150}{(N+Z+1)}\right]
\end{equation}
\noindent
in unit of MeV, with $N+Z$ being the mass number for the target nucleus. Values of the constants $C_2$ and $C_3$ are given by
\begin{equation} \label{eq:urr-constant-temperature-formula}
C_2 = \sqrt{4a} \qquad \text{and} \qquad C_3 = \frac{1}{12\sqrt{2aq}} \;,
\end{equation}
\noindent
with $q$ defined as
\begin{equation} \label{eq:urr-constant-temperature-formula}
q = 0.14592(N+Z+1)^{2/3} \;,
\end{equation}
\noindent
where $N+Z$ is again the mass number for the target nucleus and $a$ is the level density parameter.
At higher energies $E_x>E_0$, the energy dependence of the mean level spacing is calculated
via the Fermi-Gas formula
\begin{equation} \label{eq:urr-constant-temperature-formula}
D^{-1} \propto C_3\frac{\text{exp}\left[C_2\sqrt{E_x-PE}\right]}{(E_x-PE)^{3/2}} \;.
\end{equation}
Note that the two formulae agree at the matching energy (i.e., at $E_x=E_0$).
Radiation widths $\langle\Gamma_\gamma\rangle$ are assumed to depend only on parity $\pi$ and on $E$. The energy
dependence is calculated with the giant dipole resonance model. Fission widths $\langle\Gamma_f\rangle$ may vary with spin as well as parity and incident neutron energy $E$. Energy dependence is calculated with the Hill-Wheeler fission barrier transmission coefficients \cite{hill1953nuclear}. For a given $J^\pi$, the energy dependence of the fission widths is taken to be
\begin{equation} \label{eq:urr-condensed-hill-wheeler-fission}
\langle\Gamma_f(E)\rangle = \langle\Gamma_f(0)\rangle \frac{1+\text{exp}\left[E_{HW}/W_{HW}\right]}{1+\text{exp}\left[-(E-E_{HW})/W_{HW}\right]} \;,
\end{equation}
\noindent
where the Hill-Wheeler threshold energy $E_{HW}$ and the Hill-Wheeler threshold width $W_{HW}$ are input quantities. This equation may be written in more ``standard'' notation as
\begin{equation} \label{eq:urr-standard-hill-wheeler-fission}
\langle\Gamma_f(E)\rangle = \langle\Gamma_f(0)\rangle \frac{1+\text{exp}\left[2\pi(E_f-BE)/\hbar\omega\right]}{1+\text{exp}\left[-2\pi(E_x-(E_{f}-BE))/\hbar\omega\right]} \;,
\end{equation}
\noindent
where, as above, $E_x$ is the excitation energy of the neutron and $BE$ is the binding energy. Also,
$E_f$ is the fission barrier height, and $\hbar\omega$ the width of the fission barrier.
Finally, a few words regarding the derivation of Eq. \ref{eq:urr-partial-xs} are warranted. That
derivation is based on several assumptions:
\begin{enumerate}
\item The Moldauer prescription \cite{moldauer_1980} for width fluctuations is used. That is, the width fluctuation
correction factor is introduced to compensate for the non-unity of the ratio
\begin{equation} \label{eq:urr-trans-coeff-ratio}
\left\langle\frac{T_aT_b}{T}\right\rangle / \frac{\langle T\rangle}{\langle T_a\rangle\langle T_b\rangle} \;.
\end{equation}
\item Partial widths obey a chi-squared distribution with $\nu_c$ degrees of freedom (where the value of $\nu_c$ depends on the number of channels of this de-excitation); averages are therefore weighted
with this distribution. In the Moldauer prescription for width fluctuations, simple channels
have 1 $< \nu_c <$ 1.78; for lumped channels, $\nu_c$ is a function of $T_c$.
\item Channels with the same transmission coefficients may be combined by introducing multiplicities.
\end{enumerate}
The integral of Eq. \ref{eq:urr-partial-xs} is described by Fr\"{o}hner as the ``width fluctuation correction or
Dresner factor.'' One (relatively modest) difference between SAMMY and the original FITACS
coding is the algorithm for calculating the Dresner integral; in SAMMY, the coding has been refined
to increase both speed and accuracy of calculation by using a non-uniform grid designed specifically
for this task. (Note: Prior to release 7 of the code, the Moldauer correction was inadvertently disabled in
code. This has now been fixed.)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Derivation of Non-Elastic Average Cross Section} \label{sec:derivation-urr-non-elastic-xs}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
......@@ -191,6 +191,7 @@ SET(SAMTRY
tr158
tr187
tr072
tr190
)
foreach(INPUT ${SAMTRY})
......
7000.0000000000 0.0000024000 0.0000004800 0.0211033233 0.0077404310
7250.0000000000 0.0000028000 0.0000005600 0.0237595870 0.0087332739
7350.0000000000 0.0000030000 0.0000006000 0.0247388917 0.0090999932
7700.0000000000 0.0000035000 0.0000007000 0.0279215394 0.0102960794
8000.0000000000 0.0000040000 0.0000008000 0.0304395549 0.0112490855
8200.0000000000 0.0000043000 0.0000008600 0.0320421142 0.0118599422
8400.0000000000 0.0000046000 0.0000009200 0.0335966225 0.0124562847
8700.0000000000 0.0000051000 0.0000010200 0.0358531158 0.0133300309
9000.0000000000 0.0000056000 0.0000011200 0.0380349472 0.0141851962
9150.0000000000 0.0000058000 0.0000011600 0.0391015749 0.0146073822
9600.0000000000 0.0000065000 0.0000013000 0.0422163954 0.0158584260
10000.0000000000 0.0000072000 0.0000014400 0.0448925312 0.0169571997
10400.0000000000 0.0000083000 0.0000016600 0.0474918526 0.0180485127
10650.0000000000 0.0000090000 0.0000018000 0.0490813530 0.0187287424
10850.0000000000 0.0000096000 0.0000019200 0.0503344094 0.0192723918
11200.0000000000 0.0000106000 0.0000021200 0.0524906844 0.0202240053
11650.0000000000 0.0000119000 0.0000023800 0.0551981205 0.0214499624
12000.0000000000 0.0000129000 0.0000025800 0.0572568223 0.0224069910
12400.0000000000 0.0000140000 0.0000028000 0.0595618654 0.0235061170
12800.0000000000 0.0000152000 0.0000030400 0.0618189123 0.0246121151
13096.0000000000 0.0000161000 0.0000032200 0.0634596727 0.0254355972
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23200.0000000000 0.0084151000 0.0016830200 0.1087444608 0.0569523887
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27500.0000000000 0.0111997000 0.0022399400 0.1237309167 0.0717801838
28300.0000000000 0.0117177000 0.0023435400 0.1263247853 0.0745634595
28800.0000000000 0.0120416000 0.0024083200 0.1279186650 0.0763032872
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30000.0000000000 0.0128186000 0.0025637200 0.1316613029 0.0804738055
31100.0000000000 0.0134665000 0.0026933000 0.1349954734 0.0842853865
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35000.0000000000 0.0157637000 0.0031527400 0.1461577971 0.0976202945
36200.0000000000 0.0164705000 0.0032941000 0.1494056098 0.1016442241
37000.0000000000 0.0169417000 0.0033883400 0.1515270934 0.1043017808
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43800.0000000000 0.0207403000 0.0041480600 0.1683278087 0.1259248360
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46000.0000000000 0.0219164000 0.0043832800 0.1733744613 0.1325094959
46398.0000000000 0.0221118000 0.0044223600 0.1742675727 0.1336781736
46800.0000000000 0.0264436000 0.0052887200 0.1751643779 0.1348511887
47300.0000000000 0.0318099000 0.0063619800 0.1762723568 0.1363003953
47600.0000000000 0.0350296000 0.0070059200 0.1769333206 0.1371644010
48200.0000000000 0.0414691000 0.0082938200 0.1782466106 0.1388807317
49000.0000000000 0.0500551000 0.0100110200 0.1799802813 0.1411440198
50000.0000000000 0.0607877000 0.0121575400 0.1821207635 0.1439327652
50900.0000000000 0.0644711000 0.0128942200 0.1840224947 0.1464042463
51200.0000000000 0.0656990000 0.0131398000 0.1846513797 0.1472203088
51500.0000000000 0.0669268000 0.0133853600 0.1852777682 0.1480320656
51922.0000000000 0.0691088000 0.0138217600 0.1861548618 0.1491671010
52200.0000000000 0.0705462000 0.0141092400 0.1867300418 0.1499107880
52500.0000000000 0.0725882000 0.0145176400 0.1873484395 0.1507091986
53500.0000000000 0.0793949000 0.0158789800 0.1893931772 0.1533419532
54200.0000000000 0.0841596000 0.0168319200 0.1907938872 0.1551585828
55000.0000000000 0.0896049000 0.0179209800 0.1924030256 0.1572083541
55700.0000000000 0.0943695000 0.0188739000 0.1937940092 0.1589789961
56100.0000000000 0.0970922000 0.0194184400 0.1945839120 0.1599812974
56700.0000000000 0.1011800000 0.0202360000 0.1957618806 0.1614716835
57100.0000000000 0.1039000000 0.0207800000 0.1965427829 0.1624566144
57900.0000000000 0.1093400000 0.0218680000 0.1980942163 0.1644061594
58300.0000000000 0.1120700000 0.0224140000 0.1988646945 0.1653705972
59100.0000000000 0.1175100000 0.0235020000 0.2003959818 0.1672794543
60000.0000000000 0.1236400000 0.0247280000 0.2021031656 0.1693945705
60300.0000000000 0.1248800000 0.0249760000 0.2026685707 0.1700923331
61200.0000000000 0.1286200000 0.0257240000 0.2043545572 0.1721627564
62000.0000000000 0.1319500000 0.0263900000 0.2058403317 0.1739755069
63200.0000000000 0.1369300000 0.0273860000 0.2080470113 0.1766459856
64199.9960000000 0.1410900000 0.0282180000 0.2098665196 0.1788275576
65000.0000000000 0.1444100000 0.0288820000 0.2113098938 0.1805445803
66100.0000000000 0.1489800000 0.0297960000 0.2132769640 0.1828650133
67000.0000000000 0.1527200000 0.0305440000 0.2148718386 0.1847290168
68000.0000000000 0.1568700000 0.0313740000 0.2166206546 0.1867645201
68900.0000000000 0.1606100000 0.0321220000 0.2181886736 0.1885646334
69400.0000000000 0.1626900000 0.0325380000 0.2190547826 0.1895518577
70000.0000000000 0.1651800000 0.0330360000 0.2200891232 0.1907246419
72000.0000000000 0.1734900000 0.0346980000 0.2235002303 0.1945410914
72500.0000000000 0.1755700000 0.0351140000 0.2243440996 0.1954732612
73100.0000000000 0.1780600000 0.0356120000 0.2253528982 0.1965805332
73700.0000000000 0.1805500000 0.0361100000 0.2263563917 0.1976754558
74100.0000000000 0.1822100000 0.0364420000 0.2270230487 0.1983987074
75000.0000000000 0.1859500000 0.0371900000 0.2285151490 0.2000062855
75800.0000000000 0.1892800000 0.0378560000 0.2298329965 0.2014127885
76500.0000000000 0.1921800000 0.0384360000 0.2309797782 0.2026263669
77000.0000000000 0.1942600000 0.0388520000 0.2317950094 0.2034834874
77600.0000000000 0.1967500000 0.0393500000 0.2327693252 0.2045014903
78400.0000000000 0.2000800000 0.0400160000 0.2340620485 0.2058411416
78900.0000000000 0.2021500000 0.0404300000 0.2348659282 0.2066683793
79400.0000000000 0.2042300000 0.0408460000 0.2356674566 0.2074877848
80000.0000000000 0.2067200000 0.0413440000 0.2366250396 0.2084609655
80700.0000000000 0.2089600000 0.0417920000 0.2377372711 0.2095825572
82000.0000000000 0.2131000000 0.0426200000 0.2397882684 0.2116267788
82051.0000000000 0.2134200000 0.0426840000 0.2398686987 0.2117059573
82700.0000000000 0.2174600000 0.0434920000 0.2408855452 0.2127069662
83300.0000000000 0.2213400000 0.0442680000 0.2418214034 0.2136215318
84000.0000000000 0.2258600000 0.0451720000 0.2429089716 0.2146755273
85000.0000000000 0.2323200000 0.0464640000 0.2444533132 0.2161573326
85300.0000000000 0.2342600000 0.0468520000 0.2449150713 0.2165964256
86100.0000000000 0.2394300000 0.0478860000 0.2461406801 0.2177552421
86800.0000000000 0.2439600000 0.0487920000 0.2472085933 0.2187549528
87500.0000000000 0.2484800000 0.0496960000 0.2482709638 0.2197414777
88300.0000000000 0.2536500000 0.0507300000 0.2494800332 0.2208530383
89000.0000000000 0.2581800000 0.0516360000 0.2505323849 0.2218119808
90000.0000000000 0.2646400000 0.0529280000 0.2520281934 0.2231599354
90300.0000000000 0.2665800000 0.0533160000 0.2524751408 0.2235593583
91200.0000000000 0.2724000000 0.0544800000 0.2538105185 0.2247440960
92800.0000000000 0.2827400000 0.0565480000 0.2561671405 0.2268009151
93600.0000000000 0.2879100000 0.0575820000 0.2573370652 0.2278060690
94400.0000000000 0.2930800000 0.0586160000 0.2585010409 0.2287960300
95000.0000000000 0.2969600000 0.0593920000 0.2593704418 0.2295286632
96000.0000000000 0.3034200000 0.0606840000 0.2608126892 0.2307312502
96800.0000000000 0.3085900000 0.0617180000 0.2619603908 0.2316770052
97700.0000000000 0.3144100000 0.0628820000 0.2632452286 0.2327237857
98500.0000000000 0.3195800000 0.0639160000 0.2643814622 0.2336392600
99300.0000000000 0.3247500000 0.0649500000 0.2655128999 0.2345408351
100000.0000000000 0.3282900000 0.0656580000 0.2664983698 0.2353184684
103440.0000000000 0.3451100000 0.0690220000 0.2712849443 0.2389919921
110000.0000000000 0.3774700000 0.0754940000 0.2801632293 0.2453574286
120000.0000000000 0.4241500000 0.0848300000 0.2931077441 0.2536257586
###########################################################
# Test for URR fitting of > 15 datasets
###########################################################
###########################################################
sammy ctest_0 ctest_0.cfg
###########################################################
urr-case.inp
urr-case.par
data/data-0.dat
data/data-1.dat
data/data-2.dat
data/data-3.dat
data/data-4.dat
data/data-5.dat
data/data-6.dat
data/data-7.dat
data/data-8.dat
data/data-9.dat
data/data-10.dat
data/data-11.dat
data/data-12.dat
data/data-13.dat
data/data-14.dat
data/data-15.dat
cp data16.lst results/t190.lst
LST answers/t190.lst results/t190.lst
CAPTURE CROSS SECTION
ABSOLUTE UNCERTAINTY
500.020 0.070 0.039
510.022 3.097 0.056
520.023 0.049 0.088
530.043 8.053 0.082
550.001 1.025 0.049
560.017 0.081 0.082
570.015 4.005 0.095
590.018 3.057 0.072
600.051 9.024 0.026
620.041 7.026 0.086
630.016 5.007 0.081
CAPTURE CROSS SECTION
ABSOLUTE UNCERTAINTY
500.020 0.260 0.093
510.022 0.587 0.086
520.023 0.074 0.049
530.043 0.241 0.038
550.001 0.640 0.019
560.017 0.506 0.025
570.015 0.507 0.078
590.018 0.638 0.084
600.051 0.562 0.063
620.041 0.588 0.008
630.016 0.135 0.048
650.006 0.189 0.017
670.044 0.997 0.063
680.065 0.270 0.024
700.004 0.458 0.025
720.000 0.636 0.003
740.097 0.983 0.058
760.038 0.711 0.097
790.072 0.567 0.028
810.050 0.399 0.011
830.027 0.352 0.041
860.063 0.545 0.078
880.022 0.114 0.010
910.071 0.577 0.064
\ No newline at end of file
CAPTURE CROSS SECTION
ABSOLUTE UNCERTAINTY
5.500e+03 3.629e+00 3.830e-01
6.500e+03 2.883e+00 2.820e-01
7.500e+03 2.452e+00 2.300e-01
8.500e+03 2.166e+00 1.950e-01
9.500e+03 2.060e+00 1.850e-01
1.050e+04 1.811e+00 1.560e-01
1.150e+04 1.851e+00 1.560e-01
1.250e+04 1.729e+00 1.430e-01
1.350e+04 1.568e+00 1.260e-01
1.450e+04 1.538e+00 1.230e-01
1.550e+04 1.365e+00 1.070e-01
1.650e+04 1.319e+00 1.030e-01
1.750e+04 1.191e+00 9.300e-02
1.850e+04 1.187e+00 9.200e-02
1.950e+04 1.189e+00 9.100e-02
2.100e+04 1.117e+00 8.600e-02
2.300e+04 1.048e+00 8.000e-02
2.500e+04 9.622e-01 7.400e-02
2.700e+04 9.345e-01 7.200e-02
2.900e+04 8.781e-01 6.600e-02
3.100e+04 8.434e-01 6.500e-02
3.300e+04 8.682e-01 6.700e-02
3.500e+04 8.167e-01 6.300e-02
3.700e+04 7.652e-01 5.900e-02
3.900e+04 7.286e-01 5.500e-02
4.100e+04 6.999e-01 6.300e-02
4.300e+04 6.850e-01 6.100e-02
4.500e+04 6.613e-01 5.800e-02
4.700e+04 5.930e-01 5.200e-02
4.900e+04 6.048e-01 5.200e-02
5.100e+04 5.811e-01 5.000e-02
5.300e+04 5.732e-01 4.800e-02
5.500e+04 5.643e-01 4.700e-02
5.700e+04 5.712e-01 4.700e-02
5.900e+04 5.524e-01 4.500e-02
6.100e+04 5.356e-01 4.300e-02
6.300e+04 5.455e-01 4.400e-02
6.500e+04 5.365e-01 4.300e-02
6.700e+04 4.989e-01 4.000e-02
6.900e+04 4.979e-01 4.000e-02
7.100e+04 4.831e-01 3.900e-02
7.300e+04 4.732e-01 3.800e-02
7.500e+04 4.890e-01 3.900e-02
7.700e+04 4.821e-01 3.900e-02
7.900e+04 4.573e-01 3.700e-02
8.200e+04 4.534e-01 3.600e-02
8.600e+04 4.653e-01 3.700e-02
9.000e+04 4.663e-01 3.700e-02
9.400e+04 4.494e-01 3.600e-02
9.800e+04 4.148e-01 3.300e-02
1.020e+05 4.088e-01 3.300e-02
1.060e+05 4.247e-01 3.400e-02
1.100e+05 4.296e-01 3.400e-02
1.140e+05 4.098e-01 3.300e-02
1.180e+05 3.920e-01 3.100e-02
1.240e+05 3.861e-01 3.100e-02
1.320e+05 3.811e-01 3.000e-02
1.400e+05 3.772e-01 3.000e-02
1.480e+05 3.395e-01 2.700e-02
1.560e+05 3.316e-01 2.600e-02
1.640e+05 3.227e-01 2.500e-02
1.720e+05 3.168e-01 2.500e-02
1.800e+05 3.108e-01 2.400e-02
1.880e+05 3.019e-01 2.400e-02
1.960e+05 2.901e-01 2.300e-02
2.075e+05 2.881e-01 2.300e-02
2.225e+05 2.802e-01 2.200e-02
2.375e+05 2.752e-01 2.200e-02
2.525e+05 2.762e-01 2.200e-02
2.675e+05 2.712e-01 2.200e-02
2.825e+05 2.425e-01 2.100e-02
2.975e+05 2.415e-01 1.900e-02
3.125e+05 2.406e-01 1.900e-02
3.275e+05 2.237e-01 1.900e-02
3.425e+05 2.128e-01 1.700e-02
CAPTURE CROSS SECTION
ABSOLUTE UNCERTAINTY
2.200e+04 9.050e-01 5.000e-02
2.600e+04 7.710e-01 4.100e-02
3.000e+04 7.100e-01 3.700e-02
3.400e+04 6.760e-01 3.500e-02
3.800e+04 6.400e-01 3.300e-02
4.200e+04 5.770e-01 2.900e-02
4.600e+04 5.320e-01 2.700e-02
5.000e+04 5.060e-01 2.500e-02
5.400e+04 5.010e-01 2.500e-02
5.800e+04 5.000e-01 2.500e-02
6.200e+04 4.600e-01 2.300e-02
6.600e+04 4.470e-01 2.200e-02
7.000e+04 4.400e-01 2.200e-02
7.400e+04 4.400e-01 2.200e-02
7.800e+04 4.130e-01 2.000e-02
8.200e+04 4.030e-01 2.000e-02
8.600e+04 3.900e-01 1.900e-02
9.000e+04 3.860e-01 1.900e-02
9.400e+04 3.720e-01 1.800e-02
9.800e+04 3.630e-01 1.800e-02
1.050e+05 3.400e-01 1.600e-02
1.150e+05 3.240e-01 1.600e-02
1.250e+05 3.210e-01 1.800e-02
1.350e+05 3.130e-01 1.800e-02
1.450e+05 2.870e-01 1.600e-02
1.550e+05 2.800e-01 1.600e-02
1.650e+05 2.690e-01 1.500e-02
1.750e+05 2.660e-01 1.500e-02
1.850e+05 2.540e-01 1.500e-02
1.950e+05 2.500e-01 1.400e-02
2.050e+05 2.320e-01 1.300e-02
2.150e+05 2.440e-01 1.400e-02
2.250e+05 2.290e-01 1.300e-02
2.350e+05 2.260e-01 1.300e-02
2.450e+05 2.230e-01 1.300e-02
2.550e+05 2.160e-01 1.200e-02
2.650e+05 2.300e-01 1.300e-02
2.750e+05 2.220e-01 1.300e-02
2.850e+05 2.190e-01 1.300e-02
2.950e+05 2.020e-01 1.200e-02
3.100e+05 1.950e-01 1.100e-02
3.300e+05 1.860e-01 1.100e-02
3.500e+05 1.770e-01 1.000e-02
3.700e+05 1.660e-01 1.000e-02
3.900e+05 1.580e-01 9.000e-03
4.100e+05 1.560e-01 9.000e-03
4.300e+05 1.550e-01 9.000e-03
4.500e+05 1.500e-01 9.000e-03
CAPTURE CROSS SECTION
ABSOLUTE UNCERTAINTY
2.365e+04 9.370e-01 2.900e-02
8.159e+04 4.430e-01 1.600e-02
1.278e+05 3.460e-01 1.400e-02
1.368e+05 3.400e-01 8.900e-03
1.675e+05 3.120e-01 1.100e-02
1.833e+05 2.990e-01 1.100e-02
2.191e+05 2.610e-01 1.200e-02
2.726e+05 2.420e-01 7.100e-03
3.080e+05 2.240e-01 5.500e-03
3.516e+05 2.050e-01 6.000e-03
3.756e+05 1.900e-01 7.100e-03
4.668e+05 1.810e-01 9.000e-03
5.549e+05 1.860e-01 1.600e-02
6.435e+05 1.630e-01 4.500e-03
6.994e+05 1.530e-01 5.800e-03
9.470e+05 1.360e-01 6.100e-03
1.181e+06 1.080e-01 6.400e-03
TOTAL CROSS SECTION
ABSOLUTE UNCERTAINTY
2.450e+04 1.153e+01 5.000e-02
TOTAL CROSS SECTION
ABSOLUTE UNCERTAINTY
4.800e+04 1.004e+01 1.700e-01
6.300e+04 9.586e+00 1.642e-01
7.800e+04 9.169e+00 1.621e-01
9.200e+04 8.818e+00 1.604e-01
1.110e+05 8.519e+00 1.598e-01
1.370e+05 8.164e+00 1.582e-01
1.720e+05 7.862e+00 1.578e-01
1.950e+05 7.663e+00 7.218e-02
2.230e+05 7.514e+00 1.573e-01
2.440e+05 7.453e+00 7.264e-02
2.970e+05 7.194e+00 7.125e-02
3.500e+05 7.118e+00 7.663e-02
4.010e+05 7.131e+00 6.835e-02
4.580e+05 6.998e+00 6.720e-02
5.100e+05 6.934e+00 4.873e-02
5.680e+05 6.866e+00 7.713e-02
6.100e+05 6.923e+00 6.343e-02
6.700e+05 6.794e+00 1.076e-01
7.150e+05 6.931e+00 6.075e-02
7.730e+05 6.890e+00 8.184e-02
8.210e+05 6.899e+00 5.979e-02
9.240e+05 6.960e+00 5.726e-02
1.023e+06 6.928e+00 4.951e-02
1.128e+06 6.958e+00 6.799e-02
1.230e+06 6.948e+00 6.980e-02
1.333e+06 6.928e+00 1.654e-01
1.533e+06 7.085e+00 4.662e-02
1.631e+06 7.072e+00 6.455e-02
1.734e+06 7.016e+00 1.116e-01
1.825e+06 7.294e+00 6.763e-02
1.931e+06 7.280e+00 5.277e-02
2.025e+06 7.262e+00 7.858e-02
2.134e+06 7.278e+00 5.194e-02
2.279e+06 7.155e+00 7.749e-02
2.429e+06 7.228e+00 5.350e-02
2.574e+06 7.166e+00 6.832e-02
2.791e+06 6.909e+00 6.607e-02
2.994e+06 7.043e+00 6.629e-02
3.188e+06 6.810e+00 7.141e-02
3.387e+06 6.771e+00 7.043e-02
3.585e+06 6.763e+00 7.412e-02
3.781e+06 6.468e+00 7.652e-02
3.974e+06 6.529e+00 8.132e-02
4.185e+06 6.373e+00 9.934e-02
4.389e+06 6.218e+00 1.461e-01
4.598e+06 6.106e+00 8.079e-02
4.807e+06 5.935e+00 9.212e-02
INELASTIC CROSS SECTION
RELAT. UNCERT.
7000.000 0.0000024 0.20
7250.000 0.0000028
7350.000 0.0000030
7700.000 0.0000035
8000.000 0.0000040
8200.000 0.0000043
8400.000 0.0000046
8700.000 0.0000051
9000.000 0.0000056
9150.000 0.0000058
9600.000 0.0000065
10000.000 0.0000072
10400.000 0.0000083
10650.000 0.0000090
10850.000 0.0000096
11200.000 0.0000106
11650.000 0.0000119
12000.000 0.0000129
12400.000 0.0000140
12800.000 0.0000152
13096.000 0.0000161
13250.000 0.0001910
13700.000 0.0007024
14300.000 0.0013843
14800.000 0.0019525
15300.000 0.0024295
16000.000 0.0030124
17200.000 0.0040115
17900.000 0.0045943
18400.000 0.0050106
18900.000 0.0054269
19400.000 0.0058432
19800.000 0.0061763
20000.000 0.0063428
20500.000 0.0066666
21000.000 0.0069904
22100.000 0.0077027
23200.000 0.0084151
23700.000 0.0087389
24200.000 0.0090626
24600.000 0.0093217
25000.000 0.0095807
25700.000 0.0100340
26200.000 0.0103578
27200.000 0.0110054
27500.000 0.0111997
28300.000 0.0117177
28800.000 0.0120416
29300.000 0.0123653
30000.000 0.0128186
31100.000 0.0134665
31800.000 0.0138789
32099.998 0.0140556
32800.000 0.0144679
34200.000 0.0152925
35000.000 0.0157637
36200.000 0.0164705
37000.000 0.0169417
37900.000 0.0174718
39100.000 0.0181786
40000.000 0.0187088
41000.000 0.0192434
42000.000 0.0197780
43000.000 0.0203125
43800.000 0.0207403
44300.000 0.0210076
45200.000 0.0214887
46000.000 0.0219164
46398.000 0.0221118
46800.000 0.0264436
47300.000 0.0318099
47600.000 0.0350296
48200.000 0.0414691
49000.000 0.0500551
50000.000 0.0607877
50900.000 0.0644711
51200.000 0.0656990
51500.000 0.0669268
51922.000 0.0691088
52200.000 0.0705462
52500.000 0.0725882
53500.000 0.0793949
54200.000 0.0841596
55000.000 0.0896049
55700.000 0.0943695
56100.000 0.0970922
56700.000 0.1011800
57100.000 0.1039000
57900.000 0.1093400
58300.000 0.1120700
59100.000 0.1175100
60000.000 0.1236400
60300.000 0.1248800
61200.000 0.1286200
62000.000 0.1319500
63200.000 0.1369300
64199.996 0.1410900
65000.000 0.1444100
66100.000 0.1489800
67000.000 0.1527200
68000.000 0.1568700
68900.000 0.1606100
69400.000 0.1626900
70000.000 0.1651800
72000.000 0.1734900
72500.000 0.1755700
73100.000 0.1780600
73700.000 0.1805500
74100.000 0.1822100
75000.000 0.1859500
75800.000 0.1892800
76500.000 0.1921800
77000.000 0.1942600
77600.000 0.1967500
78400.000 0.2000800
78900.000 0.2021500
79400.000 0.2042300
80000.000 0.2067200
80700.000 0.2089600
82000.000 0.2131000
82051.000 0.2134200
82700.000 0.2174600
83300.000 0.2213400
84000.000 0.2258600
85000.000 0.2323200
85300.000 0.2342600
86100.000 0.2394300
86800.000 0.2439600
87500.000 0.2484800
88300.000 0.2536500
89000.000 0.2581800
90000.000 0.2646400
90300.000 0.2665800
91200.000 0.2724000
92800.000 0.2827400
93600.000 0.2879100
94400.000 0.2930800
95000.000 0.2969600
96000.000 0.3034200
96800.000 0.3085900
97700.000 0.3144100
98500.000 0.3195800
99300.000 0.3247500
100000.000 0.3282900
103440.000 0.3451100
110000.000 0.3774700
120000.000 0.4241500
129850.008 0.4635100
140000.000 0.5200600
151150.000 0.5638000
160000.000 0.6282200
171430.000 0.6779800
172140.000 0.6810700
180000.000 0.7375600
197950.000 0.8196900
200000.000 0.8337600
TOTAL CROSS SECTION
ABSOLUTE UNCERTAINTY
400.000 1.367 0.538
401.000 1.807 0.117
403.000 1.163 0.081
404.000 1.792 0.627
405.000 1.778 0.480
407.000 1.758 0.258
408.000 1.251 0.465
409.000 1.796 0.277
410.000 1.293 0.551
412.000 1.043 0.338
TOTAL CROSS SECTION
ABSOLUTE UNCERTAINTY
500.000 8.100 1.008
501.000 8.700 1.008
503.000 7.300 1.008
504.000 0.600 1.001
505.000 0.200 1.009
507.000 0.200 1.003
508.000 9.300 1.007
509.000 7.000 1.007
510.000 5.400 1.007
512.000 5.900 1.009
513.000 5.600 1.000
514.000 5.800 1.007
516.000 5.500 1.004
517.000 5.100 1.006
518.000 5.500 1.006
520.000 7.800 1.009
521.000 7.100 1.006
522.000 1.800 1.005
524.000 5.500 1.007
525.000 8.600 1.004
526.000 8.700 1.002
528.000 2.500 1.009
529.000 6.800 1.007
531.000 9.000 1.004
532.000 2.600 1.000
533.000 8.500 1.008
535.000 5.800 1.005
536.000 7.200 1.007
538.000 2.000 1.003
539.000 9.900 1.003
540.000 0.300 1.001
542.000 3.800 1.002
543.000 4.600 1.003
545.000 1.500 1.001
546.000 7.700 1.001
\ No newline at end of file
TOTAL CROSS SECTION
ABSOLUTE UNCERTAINTY
500.000 4.700 1.385
501.000 3.100 1.074
503.000 9.500 1.864
504.000 8.200 1.948
505.000 9.100 1.861
507.000 0.200 1.807
508.000 7.400 1.788
509.000 7.600 1.871
510.000 3.000 1.856
512.000 3.000 1.782
513.000 4.800 1.715
514.000 3.700 1.732
516.000 2.200 1.597
517.000 2.800 1.606
518.000 8.800 1.958
520.000 8.700 1.304
521.000 9.600 1.339
522.000 1.600 1.817
524.000 7.600 1.114
525.000 5.000 1.181
\ No newline at end of file
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