\section{Fission with improved multiplicity sampling} As an alternative to the fission model described in the previous section there is a modified model that produces more accurate multiplicity distributions for the emitted neutrons and gamma rays from spontaneous and neutron-induced fission. This was motivated by detailed statistical studies of fission chains in multiplying media. This model is data-driven and incorporates all available multiplicity measurements found in the literature. Empirical models are employed whenever multiplicity data are not available. Essentially no data are available for the correlations between the neutrons and gammas, so this model samples these distributions independently. By default, this model effectively scales the multiplicity data to match the average multiplicity value ($\bar{\nu}$) found in the GEANT4 evaluated data library. Therefore, only isotopes that have a measured $\bar{\nu}$ in the data library will emit fission gammas or neutrons. At present the gammas and neutrons are emitted isotropically. The data and empirical models are described in detail in the following subsections. %\section{Neutrons emitted by fission\label{neutrons}} \subsection{Neutron number distribution} Based on reasonable assumptions about the distribution of excitation energy among fission fragments, Terrell~\cite{Terrell 1957} showed that the probability P$_\nu$ of observing $\nu$ neutrons from fission can be approximated by a Gaussian-like distribution \begin{equation} \sum_{n=0}^{\nu}P_n = \frac{1}{2\pi}\int_{-\infty}^{\frac{\nu-\bar{\nu} + \frac{1}{2}+b}{\sigma}}e^{-\frac{t^2}{2}dt} \end{equation} where $\bar{\nu}$ is the average number of neutrons, $\sigma$ (set to 1.079) is the width of the distribution, and $b$ is a small correction factor ($b<0.01$) that ensures that the discrete probability distribution has the correct average $\bar{\nu}$. This model is used when no explicit multiplicity data are available. \subsubsection*{Neutron-induced fission data} Zucker and Holden~\cite{Zucker and Holden 1986} measured the neutron multiplicity distributions for $^{235}$U, $^{238}$U, and $^{239}$Pu (see Tables~\ref{Neutron number distribution for induced fission in 235U} -\ref{Neutron number distribution for induced fission in 239Pu (continued)}), as a function of the incident neutron energy $E_n$ from zero through ten MeV in increments of one MeV. Fig.~\ref{235U induced fission 6MeV} shows the neutron number distribution for induced fission of $^{235}$U. Gwin, Spencer and Ingle~\cite{Gwin 1984} measured the distribution at thermal energies for $^{235}$U. In addition, there are many measurements of $\bar{\nu}$, the average number of emitted neutrons, for many isotopes. Since there are multiple methods for parameterizing the multiplicity data and renormalizing the overall distributions to agree with the specific measured values of $\bar{\nu}$, we provide four options for generating neutron multiplicity distributions. %% \notgeant{These options are selected by the internal variable {\tt nudist}, default=3.} \begin{table}[ht] \footnotesize \begin{center} \begin{tabular}{|c|ccccccc|} \hline $E_n$ & $\nu$=0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 0 & .0317223 & .1717071 & .3361991 & .3039695 & .1269459 & .0266793 & .0026322 \\ 1 & .0237898 & .1555525 & .3216515 & .3150433 & .1444732 & .0356013 & .0034339 \\ 2 & .0183989 & .1384891 & .3062123 & .3217566 & .1628673 & .0455972 & .0055694 \\ 3 & .0141460 & .1194839 & .2883075 & .3266568 & .1836014 & .0569113 & .0089426 \\ 4 & .0115208 & .1032624 & .2716849 & .3283426 & .2021206 & .0674456 & .0128924 \\ 5 & .0078498 & .0802010 & .2456595 & .3308175 & .2291646 & .0836912 & .0187016 \\ 6 & .0046272 & .0563321 & .2132296 & .3290407 & .2599806 & .1045974 & .0265604 \\ 7 & .0024659 & .0360957 & .1788634 & .3210507 & .2892537 & .1282576 & .0360887 \\ 8 & .0012702 & .0216090 & .1472227 & .3083032 & .3123950 & .1522540 & .0462449 \\ 9 & .0007288 & .0134879 & .1231200 & .2949390 & .3258251 & .1731879 & .0551737 \\ 10& .0004373 & .0080115 & .1002329 & .2779283 & .3342611 & .1966100 & .0650090 \\ \hline \end{tabular} \end{center} \caption{Neutron number distribution for induced fission in $^{235}$U.} \label{Neutron number distribution for induced fission in 235U} \end{table} \begin{table}[ht] \footnotesize \begin{center} \begin{tabular}{|c|c|c|} \hline $E_n$ & $\nu$=7 & $\bar{\nu}$ \\ \hline 0 & .0001449 & 2.4140000 \\ 1 & .0004546 & 2.5236700 \\ 2 & .0011093 & 2.6368200 \\ 3 & .0019504 & 2.7623400 \\ 4 & .0027307 & 2.8738400 \\ 5 & .0039148 & 3.0386999 \\ 6 & .0056322 & 3.2316099 \\ 7 & .0079244 & 3.4272800 \\ 8 & .0107009 & 3.6041900 \\ 9 & .0135376 & 3.7395900 \\ 10& .0175099 & 3.8749800 \\ \hline \end{tabular} \end{center} \caption{Neutron number distribution for induced fission in $^{235}$U (continued).} \label{Neutron number distribution for induced fission in 235U (continued)} \end{table} \begin{table}[ht] \footnotesize \begin{center} \begin{tabular}{|c|ccccccc|} \hline $E_n$ & $\nu$=0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 0 & .0396484 & .2529541 & .2939544 & .2644470 & .1111758 & .0312261 & .0059347 \\ 1 & .0299076 & .2043215 & .2995886 & .2914889 & .1301480 & .0363119 & .0073638 \\ 2 & .0226651 & .1624020 & .2957263 & .3119098 & .1528786 & .0434233 & .0097473 \\ 3 & .0170253 & .1272992 & .2840540 & .3260192 & .1779579 & .0526575 & .0130997 \\ 4 & .0124932 & .0984797 & .2661875 & .3344938 & .2040116 & .0640468 & .0173837 \\ 5 & .0088167 & .0751744 & .2436570 & .3379711 & .2297901 & .0775971 & .0225619 \\ 6 & .0058736 & .0565985 & .2179252 & .3368863 & .2541575 & .0933127 & .0286200 \\ 7 & .0035997 & .0420460 & .1904095 & .3314575 & .2760413 & .1112075 & .0355683 \\ 8 & .0019495 & .0309087 & .1625055 & .3217392 & .2943792 & .1313074 & .0434347 \\ 9 & .0008767 & .0226587 & .1356058 & .3076919 & .3080816 & .1536446 & .0522549 \\ 10& .0003271 & .0168184 & .1111114 & .2892434 & .3160166 & .1782484 & .0620617 \\ \hline \end{tabular} \end{center} \caption{Neutron number distribution for induced fission in $^{238}$U.} \label{Neutron number distribution for induced fission in 238U} \end{table} \begin{table}[ht] \footnotesize \begin{center} \begin{tabular}{|c|cc|c|} \hline $E_n$ & $\nu$=7 & 8 & $\bar{\nu}$ \\ \hline 0 & .0005436 & .0001158 & 2.2753781 \\ 1 & .0006947 & .0001751 & 2.4305631 \\ 2 & .0009318 & .0003159 & 2.5857481 \\ 3 & .0013467 & .0005405 & 2.7409331 \\ 4 & .0020308 & .0008730 & 2.8961181 \\ 5 & .0030689 & .0013626 & 3.0513031 \\ 6 & .0045431 & .0031316 & 3.2064881 \\ 7 & .0065387 & .0031316 & 3.3616731 \\ 8 & .0091474 & .0046284 & 3.5168581 \\ 9 & .0124682 & .0067176 & 3.6720432 \\ 10& .0166066 & .0095665 & 3.8272281 \\ \hline \end{tabular} \end{center} \caption{Neutron number distribution for induced fission in $^{238}$U (continued).} \label{Neutron number distribution for induced fission in 238U (continued)} \end{table} \begin{table}[ht] \footnotesize \begin{center} \begin{tabular}{|c|ccccccc|} \hline $E_n$ & $\nu$=0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 0 & .0108826 & .0994916 & .2748898 & .3269196 & .2046061 & .0726834 & .0097282 \\ 1 & .0084842 & .0790030 & .2536175 & .3289870 & .2328111 & .0800161 & .0155581 \\ 2 & .0062555 & .0611921 & .2265608 & .3260637 & .2588354 & .0956070 & .0224705 \\ 3 & .0045860 & .0477879 & .1983002 & .3184667 & .2792811 & .1158950 & .0301128 \\ 4 & .0032908 & .0374390 & .1704196 & .3071862 & .2948565 & .1392594 & .0386738 \\ 5 & .0022750 & .0291416 & .1437645 & .2928006 & .3063902 & .1641647 & .0484343 \\ 6 & .0014893 & .0222369 & .1190439 & .2756297 & .3144908 & .1892897 & .0597353 \\ 7 & .0009061 & .0163528 & .0968110 & .2558524 & .3194566 & .2134888 & .0729739 \\ 8 & .0004647 & .0113283 & .0775201 & .2335926 & .3213289 & .2356614 & .0886183 \\ 9 & .0002800 & .0071460 & .0615577 & .2089810 & .3200121 & .2545846 & .1072344 \\ 10& .0002064 & .0038856 & .0492548 & .1822078 & .3154159 & .2687282 & .1295143 \\ \hline \end{tabular} \end{center} \caption{Neutron number distribution for induced fission in $^{239}$Pu.} \label{Neutron number distribution for induced fission in 239Pu} \end{table} \begin{table}[ht] \footnotesize \begin{center} \begin{tabular}{|c|cc|c|} \hline $E_n$ & $\nu$=7 & 8 & $\bar{\nu}$ \\ \hline 0 & .0006301 & .0001685 & 2.8760000 \\ 1 & .0011760 & .0003469 & 3.0088800 \\ 2 & .0025946 & .0005205 & 3.1628300 \\ 3 & .0048471 & .0007233 & 3.3167800 \\ 4 & .0078701 & .0010046 & 3.4707300 \\ 5 & .0116151 & .0014149 & 3.6246800 \\ 6 & .0160828 & .0029917 & 3.7786300 \\ 7 & .0213339 & .0020017 & 3.9325800 \\ 8 & .0274895 & .0039531 & 4.0865300 \\ 9 & .0347255 & .0054786 & 4.2404900 \\ 10& .0432654 & .0075217 & 4.3944400 \\ \hline \end{tabular} \end{center} \caption{Neutron number distribution for induced fission in $^{239}$Pu (continued).} \label{Neutron number distribution for induced fission in 239Pu (continued)} \end{table} \begin{figure}[ht] \begin{center} \includegraphics[scale=0.4, angle=-90]{hadronic/theory_driven/Fission/eps/U235_6MeV_nudist.ps} \end{center} \caption{Induced fission in $^{235}$U, incident neutron energy = 6MeV} \label{235U induced fission 6MeV} \end{figure} The first option %% \notgeant{ ({\tt nudist=0})} uses a fit to the Zucker and Holden data \cite{Zucker and Holden 1986} by Valentine~\cite{Valentine 1996}~\cite{Valentine 2000}. Valentine expressed the P$_{\nu}$'s (for $\nu=0$, ..., 8) as 5$^{th}$ order polynomials in $E_n$, the incident neutron energy. These functions P$_{\nu}(E_n)$ are used to sample the neutron multiplicity for $E_n$ in the range 0 to 10 MeV. When $E_n$ is greater than 10 MeV, $E_n$=10 MeV is used to generate P$_{\nu}$. In addition to using the Zucker and Holden data above for incident neutron energies $E_n$ above 1 MeV, the second option %% \notgeant{ ({\tt nudist=1})} also uses the Gwin, Spencer and Ingle data~\cite{Gwin 1984} for $^{235}$U at thermal energies (0 MeV) to generate P$_{\nu}(E_n)$ polynomials. As in the first option, when $E_n$ is greater than 10 MeV, $E_n$=10 MeV is used to generate P$_{\nu}$. The third option %% \notgeant{ ({\tt nudist=2})} implements an alternative polynomial fit from Valentine ~\cite{Valentine 2000} of P$_{\nu}$ as a function of $\bar{\nu}$ instead of $E_n$, following the suggestion of Frehaut~\cite{Frehaut 1988}. % %{\it"A unique %relationship P$_{\nu}(\bar{\nu})$ can sufficiently %well capture the multiplicity distributions of a number of major %isotopes. This distribution is expressed as a function of the average %number of neutrons emitted $\bar{\nu}$.}" % When a neutron induces a fission, the algorithm converts the incident neutron energy $E_n$ into $\bar{\nu}$ using conversion tables (typically ENDF/EDNL), generates the P$_{\nu}$ distributions for that value of $\bar{\nu}$, and then samples the P$_{\nu}$ distributions to determine $\nu$. The least-square fits to the $^{235}$U data are used for both $^{235}$U and $^{233}$U neutron induced fission, the fits to $^{238}$U are used for $^{232}$U, $^{234}$U, $^{236}$U and $^{238}$U, while the fits to $^{239}$Pu are used for $^{239}$Pu and $^{241}$Pu. Data comes from Zucker and Holden. For $^{235}$U, data comes from Zucker and Holden for $E_n$ greater than 1 MeV, and Gwin, Spencer and Ingle for 0 MeV. The fits are only used when $\bar{\nu}$ is in the range of the $\bar{\nu}$'s for the tabulated data. Otherwise, Terrell's approximation is used. The fourth option, which is the default %% \notgeant{ ({\tt nudist=3})} , is similar to the third option except that the P$_{\nu}$ distributions are not functions of $\bar{\nu}$, but are left intact as multiplicity distributions for the data listed in Gwin, Spencer and Ingle, and for the data listed in Zucker and Holden. The multiplicity distribution P$_{\nu}$ from which the number of neutrons will be sampled is selected based on the value of $\bar{\nu}$ for a given induced fission event. For instance, if P$_{\nu}(1 MeV)$ has $\bar{\nu}=2.4$, P$_{\nu}(2 MeV)$ has $\bar{\nu}=2.6$, and $\bar{\nu}$ is 2.45 at the energy of the incident fission-inducing neutron (this value $\bar{\nu}$ comes typically from cross-section data libraries such and ENDF/ENDL), the probability of sampling the number of neutrons ${\nu}$ from P$_{\nu}(1 MeV)$ and P$_{\nu}(2 MeV)$ will be 25\% and 75\%, respectively. This technique is only used when $\bar{\nu}$ is in the range of the $\bar{\nu}$'s for the tabulated data. Otherwise, Terrell's approximation is used. This last way of computing ${\nu}$ has several advantages: first, the data as listed in the original papers is used exactly, as opposed to approximated by low-ordered polynomials least-square fitting the original data. Second, the data from the Gwin, Spencer and Ingle paper, and the data from the Zucker and Holden paper is entered as-is as a table in the code, and can easily be checked and maintained if necessary by the application developer. Third the method provides a simple and statistically correct mechanism of sampling the data tables. % \notgeant{The fission module behaves in this % manner when the 'nudist' option is set to 3, which is also the default % behavior.} \subsubsection*{Spontaneous fission data} For $^{252}$Cf, the fission module can be set to use either the measurements by Spencer~\cite{Spencer 1982} %% \notgeant{ ({\tt ndist=0})} , which is the default, or Boldeman~\cite{Boldeman 1985} %% \notgeant{ ({\tt ndist=1})} . For $^{238}$U, $^{238}$Pu, $^{240}$Pu, $^{242}$Pu, $^{242}$Cm, $^{244}$Cm, the probability distribution data comes from Holden and Zucker~\cite{Holden and Zucker BNL}. The measured data is summarized in Tables~\ref{Neutron number distribution for spontaneous fission} and \ref{Neutron number distribution for spontaneous fission (continued)}. \begin{table}[ht] \footnotesize \begin{center} \begin{tabular}{|c|ccccccc|} \hline isotope & $\nu$=0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline $^{238}$U & .0481677 & .2485215 & .4253044 & .2284094 & .0423438 & .0072533 & 0 \\ $^{238}$Pu & .0540647 & .2053880 & .3802279 & .2248483 & .1078646 & .0276366 & 0 \\ $^{242}$Pu & .0679423 & .2293159 & .3341228 & .2475507 & .0996922 & .0182398 & .0031364 \\ $^{242}$Cm & .0212550 & .1467407 & .3267531 & .3268277 & .1375090 & .0373815 & .0025912 \\ $^{244}$Cm & .0150050 & .1161725 & .2998427 & .3331614 & .1837748 & .0429780 & .0087914 \\ $^{252}$Cf~\cite{Spencer 1982} & .00211 & .02467 & .12290 & .27144 & .30763 & .18770 & .06770 \\ $^{252}$Cf~\cite{Boldeman 1985} & .00209 & .02621 & .12620 & .27520 & .30180 & .18460 & .06680 \\ \hline \end{tabular} \end{center} \caption{Neutron number distribution for spontaneous fission.} \label{Neutron number distribution for spontaneous fission} \end{table} \begin{table}[ht] \footnotesize \begin{center} \begin{tabular}{|c|ccc|} \hline isotope & $\nu$=7 & 8 & 9 \\ \hline $^{238}$U & 0 & 0 & 0 \\ $^{238}$Pu & 0 & 0 & 0 \\ $^{242}$Pu & 0 & 0 & 0 \\ $^{242}$Cm & .0007551 & .0001867 & 0 \\ $^{244}$Cm & .0002744 & 0 & 0 \\ $^{252}$Cf~\cite{Spencer 1982} & .01406 & .00167 & .0001 \\ $^{252}$Cf~\cite{Boldeman 1985} & .01500 & .00210 & 0 \\ \hline \end{tabular} \end{center} \caption{Neutron number distribution for spontaneous fission (continued).} \label{Neutron number distribution for spontaneous fission (continued)} \end{table} If no full multiplicity distribution data exists, the fission module uses Terrell~\cite{Terrell 1957}'s approximation with $\bar{\nu}$ from Ensslin~\cite{Ensslin 1998}. Ensslin has $\bar{\nu}$ data for the isotopes in table~\ref{Nubar for spontaneous fission}. \begin{table}[ht] \footnotesize \begin{center} \begin{tabular}{|c|c|} \hline isotope & $\bar{\nu}$ \\ \hline $^{232}$Th & 2.14 \\ $^{232}$U & 1.71\\ $^{233}$U & 1.76\\ $^{234}$U & 1.81\\ $^{235}$U & 1.86\\ $^{236}$U & 1.91\\ $^{238}$U & 2.01\\ $^{237}$Np & 2.05\\ $^{238}$Pu & 2.21\\ $^{239}$Pu & 2.16\\ $^{240}$Pu & 2.156\\ $^{241}$Pu & 2.25\\ $^{242}$Pu & 2.145\\ $^{241}$Am & 3.22\\ $^{242}$Cm & 2.54\\ $^{244}$Cm & 2.72\\ $^{249}$Bk & 3.40\\ $^{252}$Cf & 3.757\\ \hline \end{tabular} \end{center} \caption{Average number of neutrons per spontaneous fission.} \label{Nubar for spontaneous fission} \end{table} \subsection{Neutron energy distribution} All of the fission spectra in the Evaluated Nuclear Data Library, ENDL~\cite{ENDL 1975} are defined by a simple analytical function, a Watt spectrum defined as \begin{equation} W(a,b,E') = Ce^{-aE'}sinh(\sqrt{bE'}) \end{equation} where $C=\sqrt{\pi\frac{b}{4a}}\frac{e^{\frac{b}{4a}}}{a}$, and E' is the secondary neutron energy. The Watt spectrum for $^{235}$U and an incident neutron energy of 6 MeV is shown in Fig.~\ref{Watt spectrum for U235}. \begin{figure}[ht] \begin{center} \includegraphics[scale=0.4, angle=-90]{hadronic/theory_driven/Fission/eps/Wattspectrum_U235_6MeV.ps} \end{center} \caption{Watt spectrum for $^{235}$U and an incident neutron energy of 6 MeV.} \label{Watt spectrum for U235} \end{figure} The coefficients a and b vary weakly from one isotope to another and also vary weakly with the incident neutron energy. In the fission module, b is set identical to 1.0, and a is parametrized as a simple function of the incident neutron energy, as implemented in TART~\cite{TART 2003, Cullen 2004}. The fissioning isotope and incident neutron energy determine the value of a, and the energy E' of the secondary neutron emitted is sampled using the Los Alamos' Monte Carlo sampler attributed to Mal Kalos~\cite{Everett 1983}. The Watt spectrum is used for all isotopes except $^{252}$Cf, for which a special treatment summarized by Valentine~\cite{Valentine 2000} is applied. The neutron spectrum for $^{252}$Cf is sampled from the Mannhart~\cite{Mannhart 1987} corrected Maxwellian distribution, the Madland and Nix~\cite{Madland 1984} or the Watt fission spectra from Froehner~\cite{Froehner 1990}. %% \notgeant{These options are selected by the internal variable {\tt neng=0(default),1,2} respectively.} The Mannhart distribution is used by default. %\section{Gammas emitted by fission\label{gammas}} \subsection{Gamma-ray number distribution} The fission module uses Brunson~\cite{Brunson 1982}'s double Poisson model for the spontaneous fission gamma ray multiplicity of $^{252}$Cf (see Fig.~\ref{Fission gamma-ray multiplicity for 252Cf}). \begin{equation} \Pi(G)=0.682\frac{7.20^Ge^{-7.20}}{G!}+0.318\frac{10.71^Ge^{-10.72}}{G!} \end{equation} where $G$ is the gamma ray multiplicity. \begin{figure}[ht] \begin{center} \includegraphics[scale=0.4, angle=-90]{hadronic/theory_driven/Fission/eps/Cf252_nugdist.ps} \end{center} \caption{Fission gamma-ray multiplicity for $^{252}$Cf.} \label{Fission gamma-ray multiplicity for 252Cf} \end{figure} The prompt gamma ray multiplicity ranges from 0 to 20 gama rays per fission with an average of 8.32 gamma rays per fission. This model is a fit to experimental data measured by Brunson himself. For other isotopes, there is no data available for the multiplicity of prompt gamma rays. Valentine~\cite{Valentine 2001} used an approximation that was adopted by the fission module. The probability of emitting $G$ fission gamma rays obeys the negative binomial distribution: \begin{equation} \Pi(G)=\left(\begin{array}{c} \alpha+G-1 \\ G \end{array} \right) p^G(1-p)^G \end{equation} where the parameter $p$ can be written as $p=\frac{\alpha}{\alpha+\bar{G}}$, $\alpha$ is approximately 26 and $\bar{G}$ is the average number of gamma rays per fission. $\bar{G}$ is approximated by \begin{equation} \bar{G} = \frac{E_t(\bar{\nu}, Z, A)}{\bar{E}} \end{equation} where $E_t(\bar{\nu}, Z, A)=(2.51(\pm0.01)-1.13\cdot10^{-5}(\pm7.2\cdot10^{-8})Z^2\sqrt{A})\nu+4.0$ is the total prompt gamma ray energy, and $\bar{E} = -1.33(\pm0.05)+119.6(\pm2.5)\frac{Z^{\frac{1}{3}}}{A}$ is the average prompt gamma ray energy. The multiplicity distribution for the spontaneous fission of $^{238}$U is shown in Fig.~\ref{Fission gamma-ray multiplicity for 238U}. \begin{figure}[ht] \begin{center} \includegraphics[scale=0.4, angle=-90]{hadronic/theory_driven/Fission/eps/U238_nugdist.ps} \end{center} \caption{Fission gamma-ray multiplicity for spontaneous fission of $^{238}$U.} \label{Fission gamma-ray multiplicity for 238U} \end{figure} These multiplicity distributions are only estimates and are not measured data. The fission module uses this model for estimating the number of gamma rays from both spontaneous and induced fission. \subsection{Gamma-ray energy distribution} The fission module implements Valentine's~\cite{Valentine 2000} model for the energy spectra of fission gamma-rays. The only measured energy spectra for fission gamma-rays are for the spontaneous fission of $^{252}$Cf and for the thermal-neutron-induced fission of $^{235}$U. Both spectra are similar~\cite{Wagemans 1991}. Because the $^{235}$U measurements are more precise, this data will be used for the fission gamma-ray spectrum. The energy spectrum of the prompt fission gamma rays is obtained from Maienschein's measurements~\cite{Maienschein 1958}~\cite{Goldstein 1959}: \begin{equation} N(E) = \left\{ \begin{array}{ll} 38.13 (E-0.085)e^{1.648E}& E<0.3\ \mathrm{MeV} \\ 26.8 e^{-2.30E} & 0.3 \parbox[t]{4in} {Use fits to the Zucker and Holden tabulated P$_\nu$ distribution as a function of energy for $^{238}$U and $^{239}$Pu, and a fit to the Zucker and Holden data as well as the Gwin, Spencer and Ingle data (at thermal energies) as a function of energy for $^{235}$U.}\\ \indent 2 \> \parbox[t]{4in} {Use the fit to the Zucker and Holden tabulated P$_\nu$ distributions as a function of $\bar{\nu}$. The $^{238}$U fit is used for the $^{232}$U, $^{234}$U, $^{236}$U and $^{238}$U isotopes, the $^{235}$U fit for $^{233}$U and $^{235}$U, the $^{239}$Pu fit for $^{239}$Pu and $^{241}$Pu.}\\ \indent 3 (default) \> \parbox[t]{4in} {Use the discrete Zucker and Holden tabulated P$_\nu$ distributions and corresponding $\bar{\nu}$s. Sampling based on the incident neutron $\bar{\nu}$. The $^{238}$U data tables are used for the $^{232}$U, $^{234}$U, $^{236}$U and $^{238}$U isotopes, the $^{235}$U data for $^{233}$U and $^{235}$U, the $^{239}$Pu data for $^{239}$Pu and $^{241}$Pu.} \end{tabbing} \subsection*{void setcf252\_(int *ndist, int *neng)} This function is specific to the spontaneous fission of $^{252}$Cf. It selects the data to be sampled for the neutron number and energy distributions and takes the following arguments: \begin{tabbing} \indent ndist: \= Sample the number of neutrons \\ \indent \> 0 (default) \= from the tabulated data measured by Spencer \\ \indent \> 1 \> from Boldeman's data \\ \\ \indent neng: Sample the spontaneous fission neutron energy \\ \indent \> 0 (default)\> from Mannhart corrected Maxwellian spectrum \\ \indent \> 1 \> from Madland-Nix theoretical spectrum \\ \indent \> 2 \> from the Froehner Watt spectrum \\ \end{tabbing}