diff --git a/ACEFormat.pdf b/ACEFormat.pdf index 54a9f62..1f449b0 100644 Binary files a/ACEFormat.pdf and b/ACEFormat.pdf differ diff --git a/src/ContinuousEnergyNeutron.tex b/src/ContinuousEnergyNeutron.tex index 1ac5198..e2c8261 100644 --- a/src/ContinuousEnergyNeutron.tex +++ b/src/ContinuousEnergyNeutron.tex @@ -831,21 +831,40 @@ \subsubsubsection{\var{LAW}=61---Like \var{LAW}=44, but tabular angular distribu \end{description} \subsubsubsection{\var{LAW}=66---$N$-body phase space distribution}\label{sec:LAW66} -\begin{LAWTable}{\var{LAW}=66 (From ENDF-6 \MF=6 \var{LAW}=6)} - \var{LDAT}(1) & \var{NPSX} & Number of bodies in the phase space \\ - \var{LDAT}(2) & $A_{P}$ & Total mass ratio for the \var{NPSX} particles. - \label{tab:LAW66} -\end{LAWTable} +\begin{ThreePartTable} + \begin{TableNotes} + \item[$\dagger$] \label{tn:LAW66FractionInterpolationScheme} + \begin{description} + \item[\var{INTT}=1] histogram distribution, and + \item[\var{INTT}=2] linear-linear distribution. + \end{description} + \end{TableNotes} + \begin{LAWTable}{\var{LAW}=66 (From ENDF-6 \MF=6 \var{LAW}=6)} + \var{LDAT}(1) & \var{NPSX} & Number of bodies in the phase space \\ + \var{LDAT}(2) & $A_{P}$ & Total mass ratio for the \var{NPSX} particles \\ + \var{LDAT}(3) & \var{INTT} & Interpolation flag\tnotex{tn:LAW66FractionInterpolationScheme} \\ + \var{LDAT}(4) & $N_{P}$ & Number of points in the distribution \\ + \var{LDAT}(5) & $T(j),j=1,\ldots,N_{P}$ & Fraction of max energy \\ + \var{LDAT}(5+$N_{P}$) & $\PDF(j),j=1,\ldots,N_{P}$ & Probability density function \\ + \var{LDAT}(5+$2N_{P}$) & $\CDF(j),j=1,\ldots,N_{P}$ & Cumulative density function + \label{tab:LAW66} + \end{LAWTable} +\end{ThreePartTable} -The outgoing energy is +The outgoing center-of-mass energy is \begin{align} - E_{\mathrm{out}} &= T(\xi)E_{i}^{\mathrm{max}} \\ + E_{\mathrm{out}}^{\mathrm{CM}} &= TE_{i}^{\mathrm{max}} \\ \intertext{where} - E_{i}^{\mathrm{max}} &= \frac{A_{p}-1}{A_{p}}\left( \frac{A}{A+1}E_{\mathrm{in}}+Q \right) \\ - \intertext{and $T(\xi)$ is sampled from:} - P_{i}(\mu,E_{\mathrm{in}},T) &= C_{n}\sqrt{T}\left( E_{i}^{\mathrm{max}}-T \right)^{3n/2-4} + E_{i}^{\mathrm{max}} &= \frac{A_{p}-1}{A_{p}}\left( \frac{A}{A+1}E_{\mathrm{in}}+Q \right). \\ + \intertext{With $n=\mathrm{NPSX}$, the analytic distribution for $T$ is:} + P(T) &= C_{n}\sqrt{T}\left( 1 - T \right)^{3n/2-4} \\ + \intertext{where $C_{n}$ is taken to be:} + C_{n=3} &= \frac{8}{\pi}\\ + C_{n=4} &= \frac{105}{16} \\ + C_{n=5} &= \frac{256}{7\pi} \label{eq:LAW66} \end{align} +The cosine of the center-of-mass scattering angle, $\mu_{\mathrm{CM}}$, is isotropic. \subsubsubsection{\var{LAW}=67---Laboratory Angle-Energy Law}\label{sec:LAW67} \begin{ThreePartTable}