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Maxwellian and Evaporation Formulae Fix #21

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Maxwellian and Evaporation Formulae Fix #21

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Fixes incorrect formulae in LAW9 and LAW7
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@HunterBelanger
HunterBelanger committed Mar 27, 2021
commit 7ea6cc33e6ca6446963ba65d1a01d0dee62eb522
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5 changes: 2 additions & 3 deletions src/ContinuousEnergyNeutron.tex
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Expand Up @@ -602,7 +602,7 @@ \subsubsubsection{\var{LAW}=7---Simple Maxwellian Fission Spectrum}\label{sec:LA
\begin{description}
\item[$I$] is the normalization constant
\begin{equation}
I = \theta^{{3/2}} \frac{\sqrt{\pi}}{2} \erf\left( \sqrt{(E-U)/\theta} \right) - \sqrt{(E-U)/\theta}\ e^{-(E-U)/\theta},
I = \theta^{{3/2}} \bigg[\frac{\sqrt{\pi}}{2} \erf\left( \sqrt{(E-U)/\theta} \right) - \sqrt{(E-U)/\theta}\ e^{-(E-U)/\theta}\bigg],
\label{eq:LAW7I}
\end{equation}
\item[$\theta$] is tabulated as a function of incident energy, $E$; and
Expand All @@ -623,7 +623,7 @@ \subsubsubsection{\var{LAW}=9---Evaporation Spectrum}\label{sec:LAW9}
\end{LAWTable}
The outgoing energy, $E_{\mathrm{out}}$, can be calculated as
\begin{equation}
f(E\rightarrow E_{\mathrm{out}}) = \frac{\sqrt{E_{\mathrm{out}}}}{I}\ e^{-E_{\mathrm{out}}/\theta(E)}
f(E\rightarrow E_{\mathrm{out}}) = \frac{E_{\mathrm{out}}}{I}\ e^{-E_{\mathrm{out}}/\theta(E)}
\label{eq:LAW9f}
\end{equation}
where:
Expand All @@ -636,7 +636,6 @@ \subsubsubsection{\var{LAW}=9---Evaporation Spectrum}\label{sec:LAW9}
\item[$\theta$] is tabulated as a function of incident energy, $E$; and
\item[$U$] is a constant introduced to define the proper upper limit for the final particle energy such that $0\leq E_{\mathrm{out}} \leq (E-U)$.
\end{description}
\textbf{Note:} \Equationref{eq:LAW9f} is the same as \Equationref{eq:LAW7f}; just the definitions of $I$ in \Equationref{eq:LAW7I} and \Equationref{eq:LAW9I} are different.

\subsubsubsection{\var{LAW}=11---Energy Dependent Watt Spectrum}\label{sec:LAW11}
\begin{LAWTable}{\var{LAW}=11 (From ENDF-6, \MF=5, \var{LF}=11)}
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