From 7dfcc480ba1e19bd3232349fc733caef94034292 Mon Sep 17 00:00:00 2001
From: stainer_t <thomas.stainer@oecd-nea.org>
Date: Mon, 8 Sep 2025 13:48:49 +0200
Subject: Initial commit from Polytechnique Montreal

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 doc/IGE335/Section5.01.tex | 50 ++++++++++++++++++++++++++++++++++++++++++++++
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+\subsection{Scattering cross sections}\label{sect:ExXSData}
+
+In DRAGON, the angular dependence of the
+scattering cross section is expressed in a Legendre series expansion of
+the form:
+  $$
+\Sigma_{s}(\Omega\cdot\Omega')=\Sigma_{s}(\mu)=
+\sum_{l=0}^{L}\left({{(2l+1)}\over{4\pi}}\right)\Sigma_{s,l}P_{l}(\mu).
+  $$
+Since the Legendre polynomials satisfy the following
+orthogonality conditions:
+  $$
+\int_{-1}^{1} d\mu P_{l}(\mu)P_{m}(\mu) =
+\left({{2\delta_{l,m}}\over{(2l+1)}}\right),
+  $$
+we will have
+  $$
+\Sigma_{s,l}=\int_{-1}^{1}d\mu\int_{0}^{2\pi}d\varphi\Sigma_{s}(\mu)P_{l}(\mu)=
+2\pi \int_{-1}^{1}d\mu\Sigma_{s}(\mu)P_{l}(\mu).
+  $$
+
+Let us now consider the following three-group (\dusa{ngroup}=3) isotropic and
+linearly anisotropic scattering cross sections ($L$=\dusa{naniso}=2) given by:
+
+\begin{center}
+\begin{tabular}{|llccc|}\hline\hline
+$l$ & $g$ &  $\Sigma_{s,l}^{g\to 1}$ (\xsunit)
+          &  $\Sigma_{s,l}^{g\to 2}$ (\xsunit)
+          &  $\Sigma_{s,l}^{g\to 3}$ (\xsunit) \\ \hline
+    &  1  & 0.90 & 0.80 & 0.00 \\
+0   &  2  & 0.00 & 0.70 & 0.60 \\
+    &  3  & 0.00 & 0.30 & 0.40 \\ \hline
+    &  1  & 0.09 & 0.05 & 0.08 \\
+1   &  2  & 0.00 & 0.07 & 0.06\\
+    &  3  & 0.03 & 0.00 & 0.04 \\ \hline\hline
+\end{tabular}
+\end{center}
+
+\noindent
+In DRAGON this scattering cross section must be entered as
+
+\begin{verbatim}
+SCAT  (* L=0 *) 1 1 (* 3->1 *)      (* 2->1 *)      (* 1->1 *) 0.90
+                3 3 (* 3->2 *) 0.30 (* 2->2 *) 0.70 (* 1->2 *) 0.80 
+                2 3 (* 3->3 *) 0.40 (* 2->3 *) 0.60 (* 1->3 *)
+SCAT  (* L=1 *) 3 3 (* 3->1 *) 0.03 (* 2->1 *) 0.00 (* 1->1 *) 0.09
+                2 2 (* 3->2 *)      (* 2->2 *) 0.07 (* 1->2 *) 0.05 
+                3 3 (* 3->3 *) 0.04 (* 2->3 *) 0.06 (* 1->3 *) 0.08 
+\end{verbatim}
+
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