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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+\section{Contents of a \dir{microlib} directory}\label{sect:microlibdir}
+
+A \dir{microlib} directory contains the set of multigroup microscopic 
+cross sections associated with a set of isotopes. It also includes a \dir{macrolib} directory
+where the macroscopic cross sections for the mixtures to which are associated these
+isotopes are stored (see \Sect{macrolibdir}). Finally it may contains a \dir{depletion} directory
+(see \Sect{microlibdirdepletion}) which is required for burnup calculation and a \dir{selfshield}
+directory which is generated by the \moc{SHI:} or \moc{USS:} operator (see
+\Sect{subgroupdirselfshield}). It is
+therefore multi-level, namely, it contains sub-directories. Note that the contents of such a
+directory will vary depending on the operator which was used to create or modify it. Here for
+convenience we will define the variable
+$\mathcal{M}$ to identify the creation operator:
+\begin{displaymath}
+\mathcal{M} = \left\{
+\begin{array}{ll}
+1 & \textrm{if the microlib is created or modified by the \moc{LIB:} or \moc{EVO:} operator}\\
+2 & \textrm{if the microlib is created or modified by the \moc{EDI:} or
+\moc{C2M:} operator}\\
+3 & \textrm{if the microlib is modified by the \moc{SHI:} or \moc{USS:} operator}\\
+4 & \textrm{if the microlib is part of a {\sc compo} object and is created by the \moc{COMPO:} operator}
+\end{array} \right.
+\end{displaymath}
+
+In the case where the \moc{LIB:} or \moc{C2M:} operator is used to create the microlib, it appears on the root
+level of the data structure. For the other case it is embedded as a
+subdirectory of a surrounding data structure.
+
+\subsection{State vector content for the \dir{microlib} data structure}\label{sect:microlibstate}
+
+The dimensioning parameters for the \dir{microlib} data structure, which are stored in
+the state vector $\mathcal{S}^{m}$, represent:
+
+\begin{itemize}
+\item The maximum number of mixtures $M_{m}=\mathcal{S}^{m}_{1}$
+\item The number of isotopes $N_{I}=\mathcal{S}^{m}_{2}$ 
+\item The number of groups ${G}=\mathcal{S}^{m}_{3}$ 
+\item The order for the scattering anisotropy $L=\mathcal{S}^{m}_{4}$
+($L=1$ is an isotropic collision; $L=2$ is a linearly anisotropic collision,
+etc.)
+\item The transport correction option $I_{tr}=\mathcal{S}^{m}_{5}$ 
+\begin{displaymath}
+I_{tr} = \left\{
+\begin{array}{ll}
+0 & \textrm{do not use a transport correction}\\
+1 & \textrm{use an APOLLO-type transport correction (micro-reversibility at
+all energies)}\\
+2 & \textrm{recover a transport correction from the cross-section library}\\
+3 & \textrm{use a WIMS-type transport correction (micro-reversibility below
+4eV;}\\
+  & \textrm{1/E current spectrum elsewhere)}\\
+4 & \textrm{use a leakage correction based on {\tt NTOT1} data.}
+\end{array} \right.
+\end{displaymath}
+\item Format of the included \dir{macrolib} $I_{p}=\mathcal{S}^{m}_{6}$
+\begin{displaymath}
+I_{p} = \left\{
+\begin{array}{ll}
+0 & \textrm{for the direct macroscopic cross sections} \\
+1 & \textrm{for the adjoint macroscopic cross sections}
+\end{array} \right.
+\end{displaymath}
+\item Option for removing delayed neutron effects from the \dir{microlib}
+$I_{t}=\mathcal{S}^{m}_{7}$ 
+\begin{displaymath}
+I_{t} = \left\{
+\begin{array}{ll}
+1 & \textrm{include the delayed and prompt neutron effect} \\
+2 & \textrm{consider only the prompt neutrons. This option is only available
+with}\\
+& \textrm{MATXS--type libraries.}
+\end{array} \right.
+\end{displaymath}
+\item The number of independent libraries $N_{\mathrm{lib}}=\mathcal{S}^{m}_{8}$ 
+\item The number of fast groups without self-shielding $N_{g,f}=\mathcal{S}^{m}_{9}$ 
+
+Represents the number of fast energy groups to be treated without including resonance
+effects. It is automatically determined from the cross-section libraries. This value,
+which is only used by the self-shielding operator, can be modified using the keyword \moc{GRMAX}.
+
+\item The maximum index of all groups with self-shielding $N_{g,e}=\mathcal{S}^{m}_{10}$.
+
+In the case of a WIMS--type library, it represents the total number of energy groups above
+$4.0$ eV. Otherwise, it is automatically determined from the cross-section libraries. This
+value, is used by the self-shielding operator and can be modified locally in
+this operator using the keyword \moc{GRMIN}.
+
+\item The number of depleting isotopes $N_{d}=\mathcal{S}^{m}_{11}$ 
+\item The number of depleting mixtures $N_{d,f}=\mathcal{S}^{m}_{12}$ 
+\item The number of additional $\phi$--weighted editing cross sections $N_{e}=\mathcal{S}^{m}_{13}$ 
+\item The number of mixtures $N_{m}=\mathcal{S}^{m}_{14}$ 
+\item The number of resonant mixtures $N_{r}=\mathcal{S}^{m}_{15}$ 
+\item The number of energy-dependent fission spectra $G_{\rm chi}=\mathcal{S}^{m}_{16}$. By default ($G_{\rm chi}=0$),
+a unique fission spectrum is used. The theory of multiple fission spectra is presented in Ref.~\citen{mosca}.
+\item Option for processing the cross-section libraries $I_{\rm proc}=\mathcal{S}^{m}_{17}$
+\begin{displaymath}
+I_{\rm proc} = \left\{
+\begin{array}{ll}
+-1 & \textrm{skip the library processing (i.e., no interpolation).} \\
+0 & \textrm{perform an interpolation in temperature and dilution.} \\
+1 & \textrm{perform an interpolation in temperature and compute probability} \\
+  & \textrm{tables based on the tabulation in dilution.} \\
+2 & \textrm{perform an interpolation in temperature and build a new temperature-} \\
+  & \textrm{independent cross-section library in \dir{microlib} format.} \\
+3 & \textrm{perform an interpolation in temperature and compute CALENDF--type} \\
+  & \textrm{mathematical probability tables based on BIN--type cross sections. Do} \\
+  & \textrm{not compute the slowing-down correlated weight matrices. Option} \\
+  & \textrm{compatible with the subgroup projection method (SPM).} \\
+4 & \textrm{perform an interpolation in temperature and compute CALENDF--type} \\
+  & \textrm{mathematical probability tables and slowing-down correlated weight} \\
+  & \textrm{matrices based on BIN--type cross sections. Option compatible with} \\
+  & \textrm{the Ribon extended method.} \\
+5 & \textrm{perform an interpolation in temperature and compute CALENDF--type} \\
+  & \textrm{mathematical probability tables based on BIN--type cross sections. This} \\
+  & \textrm{option is similar to the $I_{\rm proc} =3$ procedure. Here, the base points of the} \\
+  & \textrm{probability tables corresponding to fission and scattering cross sections} \\
+  & \textrm{and to components of the transfer scattering matrix are also obtained} \\
+  & \textrm{using the CALENDF approach.} \\
+6 & \textrm{perform an interpolation in temperature and compute RSE--type proba-} \\
+  & \textrm{bility tables based on BIN--type cross sections. RSE is the resonance} \\
+  & \textrm{spectrum expansion method.} \\
+\end{array} \right.
+\end{displaymath}
+\item Option for computing the macrolib $I_{\rm mac}=\mathcal{S}^{m}_{18}$
+\begin{displaymath}
+I_{\rm mac} = \left\{
+\begin{array}{ll}
+0 & \textrm{do not build an embedded macrolib.} \\
+1 & \textrm{build an embedded macrolib. Mandatory if the microlib is to be used to} \\
+  & \textrm{perform micro-depletion.}
+\end{array} \right.
+\end{displaymath}
+\item The number of precursor groups producing delayed neutrons $N_{\rm del}=\mathcal{S}^{m}_{19}$.
+\item The number of fissile isotopes producing fission products with {\tt PYIELD} data $N_{\rm dfi}=\mathcal{S}^{m}_{20}$ (see Table~\ref{tabl:tabiso3})
+\item Option for completing the depletion chains with the missing isotopes $I_{\rm cmp}=\mathcal{S}^{m}_{21}$
+\begin{displaymath}
+I_{\rm cmp} = \left\{
+\begin{array}{ll}
+0 & \textrm{complete} \\
+1 & \textrm{do not complete.}
+\end{array} \right.
+\end{displaymath}
+\item The maximum number of isotopes per mixture $M_{\rm I}=\mathcal{S}^{m}_{22}$.
+\item An integer index (1, 2, 3 or 4) used to set the accuracy of the CALENDF probability
+tables. The highest the value, the more accurate are the tables. $N_{\rm
+ipreci}=\mathcal{S}^{m}_{23}$.
+\item Discontinuity factor flag $I_{\rm df}=\mathcal{S}^{m}_{24}$. This information is available in \dir{macrolib} directory (see \Sect{macrolibdir})
+\begin{displaymath}
+I_{\rm df} = \left\{
+\begin{array}{ll}
+0 & \textrm{no discontinuity factor information}\\
+1 & \textrm{multigroup boundary current information is available}\\
+2 & \textrm{boundary flux information (see \Sect{macroADF}) is available}\\
+3 & \textrm{discontinuity factor information (see \Sect{macroADF}) is available}\\
+4 & \textrm{matrix ($G \times G$) discontinuity factor information (see \Sect{macroADF}) is available.}
+\end{array} \right.
+\end{displaymath}
+\item The maximum Legendre order of the weighting functions $I_{w}=\mathcal{S}^{m}_{25}$ 
+\begin{displaymath}
+I_{w} = \left\{
+\begin{array}{ll}
+0 & \textrm{use the flux as weighting function for all cross sections}\\
+1 & \textrm{use the fundamental current ${\cal J}$ as weighting function for
+scattering cross sections}\\
+& \textrm{with order $\ge 1$ and compute both $\phi$-- and
+${\cal J}$--weighted total cross sections.}
+\end{array} \right.
+\end{displaymath}
+\item Number of companion particles in coupled sets $I_{\rm part}=\mathcal{S}^{M}_{26}$
+\begin{displaymath}
+I_{\rm part} = \left\{
+\begin{array}{ll}
+0 & \textrm{the microlib doesn't include coupled sets}\\
+>0 & \textrm{number of companion particles.}
+\end{array} \right.
+\end{displaymath}
+\item Option for performing the Sternheimer density correction for charged particle cases $I_{\rm ster}=\mathcal{S}^{m}_{27}$
+\begin{displaymath}
+I_{\rm ster} = \left\{
+\begin{array}{ll}
+0 & \textrm{do not perform the correction.} \\
+1 & \textrm{perform Sternheimer correction applied for both restricted total stopping power}\\
+& \textrm{and heat deposition cross section.}
+\end{array} \right.
+\end{displaymath}
+\end{itemize}
+
+\goodbreak
+\clearpage
+
+\subsection{The main \dir{microlib} directory}\label{sect:microlibdirmain}
+
+The following records and sub-directories will be found on the first level of a \dir{microlib}
+directory:
+\begin{DescriptionEnregistrement}{Main records and sub-directories in \dir{microlib}}{7.0cm}
+\CharEnr
+  {SIGNATURE\blank{3}}{$*12$}
+  {Signature of the \dir{microlib} data structure ($\mathsf{SIGNA}=${\tt L\_LIBRARY\blank{3}}).}
+\IntEnr
+  {STATE-VECTOR}{$40$}
+  {Vector describing the various parameters associated with this data structure $\mathcal{S}^{m}_{i}$,
+  as defined in \Sect{microlibstate}.}
+\RealEnr
+  {ENERGY\blank{6}}{$G+1$}{eV}
+  {Energy groups limits $E_{g}$}
+\RealEnr
+  {DELTAU\blank{6}}{$G$}{}
+  {Lethargy width of each group $U_{g}$}
+\OptRealEnr
+  {CHI-ENERGY\blank{2}}{$G_{\rm chi}+1$}{$G_{\rm chi}\ne 0$}{eV}
+  {$E_{\rm chi}(g)$: Group energy limits defining the energy-dependent fission spectra. By default, a unique fission spectra is used.}
+\OptIntEnr
+  {CHI-LIMITS\blank{2}}{$G_{\rm chi}+1$}{$G_{\rm chi}\ne 0$}
+  {$N_{\rm chi}(g)$: Group limit indices defining the energy-dependent fission spectra. By default, a unique fission spectra is used.}
+\DirlEnr
+  {ISOTOPESLIST}{$N_{I}$}
+  {List of {\sc isotope} directories. Each component of this list follows the \dir{isotope} specification
+  presented in Tables~\ref{tabl:tabiso1} to \ref{tabl:tabiso5} and is containing the cross section
+  information associated with a specific isotope. The name of these isotopes is specified by 
+  $\mathsf{NALIAS}_{i}$ as given in record {\tt ISOTOPESUSED}.}
+\CharEnr
+  {ISOTOPESUSED}{$(N_{I})*12$}
+  {Alias name associated with each isotope $\mathsf{NALIAS}_{i}$. The first eight characters of the name of a macroscopic residual are set to {\tt '*MAC*RES'}.}
+\OptCharEnr
+  {ISOTOPERNAME}{$(N_{I})*12$}{$\mathcal{M}=1,3$}
+  {Reference name associated with each isotope $\mathsf{NISO}_{i}$}
+\OptIntEnr
+  {ISOTOPESMIX\blank{1}}{$N_{I}$}{$\mathcal{M}\ne 4$}
+  {Mixture number associated with each isotope $N_{I}$}
+\RealEnr
+  {ISOTOPESDENS}{$N_{I}$}{(cm b)$^{-1}\ $}
+  {Isotopic density $\rho_{i}$}
+\RealEnr
+  {ISOTOPESTEMP}{$N_{I}$}{K}
+  {Isotope temperature $T_{i}$}
+\OptIntEnr
+  {ISOTOPESTODO}{$N_{I}$}{$\mathcal{M}=1,3$}
+  {=0: automatic detection of depletion for isotope $i$; =1: isotope $i$ is
+  forced to be non depleting (keeps its capability to produce energy); =2: isotope $i$ is
+  forced to be depleting; =3: isotope $i$ is at saturation.}
+\IntEnr
+  {ISOTOPESTYPE}{$N_{I}$}
+  {Type index associated with each isotope $\mathsf{ITYP}_{i}$. $=1$: the isotope is
+  not fissile and not a fission product; $=2$: fissile isotope; $=3$: fission
+  product.}
+\OptRealEnr
+  {ISOTOPESVOL\blank{1}}{$N_{I}$}{$\mathcal{M}=2, 4$}{cm$^{3}$}
+  {Volume occupied by isotope $V_{i}$}
+\OptCharEnr
+  {ILIBRARYTYPE}{$(N_{I})*8$}{$N_{\mathrm{lib}}\ge 1$}
+  {Library type associated with each isotope $\mathsf{NLTY}_{i}$}
+\OptCharEnr
+  {ILIBRARYNAME}{$(N_{\mathrm{lib}})*64$}{$N_{\mathrm{lib}}\ge 1$}
+  {Name associated with each cross-section library}
+\OptIntEnr
+  {ILIBRARYINDX}{$N_{I}$}{$N_{\mathrm{lib}}\ge 1$}
+  {Index of the cross-section library associated with each isotope $1 \le \mathsf{LLIB}_{i}\le N_{\mathrm{lib}}$}
+\OptCharEnr
+  {ISOTOPESCOH\blank{1}}{$(N_{I})*8$}{$N_{\mathrm{lib}}\ge 1$}
+  {Name of coherent scattering type at thermal energies $\mathsf{NCOH}_{i}$}
+\OptCharEnr
+  {ISOTOPESINC\blank{1}}{$(N_{I})*8$}{$N_{\mathrm{lib}}\ge 1$}
+  {Name of incoherent scattering type at thermal energies $\mathsf{NINC}_{i}$}
+\OptCharEnr
+  {ISOTOPESRESK}{$(N_{I})*8$}{$N_{\mathrm{lib}}\ge 1$}
+  {Name of resonance elastic scattering kernel (RESK) type at epithermal energies $\mathsf{NRSK}_{i}$}
+\OptIntEnr
+  {ISOTOPESNTFG}{$N_{I}$}{$N_{\mathrm{lib}}\ge 1$}
+  {Number of thermal groups involved in coherent or incoherent scattering $G_{s,i}$}
+\OptCharEnr
+  {ISOTOPESHIN\blank{1}}{$(N_{I})*12$}{$N_{\mathrm{lib}}\ge 1$}
+  {Name of resonant isotope associated with each isotope $\mathsf{NSHI}_{i}$}
+\OptIntEnr
+  {ISOTOPESSHI\blank{1}}{$N_{I}$}{$N_{\mathrm{lib}}\ge 1$}
+  {Resonant mixture associated with each isotope $I_{R,i}$}
+\OptRealEnr
+  {ISOTOPESDSN\blank{1}}{$G \times N_{I}$}{${\displaystyle N_{\mathrm{lib}}\ge 1 \atop
+  \displaystyle I_{\rm proc}=0}$}{b}
+  {Standard dilution cross section for isotope $\sigma_{\mathrm{dil},i}$ in each energy group}
+\OptRealEnr
+  {ISOTOPESDSB\blank{1}}{$G \times N_{I}$}{${\displaystyle N_{\mathrm{lib}}\ge 1 \atop
+  \displaystyle I_{\rm proc}=0}$}{b}
+  {Livolant-Jeanpierre dilution cross section for isotope $\sigma_{\mathrm{LJ},i}$ in each energy group}
+\OptIntEnr
+  {ISOTOPESNIR\blank{1}}{$N_{I}$}{$N_{\mathrm{lib}}\ge 1$}
+  {Use Goldstein-Cohen factor $\lambda_i$ in groups with index $\ge N^{\rm ir}_i$.
+  Use $\lambda=1$ in other groups}
+\OptRealEnr
+  {ISOTOPESGIR\blank{1}}{$N_{I}$}{$N_{\mathrm{lib}}\ge 1$}{1}
+  {Goldstein-Cohen parameter in low-energy resonant groups $\lambda_i$. Set to -998.0 if
+  $I_{\rm proc}=3$, to -999.0 if $I_{\rm proc}=4$, to -1000.0 if $I_{\rm proc}=5$ and to -1001.0 if $I_{\rm proc}=6$.}
+\OptRealEnr
+  {MIXTURESVOL\blank{1}}{$N_{m}$}{$\mathcal{M}=2, 4$}{cm$^{3}$}
+  {Volume occupied by each mixture}
+\OptRealEnr
+  {MIXTURESDENS}{$N_{m}$}{$\mathcal{M}=1$}{g/cm$^{3}$~~}
+  {Volumetric mass density of each mixture $\rho_{m}$}
+\OptCharEnr
+  {ADDXSNAME-P0}{$(N_{e})*8$}{$N_{e}\ge 1$}
+  {Names of the additional $\phi$--weighted editing cross sections $\mathsf{ADDXS}_{k}$ stored on \dir{macrolib}}
+\OptCharEnr
+  {PARTICLE\blank{4}}{$*1$}{$I_{\rm part}\ge 1$} 
+  {Character name of the particle associated to the microlib. Usual names for
+  particles are {\tt N} (neutrons), {\tt G} (photons), {\tt B} (electrons),
+  {\tt C} (positrons) and {\tt P} (protons).}
+\OptCharEnr
+  {PARTICLE-NAM}{($I_{\rm part}+1$)$*1$}{$I_{\rm part}\ge 1$} 
+  {Character name associated to each particle.}
+\OptIntEnr
+  {PARTICLE-NGR}{$I_{\rm part}+1$}{$I_{\rm part}\ge 1$}
+  {Number of energy groups associated to each particle.}
+\OptRealEnr
+  {PARTICLE-MC2}{$I_{\rm part}+1$}{$I_{\rm part}\ge 1$}{eV}
+  {Rest energy associated to each particle.}
+\OptRealVar
+  {\listedir{penergy}}{$G_i+1$}{$I_{\rm part}\ge 1$}{eV}
+  {Set of arrays containing energy groups limits for a companion particle. The character name
+  of each sub-directory is the concatenation of the character*1 name of the particle with ``{\tt ENERGY}''.
+  For example, {\tt GENERGY} contains the energy mesh of secondary photons ($G_i+1$ values).}
+\OptRealEnr
+  {TIMESPER\blank{4}}{$2\times 3$}{$\mathcal{M}=2$}{}
+  {Array $T_{j,i}$ that contains $T_{j,1}=t$, $T_{j,2}=B$ and $T_{j,3}=w$, the
+   lower ($j=1$) and upper bounds ($j=2$) for the reference time in days, burnup
+   in MW day T$^{-1}$ and irradiation in Kb$^{-1}$ respectively for which the
+   perturbative expansion is valid}
+\OptRealEnr
+  {K-EFFECTIVE\blank{1}}{$1$}{*}{}
+  {Effective multiplication constant $k_{\mathrm{eff}}$}
+\OptRealEnr
+  {K-INFINITY\blank{2}}{$1$}{*}{}
+  {Infinite multiplication constant $k_{\mathrm{inf}}$}
+\OptRealEnr
+  {B2\blank{2}B1HOM\blank{3}}{$1$}{*}{cm$^{-2}$~~}
+  {Homogeneous Buckling $B_{\mathrm{hom}}$}
+\OptDirEnr
+  {MACROLIB\blank{4}}{$I_{\rm mac} = 1$}
+  {Sub-directory containing the \dir{macrolib} associated with this
+  library, following the specification presented in \Sect{macrolibdirmain}.}
+\OptDirEnr
+  {DEPL-CHAIN\blank{2}}{$N_{d} \ge 1$}
+  {Sub-directory containing the \dir{depletion} associated with this library, following
+  the specification presented in \Sect{microlibdirdepletion}.}
+\OptDirEnr
+  {SHIBA\blank{7}}{$\mathcal{M}=3$}
+  {Sub-directory containing the \dir{selfshield} associated with this
+  library, following the specification presented in \Sect{shibadirselfshield}.
+  This data is used by the \moc{SHI:} self-shielding module.}
+\OptDirEnr
+  {SHIBA\_SG\blank{4}}{$\mathcal{M}=3$}
+  {Sub-directory containing the \dir{uss-selfshield} associated with this
+  library, following the specification presented in \Sect{subgroupdirselfshield}.
+  This sub-directory is present in the library builded by \moc{USS:} self-shielding module and used by \moc{USS:}.}
+\IntEnr
+  {MIXTUREGAS\blank{2}}{$N_{m}$}
+  {State of each mixture (used for stopping power correction).}
+\OptDirEnr
+  {INDEX\blank{7}}{*}
+  {Sub-directory containing indexing or table-of-content data for specific library
+  files}
+\end{DescriptionEnregistrement}
+
+One will find in \Sect{macrolibdir} the description of a 
+\dir{macrolib} directory and in 
+\Sect{isotopedir} the contents of an \dir{isotope} directory. Note that if $N_{I}=2$ and 
+\begin{displaymath}
+\mathsf{NALIAS}_{i} = \left\{
+\begin{array}{lll}
+\texttt{U235    0001} & \textrm{for}& i=1\\
+\texttt{Pu239   0003} & \textrm{for}& i=2
+\end{array} \right.
+\end{displaymath}
+then \listedir{isotope} will correspond to the following two directories:
+
+\begin{DescriptionEnregistrement}{Examples of isotopes directory in a \dir{microlib}}{7.5cm}
+\DirEnr
+  {U235\blank{4}0001}
+  {Directory where the microscopic cross sections of \Iso{U}{235} are stored. These are 
+   self-shielded cross section already interpolated in temperature. They correspond to the
+  properties of mixture $1$}
+\DirEnr
+  {Pu239\blank{3}0003}
+  {Directory where the microscopic cross sections of \Iso{Pu}{239} are stored. These are 
+   self-shielded cross section already interpolated in temperature. They correspond to the
+  properties of mixture $3$}
+\end{DescriptionEnregistrement}
+
+\subsection{State vector content for the depletion sub-directory}\label{sect:chainlibstate}
+
+The dimensioning parameters for the depletion sub-directory, which are stored in
+the state vector $\mathcal{S}^{d}$, represent:
+
+\begin{itemize}
+\item The number of depleting isotopes $N_{\mathrm{depl}}=\mathcal{S}^{d}_{1}$
+\item The number of direct fissile isotopes (i.e., producing fission products) $N_{\mathrm{dfi}}=\mathcal{S}^{d}_{2}$
+\item The number of fission fragments $N_{\mathrm{dfp}}=\mathcal{S}^{d}_{3}$. A fission fragment is produced directly by the
+fission reaction. A fission product is a fission fragment or a daughter isotope
+produced by decay or neutron-induced reaction.
+\item The number of heavy isotopes $N_{\mathrm{H}}=\mathcal{S}^{d}_{4}$ 
+
+This number represents the combination of fissile isotopes and the other isotopes produced from
+these isotopes by reactions other than fission.
+
+\item The number of fission products $N_{\mathrm{fp}}=\mathcal{S}^{d}_{5}$ 
+
+This number represents the combination of fission fragments and the other
+daughter isotopes produced by any reaction (decay or neutron induced).
+
+\item The number of other isotopes $N_{\mathrm{O}}=\mathcal{S}^{d}_{6}$ 
+
+This number represents the other depleting isotopes which are not produced by fission or by reaction
+with fission isotopes or fission products but have a depletion chain.
+
+\item The number of stable isotopes $N_{\mathrm{H}}=\mathcal{S}^{d}_{7}$ 
+
+This number represents the non-depleting isotopes producing energy (mainly
+by radiative capture). An isotope is considered to be stable if:
+\begin{itemize}
+\item its radioactive decay constant is zero
+\item the isotope has no father and no daughter
+\item energy is produced by the isotope.
+\end{itemize}
+
+\item The maximum number of depleting reactions, including radioactive decay and
+neutron-induced reactions $M_{\mathrm{R}}=\mathcal{S}^{d}_{8}$ 
+
+\item The maximum number of parent isotopes leading to the production of an isotope in the
+depletion chain $M_{\mathrm{S}}=\mathcal{S}^{d}_{9}$ 
+
+\item The number of energy-dependent fission yield matrices $N_{\mathrm{ndp}}=\mathcal{S}^{d}_{10}$ 
+
+\end{itemize}
+
+\subsection{The depletion sub-directory \dir{depletion} in
+\dir{microlib}}\label{sect:microlibdirdepletion}
+
+The following records and sub-directories will be found on the first level of a
+\dir{depletion} directory:
+
+\begin{DescriptionEnregistrement}{Main records and sub-directories in
+\dir{depletion}}{6.0cm}
+\label{tabl:tabchain}
+\IntEnr
+  {STATE-VECTOR}{$40$}
+  {$\mathcal{S}^{d}_{i}$ is the vector describing the various parameters associated with this data structure,
+  as defined in \Sect{chainlibstate}.}
+\CharEnr
+  {ISOTOPESDEPL}{$(N_{\mathrm{depl}})*12$}
+  {Reference name of the isotopes $\mathsf{NISOD}_{i}$ present in the depletion chain}
+\IntEnr
+  {CHARGEWEIGHT}{$N_{\mathrm{depl}}$}
+  {6-digit (integer number) nuclide identifier with atomic number $Z$ (2
+  digits), mass number $A$ (3 digits) and energy state $E$ (0 for ground state, 1
+  for first excited level, etc.). This identifier is not defined for pseudo
+  fission products.}
+\CharEnr
+  {DEPLETE-IDEN}{$(M_{\mathrm{R}})*8$}
+  {Reference name of the depletion reactions}
+\IntEnr
+  {DEPLETE-REAC}{$M_{\mathrm{R}}\times N_{\mathrm{depl}}$}
+  {$K_{r,i}^{\rm d}$ is the list of identifier for the depletion of an isotope.}
+\RealEnr
+  {DEPLETE-ENER}{$M_{\mathrm{R}}\times N_{\mathrm{depl}}$}{Mev}
+  {$R_{r,i}^{\rm d}$ is the energy produced with each depletion reaction $r$ of the father isotope. If {\tt H-FACTOR}
+  information is available for an isotope $i$, $R_{r,i}^{\rm d}$ contains only decay energy contributions of lumped isotopes
+  produced by reaction $r$.}
+\RealEnr
+  {DEPLETE-DECA}{$N_{\mathrm{depl}}$}{$10^{-8}$ s$^{-1}\ $}
+  {Radioactive decay constants.}
+\IntEnr
+  {PRODUCE-REAC}{$M_{\mathrm{S}}\times N_{\mathrm{depl}}$}
+  {$K_{s,i}^{\rm p}$ is the list of identifier for the production of an isotope.}
+\RealEnr
+  {PRODUCE-RATE}{$M_{\mathrm{S}}\times N_{\mathrm{depl}}$}{1}
+  {$R_{s,i}^{\rm p}$ is the branching ratio associated with each production reaction.}
+\RealEnr
+  {FISSIONYIELD}{$N_{\mathrm{ndp}} \times N_{\mathrm{dfi}}\times N_{\mathrm{dfp}}$}{1}
+  {$Y_{k,{i\to j}}$ is the fission yield for each direct fissile isotope $i$ to each fission fragment $j$ in fission yield
+  macrogroup $k$.}
+\OptRealEnr
+  {ENERGY-YIELD}{$N_{\mathrm{ndp}+1}$}{$N_\mathrm{ndp}\ge 2$}{eV}
+  {$E_{k}^{\rm fiss}$ are the energy limits of fission yield macrogroups.}
+\end{DescriptionEnregistrement}
+
+An isotope $\mathsf{NISO}_{i}$ defined in \Sect{microlibdirmain} is considered
+to be part of the depletion chain only if one can find a value of $1 \le j \le N_{\rm depl}$
+such that $\mathsf{NISO}_{i}= \mathsf{NISOD}_{j}$.
+Some depleting isotopes may be automatically added to the \dir{microlib} directory.
+In this case, the reference name in record {\tt ISOTOPERNAME} is taken equal
+to its reference name in {\tt ISOTOPESDEPL} and the alias name in record
+{\tt ISOTOPESUSED} is taken equal to the
+first 8 characters of its reference name in {\tt ISOTOPESDEPL}, completed by a
+4-digit mixture identifier. If the reference name contains an underscore, the
+alias name is truncated at the first underscore. For example, an isotope
+present in mixture 2 with a reference name equal to {\tt D2O\_3\_P5} is
+translated into an alias name equal to {\tt D2O\blank{5}0002}.
+
+\vskip 0.2cm
+
+The contents of the variables $K_{r,i}^{\rm d}$ is used to identify the type of isotope under
+consideration. For each isotope $i$, $r$ will take
+successively the values $1$ to $M_{\mathrm{D}}$ depending on the type of
+reaction $\mathsf{NREAD}_{r}$ one wishes to analyze, namely
+
+\vskip 0.2cm
+
+\begin{tabular}{|l|l|}
+\hline
+$\mathsf{NREAD}_{1}=${\tt DECAY\blank{3}} & isotope may undergo radioactive decay \\
+$\mathsf{NREAD}_{2}=${\tt NFTOT\blank{3}} & isotope may undergo fission or is a
+fission fragment \\
+& $^{1}_{0}n + ^{A}_{Z}X \to \ ^{A+1-\nu-B}_{Z-Y}U + ^{B}_{Y}V + \nu \ ^{1}_{0}n + \gamma$ \\
+$\mathsf{NREAD}_{3}=${\tt NG\blank{6}} & isotope may undergo neutron capture (mt$=$102) \\
+& $^{1}_{0}n + ^{A}_{Z}X \to \ ^{A+1}_{Z}X + \gamma$ \\
+$\mathsf{NREAD}_{4}=${\tt N2N\blank{5}} & isotope may undergo (n,2n) reaction (mt$=$16) \\
+& $^{1}_{0}n + ^{A}_{Z}X \to \ ^{A-1}_{Z}X + 2 \ ^{1}_{0}n  + \gamma$ \\
+$\mathsf{NREAD}_{5}=${\tt N3N\blank{5}} & isotope may undergo (n,3n) reaction (mt$=$17) \\
+$\mathsf{NREAD}_{6}=${\tt N4N\blank{5}} & isotope may undergo (n,4n) reaction (mt$=$37) \\
+$\mathsf{NREAD}_{7}=${\tt NA\blank{6}} & isotope may undergo (n,$\alpha$) reaction (mt$=$107) \\
+$\mathsf{NREAD}_{8}=${\tt NP\blank{6}} & isotope may undergo (n,p) reaction (mt$=$103) \\
+$\mathsf{NREAD}_{9}=${\tt N2A\blank{5}} & isotope may undergo (n,2$\alpha$) reaction (mt$=$108) \\
+$\mathsf{NREAD}_{10}=${\tt NNP\blank{5}} & isotope may undergo (n,np) reaction (mt$=$28) \\
+$\mathsf{NREAD}_{11}=${\tt ND\blank{6}} & isotope may undergo (n,d) reaction (mt$=$104)\\
+$\mathsf{NREAD}_{12}=${\tt NT\blank{6}} & isotope may undergo (n,t) reaction (mt$=$105) \\
+\hline
+\end{tabular}
+
+\vskip 0.3cm
+
+\noindent where symbols n, $\alpha$, p, d and t represent neutron, alpha particle, proton, deuteron
+and triton, respectively.
+
+\vskip 0.2cm
+
+The contents of the variable $K_{r,i}^{\rm d}$ is used to specify the
+properties of reaction $r$ for each isotope $i$ under consideration.
+Here $K_{r,i}^{\rm d}$ contains two different types of informations, namely
+$d(r)$ and $i(r)$ which are defined as follows:
+
+\begin{equation}
+  d(r)=K_{r,i}^{\rm d} \bmod \ 100 \ \ \ \ {\rm and} \ \ \ \ i(r)={K_{r,i}^{\rm d}  \over 100}
+\end{equation}
+
+\noindent where
+
+\begin{displaymath}
+d(r) = \left\{
+\begin{array}{ll}
+0 & \textrm{isotope $i$ does not deplete by reaction $\mathsf{NREAD}_{r}$} \\
+1 & \textrm{isotope $i$ will deplete by reaction $\mathsf{NREAD}_{r}$} \\
+2 & \textrm{isotope $i$ does not deplete by reaction $\mathsf{NREAD}_{r}$ but yields energy production} \\
+3 & \textrm{isotope $i$ is fissile without fission yield. Valid only for $r$ such
+that $\mathsf{NREAD}_{r}=${\tt NFTOT}} \\
+4 & \textrm{isotope $i$ is fissile with fission yield. Valid only for $r$ such
+that $\mathsf{NREAD}_{r}=${\tt NFTOT}} \\
+5 & \textrm{isotope $i$ is a fission fragment. Valid only for $r$ such
+that $\mathsf{NREAD}_{r}=${\tt NFTOT}}
+\end{array} \right.
+\end{displaymath}
+
+\noindent and $i(r)=0$ unless $4\le d(r)\le 5$. When $d(r)=4$, $i(r)$ represents the fissile
+isotope index while for $d(r)=5$, $i(r)$ represents the fission fragment index.
+The fractional yield for the production of the fission fragment $i(r')$ from the
+fissile isotope $i(r)$ is stored in matrix $Y_{i(r)\to i(r')}$.
+The contents of the vector $R_{r,i}^{\rm d}$ is the energy in MeV emitted per
+decay or reaction.
+
+\vskip 0.2cm
+
+The contents of the variables $K_{s,i}^{\rm p}$ is used to identify explicitly the parent isotope
+which can generate the current isotope $i$. The maximum number of parent reaction for this
+depletion chain is $M_{\mathrm{S}}$. $K_{s,i}^{\rm p}$ contains two different types of information,
+namely $r(s)$ and $i(s)$ which are defined as follows:
+
+\begin{equation}
+  r(s)=K_{s,i}^{\rm p}\bmod 100 \ \ \ \ {\rm and} \ \ \ \ i(s)={{K_{s,i}^{\rm p}}\over{100}}
+\end{equation}
+
+\noindent where $r(s)=0$ indicates that the list of parent isotopes is complete while $r(s)>0$
+refers to the reaction type $\mathsf{NREAD}_{r(s)}$ and can take the following values:
+
+\begin{displaymath}
+r(s) = \left\{
+\begin{array}{ll}
+1 & \textrm{isotope $i$ produced by radioactive decay}\\
+2 & \textrm{isotope $i$ produced by fission (this contribution is kept apart from record} \\
+  & \textrm{{\tt 'FISSIONYIELD'})} \\
+3 & \textrm{isotope $i$ produced by neutron capture} \\
+\ge 4 & \textrm{isotope $i$ produced by $\mathsf{NREAD}_{r(s)}$ reaction}
+\end{array} \right.
+\end{displaymath}
+
+In the case where $r(s)>0$, $i(s)$ represents the isotope index associated
+with the parent isotope and $R_{s,i}^{\rm p}$ represents the branching
+ratio in fraction for the production of isotope $\mathsf{NISOD}_{i}$ from a neutron
+reaction with the parent isotope $\mathsf{NISOD}_{i(s)}$.
+
+\goodbreak
+
+\subsection{State vector content for the {\sc shiba} self-shielding sub-directory}\label{sect:ssshibastate}
+
+The dimensioning parameters for the self-shielding sub-directory, which are stored in the state vector
+$\mathcal{S}^{s}$, represent:
+
+\begin{itemize}
+\item The first group for which self-shielding takes place $G_{\mathrm{min}}=\mathcal{S}^{s}_{1}$
+       By default $G_{\mathrm{min}}=N_{g,f}+1$
+
+\item The last group for which self-shielding takes place $G_{\mathrm{max}}=\mathcal{S}^{s}_{2}$
+       By default $G_{\mathrm{max}}=N_{g,e}$
+
+\item The maximum number of iterations in the self-shielding calculation $M_{r}=\mathcal{S}^{s}_{3}$ 
+       
+\item Enabling flag for the Livolant-Jeanpierre normalization $I_{\mathrm{lj}}=\mathcal{S}^{s}_{4}$ 
+       
+\item Enabling flag for the use of Goldstein-Cohen parameters $I_{\mathrm{gc}}=\mathcal{S}^{s}_{5}$ 
+
+\item The transport correction option used in self-shielding $I_{\mathrm{tc}}=\mathcal{S}^{s}_{6}$ 
+\begin{displaymath}
+I_{\mathrm{tc}} = \left\{
+\begin{array}{ll}
+0 & \textrm{no transport correction applied in self-shielding calculation} \\
+1 & \textrm{use transport corrected cross section in self-shielding calculation}
+\end{array} \right.
+\end{displaymath}
+
+\item Type of self-shielding model $I_{\mathrm{level}}=\mathcal{S}^{s}_{7}$ 
+\begin{displaymath}
+I_{\mathrm{level}} = \left\{
+\begin{array}{ll}
+0 & \textrm{Stamm'ler model without distributed self-shielding effects} \\
+1 & \textrm{Stamm'ler model with the Nordheim (PIC) distributed self-shielding model} \\
+2 & \textrm{Stamm'ler model with both Nordheim (PIC) distributed self-shielding model} \\
+  & \textrm{and Riemann integration method.}
+\end{array} \right.
+\end{displaymath}
+
+\item The option to indicate whether a specific flux solver or collision probability matrices
+are used to perform the self-shielding calculation $I_{\mathrm{flux}}=\mathcal{S}^{s}_{8}$
+(see \moc{PIJ} and \moc{ARM} keyword in \moc{SHI:} operator input option)
+\begin{displaymath}
+I_{\mathrm{flux}} = \left\{
+\begin{array}{rl}
+ 1 & \textrm{use a specific flux solver (the \moc{ARM} keyword was selected)} \\
+ 2 & \textrm{use collision probability matrices (the \moc{PIJ} keyword was selected)}
+\end{array} \right.
+\end{displaymath}
+
+\end{itemize}
+
+\subsection{State vector content for the subgroup self-shielding sub-directory}\label{sect:sssubgroupstate}
+
+The dimensioning parameters for the self-shielding sub-directory, which are stored in the state vector
+$\mathcal{S}^{s}$, represent:
+
+\begin{itemize}
+\item The first group for which self-shielding takes place $G_{\mathrm{min}}=\mathcal{S}^{s}_{1}$
+       By default $G_{\mathrm{min}}=N_{g,f}+1$
+
+\item The last group for which self-shielding takes place $G_{\mathrm{max}}=\mathcal{S}^{s}_{2}$
+       By default $G_{\mathrm{max}}=N_{g,e}$
+       
+\item SPH enabling flag $I_{\mathrm{sph}}=\mathcal{S}^{s}_{3}$ 
+
+\begin{displaymath}
+I_{\mathrm{sph}} = \left\{
+\begin{array}{ll}
+0 & \textrm{skip the multigroup equivalence procedure} \\
+1 & \textrm{perform a multigroup equivalence procedure (SPH procedure or} \\
+  & \textrm{Livolant-Jeanpierre equivalence)}
+\end{array} \right.
+\end{displaymath}
+
+\item The transport correction option used in self-shielding $I_{\mathrm{tc}}=\mathcal{S}^{s}_{4}$ 
+\begin{displaymath}
+I_{\mathrm{tc}} = \left\{
+\begin{array}{ll}
+0 & \textrm{no transport correction applied in self-shielding calculation} \\
+1 & \textrm{use transport corrected cross section in self-shielding calculation}
+\end{array} \right.
+\end{displaymath}
+
+\item The number of iterations in the self-shielding calculation $M_{r}=\mathcal{S}^{s}_{5}$ 
+
+\item The option to indicate whether a specific flux solver or collision probability matrices
+are used to perform the self-shielding calculation $I_{\mathrm{flux}}=\mathcal{S}^{s}_{6}$
+(see \moc{PIJ} and \moc{ARM} keyword in \moc{USS:} operator input option)
+\begin{displaymath}
+I_{\mathrm{flux}} = \left\{
+\begin{array}{rl}
+ 1 & \textrm{use a specific flux solver (the \moc{ARM} keyword was selected)} \\
+ 2 & \textrm{use collision probability matrices (the \moc{PIJ} keyword was selected)} 
+\end{array} \right.
+\end{displaymath}
+
+\item The $\gamma$ factor enabling flag $I_{\mathrm{\gamma}}=\mathcal{S}^{s}_{7}$. These factors
+are used to represent the moderator absorption effect in the Sanchez--Coste self-shielding method.
+\begin{displaymath}
+I_{\mathrm{\gamma}} = \left\{
+\begin{array}{ll}
+0 & \textrm{the $\gamma$ factors are set to 1.0} \\
+1 & \textrm{the $\gamma$ factors are computed}
+\end{array} \right.
+\end{displaymath}
+
+\item The simplified self-shielding enabling flag $I_{\mathrm{calc}}=\mathcal{S}^{s}_{8}$ 
+\begin{displaymath}
+I_{\mathrm{calc}} = \left\{
+\begin{array}{ll}
+0 & \textrm{perform a delailed self-shielding calculation} \\
+1 & \textrm{perform a simplified self-shielding calculation using data recovered from the} \\
+ & {\tt -DATA-CALC-} \textrm{ directory}
+\end{array} \right.
+\end{displaymath}
+
+\item The flag for ignoring the activation of the mutual resonance shielding model $I_{\mathrm{noco}}=\mathcal{S}^{s}_{9}$ 
+\begin{displaymath}
+I_{\mathrm{noco}} = \left\{
+\begin{array}{ll}
+0 & \textrm{follow the directives set by {\tt LIB}} \\
+1 & \textrm{ignore the directives set by {\tt LIB}}
+\end{array} \right.
+\end{displaymath}
+
+\item Maximum number of fixed point iterations for the ST scattering source convergence $I_{\mathrm{max}}=\mathcal{S}^{s}_{10}$ 
+
+\item Type of elastic slowing-down kernel in Autosecol $I_{\mathrm{ialt}}=\mathcal{S}^{s}_{11}$ 
+\begin{displaymath}
+I_{\mathrm{ialt}} = \left\{
+\begin{array}{ll}
+0 & \textrm{use exact elastic kernel} \\
+1 & \textrm{use an approximate kernel for the resonant isotopes}
+\end{array} \right.
+\end{displaymath}
+
+\item Maximum storage size for the slowing-down kernel values in Autosecol $I_{\mathrm{tra}}=\mathcal{S}^{s}_{12}$ 
+
+\item Normalization flag for the collision probabilities $I_{\mathrm{norm}}=\mathcal{S}^{s}_{13}$ 
+\begin{displaymath}
+I_{\mathrm{norm}} = \left\{
+\begin{array}{ll}
+0 & \textrm{no normalization} \\
+1 & \textrm{remove any remaining leakage from collision probabilities}
+\end{array} \right.
+\end{displaymath}
+
+\item Seed integer used by the random number generator $I_{\mathrm{seed}}=\mathcal{S}^{s}_{14}$.
+
+\end{itemize}
+
+\clearpage
+
+\subsection{The {\sc shiba} self-shielding sub-directory \dir{selfshield} in
+\dir{microlib}}\label{sect:shibadirselfshield}
+
+\begin{DescriptionEnregistrement}{Main records and sub-directories in \dir{selfshield}}{7.5cm}
+\IntEnr
+  {STATE-VECTOR}{$40$}
+  {Vector describing the various parameters associated with this data structure $\mathcal{S}^{s}_{i}$,
+  as defined in \Sect{ssshibastate}.}
+\RealEnr
+  {EPS-SHIBA\blank{3}}{$1$}{1}
+  {Value of the relative convergence criterion for the self-shielding iterations in {\tt SHI:}. }
+\end{DescriptionEnregistrement}
+
+\subsection{The subgroup self-shielding sub-directory \dir{uss-selfshield} in
+\dir{microlib}}\label{sect:subgroupdirselfshield}
+
+\begin{DescriptionEnregistrement}{Main records and sub-directories in \dir{uss-selfshield}}{7.5cm}
+\IntEnr
+  {STATE-VECTOR}{$40$}
+  {Vector describing the various parameters associated with this data structure $\mathcal{S}^{s}_{i}$,
+  as defined in \Sect{sssubgroupstate}.}
+\OptDirEnr
+  {-DATA-CALC-\blank{1}}{$I_{\mathrm{calc}} = 1$}
+  {Name of directory containing the data required by a simplified self-shielding
+  calculation. This type of calculation allows the definition of a single
+  self-shielded isotope in several resonant mixtures.}
+\DirVar
+  {\listedir{isodir}}
+  {List of sub-directories that contain isotopic subgroup information collected by the {\tt USS:} module.}
+\end{DescriptionEnregistrement}
+
+The list of directory \listedir{isodir} named $\mathsf{ISODIR}$ will be composed according to
+\begin{quote}
+\verb|WRITE(|$\mathsf{ISODIR}$,\verb|'(1HC,I5,1H/,I5)')| $iso$,$nbiso$
+\end{quote}
+\noindent where $iso$ is the isotope index and $nbiso$ is the total number of isotopes. \listedir{isodir} is defined in Table~\ref{table:isodir}.
+
+\begin{DescriptionEnregistrement}{Main records and sub-directories in \listedir{isodir}}{7.5cm}\label{table:isodir}
+\DirVar
+  {\listedir{cordir}}
+  {List of sub-directories that contain correlated isotopic subgroup information collected by the {\tt USS:} module.}
+\end{DescriptionEnregistrement}
+
+The list of directory \listedir{cordir} named $\mathsf{CORDIR}$ will be composed according to
+\begin{quote}
+\verb|WRITE(|$\mathsf{CORDIR}$,\verb|'(3HCOR,I4,1H/,I4)')| $ires$,$nires$
+\end{quote}
+\noindent where $ires$ is the correlated isotope index and $nires$ is the total number of correlated isotopes. \listedir{cordir} is defined
+in Table~\ref{table:cordir}.
+
+\begin{DescriptionEnregistrement}{Main records and sub-directories in \listedir{cordir}}{7.5cm}\label{table:cordir}
+\DirlEnr
+  {NWT0-PT\blank{5}}{$G$}
+  {List of real arrays. Each component of this list contains subgroup flux information in correlated fuel regions, as computed by {\tt USS:}.
+  Each real array has dimension $N_{\rm nbnrs}\times K_g$, where $N_{\rm nbnrs}$ is the number of correlated fuel regions and $K_g$ is the
+  number of base points in energy group $g$.}
+\OptDirlEnr
+  {ASSEMB-PHYS\blank{1}}{$N_{\rm asm}$}{$I_{\mathrm{calc}} = 1$}
+  {List of {\sc assemb-phys} directories. Each component of this list contains subgroup assembly information for the subgroup method with
+  physical probability tables. The specification of this directory is given in Sect.~\ref{sect:asminfodhdirgroup} or~\ref{sect:asminfodirgroup}
+  depending if a double-heterogeneity is present or not. A double-heterogeneity is present if $\mathcal{S}^{t}_{40}=1$
+  in the {\sc tracking} object.}
+\OptDirlEnr
+  {ASSEMB-RIBON}{$N_{\rm asm}$}{$I_{\mathrm{calc}} = 3,4$}
+  {List of {\sc assemb-ribon} directories. Each component of this list contains subgroup assembly information for the subgroup projection
+  or Ribon extended method. The specification of this directory is given in Sect.~\ref{sect:asminfodhdirgroup} or~\ref{sect:asminfodirgroup}
+  depending if a double-heterogeneity is present or not. A double-heterogeneity is present if $\mathcal{S}^{t}_{40}=1$
+  in the {\sc tracking} object.}
+\OptDirlEnr
+  {ASSEMB-RSE\blank{2}}{$N_{\rm asm}$}{$I_{\mathrm{calc}} = 6$}
+  {List of {\sc assemb-rse} directories. Each component of this list contains subgroup assembly information for the resonance spectrum
+  expansion method. The specification of this directory is given in Sect.~\ref{sect:asminfodhdirgroup} or~\ref{sect:asminfodirgroup}
+  depending if a double-heterogeneity is present or not. A double-heterogeneity is present if $\mathcal{S}^{t}_{40}=1$
+  in the {\sc tracking} object.}
+\end{DescriptionEnregistrement}
+
+\goodbreak
+
+\subsection{Contents of an \dir{isotope} directory}\label{sect:isotopedir}
+
+Each isotope directory always contains a cross section identifier record {\tt SCAT-SAVED\blank{2}}
+which must be used to verify if a given cross section type has
+been saved for this isotope.
+
+\begin{DescriptionEnregistrement}{Isotopic cross section identifier records}{7.5cm}
+\label{tabl:tabiso1}
+\OptCharEnr
+  {ALIAS\blank{7}}{$*12$}{$\mathcal{M} \ge 0$}
+  {Alias character*12 name of a microlib isotope. This record is not provided in {\sc draglib} objects.}
+\IntEnr
+  {SCAT-SAVED\blank{2}}{$L$}
+  {Vector $\kappa^{\rm scat}_{k}$ to identify the various type of
+   Legendre-dependent cross sections saved for this isotope}
+\RealEnr
+  {AWR\blank{9}}{$1$}{nau}
+  {Ratio of the isotope mass divided by the neutron mass}
+\OptDirEnr
+  {PT-TABLE\blank{4}}{$I_{\rm proc}\ge 1$}
+  {Sub-directory containing probability table information, following the specification given in \Sect{pt-table}.
+  $I_{\rm proc}$ is defined in \Sect{microlibdir}. This sub-directory is present in the microlib builded by the {\tt LIB:} module.}
+\end{DescriptionEnregistrement}
+
+Delayed neutron data can be present for some fissile isotopes on the \dir{isotope} directory. If $N_{\rm
+del}\ge 1$ precursor groups are used, the following information is available:
+
+\begin{DescriptionEnregistrement}{Delayed neutron reaction
+records}{7.5cm}
+\label{tabl:tabiso2}
+\OptRealVar
+  {\{nusid\}}{$G$}{$N_{del}\ge 1$}{b}
+  {$\nu\sigma_{{\rm f},\ell}^{{\rm D},g}$: The product of $\sigma_{\rm f}^{g}$, the fission cross section with
+   $\nu_{\ell}^{{\rm D},g}$, the averaged number of fission--emitted delayed
+   neutron produced in the precursor group $\ell$.}
+\OptRealVar
+  {\{chid\}}{$G$}{$N_{del}\ge 1$}{1}
+  {$\chi^{{\rm D},g}_\ell$: Delayed fission spectrum, normalized to one, for the delayed fission
+   neutrons in precursor group $\ell$.}
+\OptRealEnr
+  {LAMBDA-D\blank{4}}{$N_{\rm del}$}{$N_{\rm del}\ge 1$}{s$^{-1}$}
+  {$\lambda^{\rm D}_\ell$: Decay constant associated with the precursor group $\ell$. We must have
+   $0 <\lambda^{\rm D}_\ell<\lambda^{\rm D}_{\ell+1}$.}
+\end{DescriptionEnregistrement}
+
+The delayed component of the fission yields in each precursor group $\ell$ is given as
+$\nu_\ell^{{\rm D},g}$. The quantities $\pi^{{\rm D},g}$ and $\nu_\ell^{{\rm D},g} \ \sigma_{\rm f}^g$ are defined as
+$$\pi^{{\rm D},g}={\nu^{{\rm D},g} \ \sigma_{\rm f}^g \over
+   \left( \nu^g \sigma_{\rm f}^g \right)^{\rm ss}} \ \ .$$
+
+\noindent and
+
+$$\nu_\ell^{{\rm D},g} \ \sigma_{\rm f}^g=\omega_\ell \ \pi^{{\rm D},g} \
+   \left( \nu^g \sigma_{\rm f}^g \right)^{\rm ss}$$
+
+\noindent where the superscript ${\rm ss}$ indicates steady-state values. The
+delayed neutron records {\sl \{nusid\}} and {\sl \{chid\}} will be
+composed, using the following FORTRAN instructions, as $\mathsf{NUSIGD}$ and $\mathsf{CHID}$:
+  \begin{displaymath}
+    \mathtt{WRITE(}\mathsf{NUSIGD}\mathtt{,'(A6,I2.2)')} \ \mathtt{'NUSIGF'},ell
+  \end{displaymath}
+  \begin{displaymath}
+    \mathtt{WRITE(}\mathsf{CHID}\mathtt{,'(A3,I2.2)')} \ \mathtt{'CHI'},ell
+  \end{displaymath}
+for $1\leq ell \leq N_{\rm del}$. For example, in the case where two group cross sections are considered
+($N_{\rm del}=2$), the following records would be generated:
+
+\begin{DescriptionEnregistrement}{Example of delayed--neutron records in
+\dir{isotope}}{8.0cm}
+\OptRealEnr
+  {NUSIGF01\blank{4}}{$G$}{$N_{\rm del}\ge 1$}{b}
+  {$\nu\sigma_{{\rm f},1}^{{\rm D},g}$: The product of $\sigma_{\rm f}^{g}$, the fission cross section with
+   $\nu_1^{{\rm D},g}$, the averaged number of fission--emitted delayed
+   neutron produced in the precursor group 1.}
+\OptRealEnr
+  {NUSIGF02\blank{4}}{$G$}{$N_{\rm del}\ge 2$}{b}
+  {$\nu\sigma_{{\rm f},2}^{{\rm D},g}$: The product of $\sigma_{\rm f}^{g}$, the fission cross section with
+   $\nu_2^{{\rm D},g}$, the averaged number of fission--emitted delayed
+   neutron produced in the precursor group 2.}
+\OptRealEnr
+  {CHI01\blank{7}}{$G$}{$N_{\rm del}\ge 1$}{1}
+  {$\chi^{{\rm D},g}_1$: Delayed fission spectrum,
+   normalized to one, for the delayed fission neutrons in
+   precursor group 1.}
+\OptRealEnr
+  {CHI02\blank{7}}{$G$}{$N_{\rm del}\ge 2$}{1}
+  {$\chi^{{\rm D},g}_2$: Delayed fission spectrum,
+   normalized to one, for the delayed fission neutrons in
+   precursor group 2.}
+\end{DescriptionEnregistrement}
+
+\vskip 0.2cm
+
+In cases where the /isotope/ directory is produced by the edition module, some
+depletion-related information may be available in this directory, in order to facilitate
+subsequent data processing. This information is described in
+Table~\ref{tabl:tabiso3}.
+
+\begin{DescriptionEnregistrement}{Depletion-related information}{7.5cm}
+\label{tabl:tabiso3}
+\OptRealEnr
+  {MEVG\blank{8}}{$1$}{$N_d \ge 1$}{MeV}
+  {Energy in MeV produced by radiative capture. $N_d$ is defined in \Sect{microlibdir}.}
+\OptRealEnr
+  {MEVF\blank{8}}{$1$}{$N_d \ge 1$}{MeV}
+  {Energy in MeV produced by fission.}
+\OptRealEnr
+  {DECAY\blank{7}}{$1$}{$N_d \ge 1$}{10$^{-8}$ s$^{-1}$}
+  {Radioactive decay constant}
+\OptRealEnr
+  {YIELD\blank{7}}{$G+1$}{$N_d \ge 1$}{1}
+  {Fission fragment yield per energy group. The first value is the average yield
+  over all the energy spectrum. This record is given only for fission fragments.}
+\OptIntEnr
+  {PIFI\blank{8}}{$N_{\rm dfi}$}{$N_{\rm dfi} \ge 1$}
+  {Position in {\tt ISOTOPESUSED} of the mother fissile isotopes. This record is
+  given only for fission fragments.}
+\OptRealEnr
+  {PYIELD\blank{6}}{$N_{\rm dfi}$}{$N_{\rm dfi} \ge 1$}{1}
+  {Fission product yield per fissile isotope. This record is given only for
+  fission fragments.}
+\end{DescriptionEnregistrement}
+
+\vskip 0.2cm
+
+We will first consider the more usual case where constant vector reactions are
+stored on the isotopic directory. A typical example of the microscopic cross
+section directory may be:
+
+\begin{DescriptionEnregistrement}{Example of isotopic vector reaction records}{7.0cm}
+\label{tabl:tabiso4}
+\RealEnr
+  {NTOT0\blank{7}}{$G$}{b}
+  {The $\phi$--weighted multigroup total cross section $\sigma_0^{g}$}
+\RealEnr
+  {TRANC\blank{7}}{$G$}{b} 
+  {The multigroup transport correction $\sigma_{tc}^{g}$}
+\RealEnr
+  {NUSIGF\blank{6}}{$G$}{b} 
+  {The product of $\sigma_{f}^{g}$, the multigroup fission cross section with
+   $\nu^{g}$, the steady-state number of neutron produced per fission,
+   $\nu\sigma_{f}^{{\rm ss},g}$}
+\RealEnr
+  {NFTOT\blank{7}}{$G$}{b}
+  {The multigroup fission cross section $\sigma_{f}^{g}$}
+\OptRealEnr
+  {CHI\blank{9}}{$G$}{$G_{\rm chi}=0$}{}
+  {The multigroup energy spectrum of the neutron emitted by fission $\chi^{g}$}
+\OptRealEnr
+  {CHI--01\blank{5}}{$G$}{$G_{\rm chi}\ge 1$}{}
+  {The first energy-dependent multigroup energy spectrum of the neutron emitted by fission $\chi^{g,1}$}
+\OptRealEnr
+  {CHI--02\blank{5}}{$G$}{$G_{\rm chi}\ge 2$}{}
+  {The second energy-dependent multigroup energy spectrum of the neutron emitted by fission $\chi^{g,2}$}
+\OptRealEnr
+  {CHI--03\blank{5}}{$G$}{$G_{\rm chi}\ge 3$}{}
+  {The third energy-dependent multigroup energy spectrum of the neutron emitted by fission $\chi^{g,3}$}
+\OptRealEnr
+  {CHI--04\blank{5}}{$G$}{$G_{\rm chi}\ge 4$}{}
+  {The fourth energy-dependent multigroup energy spectrum of the neutron emitted by fission $\chi^{g,4}$}
+\RealEnr
+  {NG\blank{10}}{$G$}{b} 
+  {The multigroup neutron capture cross section $\sigma_{c}^{g}$}
+\RealEnr
+  {H-FACTOR\blank{4}}{$G$}{eV b}
+  {Energy production coefficients $H^{g}$ (product of each microscopic cross section
+  times the energy emitted by this reaction).}
+\OptRealEnr
+  {C-FACTOR\blank{4}}{$G$}{*}{electron b}
+  {Charge deposition coefficients $C^{g}$ (product of each microscopic cross section
+  times the charge deposed by this reaction). Information provided if {\tt PARTICLE}$=${\tt B}, {\tt C} or {\tt P}.}
+\RealEnr
+  {N2N\blank{9}}{$G$}{b} 
+  {The multigroup cross section
+   $\sigma_{(n,2n)}^{g}$ for the reaction 
+   $^{A}_{Z}X+n \to ^{A-1}_{Z}X+2n$}
+\RealEnr
+  {N3N\blank{9}}{$G$}{b} 
+  {The multigroup cross section
+   $\sigma_{(n,3n)}^{g}$ for the reaction 
+   $^{A}_{Z}X+n \to ^{A-2}_{Z}X+3n$}
+\RealEnr
+  {N4N\blank{9}}{$G$}{b} 
+  {The multigroup cross section
+   $\sigma_{(n,4n)}^{g}$ for the reaction 
+   $^{A}_{Z}X+n \to ^{A-3}_{Z}X+4n$}
+\RealEnr
+  {NP\blank{10}}{$G$}{b}
+  {The multigroup cross section
+   $\sigma_{(n,p)}^{g}$ for the reaction 
+   $^{A}_{Z}X+n \to ^{A}_{Z-1}X+p$}
+\RealEnr
+  {NA\blank{10}}{$G$}{b}
+  {The multigroup cross section
+   $\sigma_{(n,\alpha)}^{g}$ for the reaction 
+   $^{A}_{Z}X+n \to ^{A-3}_{Z-2}X+\alpha$ }
+\RealEnr
+  {NGOLD\blank{7}}{$G$}{} 
+  {The multigroup Goldstein-Cohen parameters as recovered from {\tt GIR} array in main \dir{microlib} directory
+   $\lambda^{g}$}
+\RealEnr
+  {NWT0\blank{8}}{$G$}{s$^{-1}$cm$^{-2}$}
+  {The multigroup neutron flux spectrum $\phi_{w}^{g}$} 
+\RealEnr
+  {STRD\blank{8}}{$G$}{b}
+  {The multigroup transport cross section 
+   homogenized over all directions
+   $\sigma_{\rm strd}^{g}$}
+\RealEnr
+  {STRD-X\blank{6}}{$G$}{b} 
+  {The $x-$directed multigroup transport cross
+   section $\sigma_{{\rm strd},x}^{g}$}
+\RealEnr
+  {STRD-Y\blank{6}}{$G$}{b} 
+  {The $y-$directed multigroup transport cross
+   section $\sigma_{{\rm strd},y}^{g}$}
+\RealEnr
+  {STRD-Z\blank{6}}{$G$}{b}
+  {The $z-$directed multigroup transport cross
+   section $\sigma_{{\rm strd},z}^{g}$}
+\RealEnr
+  {OVERV\blank{7}}{$G$}{cm$^{-1}$s}
+  {The average of the inverse neutron velocity \hbox{$<1/v>_{m}^g$}}
+\RealEnr
+  {NTOT1\blank{7}}{$G$}{b}
+  {The ${\cal J}$--weighted multigroup total cross section $\sigma_1^{g}$}
+\RealEnr
+  {NWT1\blank{8}}{$G$}{s$^{-1}$cm$^{-2}$}
+  {The multigroup fundamental current spectrum ${\cal J}_{w}^{g}$} 
+\RealEnr
+  {NWAT0\blank{7}}{$G$}{1}
+  {The multigroup neutron adjoint flux spectrum $\phi_{w}^{*g}$} 
+\RealEnr
+  {NWAT1\blank{7}}{$G$}{1}
+  {The multigroup fundamental adjoint current spectrum ${\cal J}_{w}^{*g}$} 
+\end{DescriptionEnregistrement}
+
+\vskip 0.2cm
+
+We can also use this isotopic directory to store time dependent cross sections in the form of a power series expansion:
+\begin{equation}
+    v_{k}^{g}(t)=\sum_{i=0}^{I} v_{k,i}^{g} t^{i}
+\label{eq:TimeSerie}
+\end{equation}
+where the presence of these various terms is specified using $\kappa_{k}$.
+Note that the last three characters of each of the records in Table~\ref{tabl:tabiso4} correspond to the extension $\mathsf{EXT}$=\verb*|'   '| that is
+associated with term $i=0$ in the power series expansion for the cross sections (see
+\Eq{TimeSerie}). For $i=1, 2$, the extension takes successively the value $\mathsf{EXT}$=\verb*|'LIN'| and $\mathsf{EXT}$=\verb*|'QUA'|.
+For example, if one considers the total cross section and assumes that $F_{i}(\kappa_{1})=1$ for $i=0,2$, then this implies the presence
+of the following additional records in the \dir{isotope}:
+
+\begin{DescriptionEnregistrement}{Additional total cross section records for $I=2$}{6.0cm}
+\RealEnr
+  {TOTAL\blank{4}LIN}{$G$}{d$^{-1}$b}
+  {array  $v_{1,1}^{g}=\Delta\sigma^{g}$ containing the first order coefficients in the power series expansion for the multigroup total
+cross section}
+\RealEnr
+  {TOTAL\blank{4}QUA}{$G$}{d$^{-2}$b}
+  {array  $v_{1,2}^{g}=\Delta^{2}\sigma^{g}$ containing the second order coefficients in the power series expansion for the multigroup
+total cross section}
+\end{DescriptionEnregistrement}
+
+\vskip 0.2cm
+
+The multigroup scattering cross section matrix, which gives the probability for a
+neutron in group $h$ to appear in group $g$ after a collision with this isotope
+is represented by the form:
+  \begin{displaymath}
+    \sigma_{s}^{h\to g}(\vec{\Omega}\to\vec{\Omega}')
+      =\sum_{\ell=0}^{L}{{2\ell+1}\over{4\pi}} P_{\ell}(\vec{\Omega}\cdot\vec{\Omega}')
+    \sigma_{\ell}^{h\to g}
+      =\sum_{\ell=0}^{L}\sum_{m=-\ell}^{\ell}
+      Y_{\ell}^{m}(\vec{\Omega})Y_{\ell}^{m}(\vec{\Omega}')\sigma_{\ell}^{h\to g}
+  \end{displaymath}
+using a spherical harmonic series expansion to order $L-1$. Assuming these 
+spherical harmonic are orthonormalized, namely:
+  \begin{displaymath}
+    \int_{4\pi} d^{2}\Omega \ Y_{\ell}^{m}(\vec{\Omega}) Y_{l'}^{m'}(\vec{\Omega})=
+    \delta_{m,m'}\delta_{\ell,\ell'}
+  \end{displaymath}
+we can define $\sigma_{\ell}^{h\to g}$ in terms of $\sigma_{s}^{h\to
+g}(\vec{\Omega}\to\vec{\Omega}')$ using the following integral:
+  \begin{displaymath}
+    \sigma_{\ell}^{h\to g}
+      =\int_{4\pi}d^{2}\Omega \ \sigma_{s}^{h\to g}(\vec{\Omega}\to\vec{\Omega}')
+     P_{\ell}(\vec{\Omega}\cdot\vec{\Omega}')
+  \end{displaymath}
+Note that this definition of $\sigma_{\ell}^{h\to g}$ is not unique and some authors
+include the factor $2l+1$ directly in different angular moments of the 
+scattering cross section.
+
+\vskip 0.2cm
+
+Here instead of storing on these $G\times G$
+matrices $\sigma_{\ell}^{h\to g}$, a vector which contains a compress form for this
+matrix will be considered. This choice is justified by the fact that the number
+of energy groups which will lead to scattering in a specific group is generally
+relatively small compared to the total number of groups in the library and that
+these groups are clustered around the final energy group.
+Here we will first define two different integer vectors $n_{\ell}^{g}$ and
+$h_{\ell}^{g}$ for each order in the scattering cross section and for each final
+energy group $g$ which will contain respectively the number of
+successive initial energy groups for which the scattering cross section does
+not vanish and the maximum energy group number for which scattering to the
+final group $g$ does not vanishes. Accordingly, for a scattering cross section
+of the form:
+
+\begin{center}
+\begin{tabular}{c||cccc}
+$\sigma_{0}^{h\to g}$ &$g=1$   & $g=2$   & $g=3$   & $g=4$    \\ \hline\hline
+$h=1$                 & $a_{1}$ & $a_{2}$ & 0       & 0        \\
+$h=2$                 & 0       & $a_{3}$ & $a_{4}$ & $a_{5}$  \\
+$h=3$                 & 0       & $a_{6}$ & $a_{7}$ & 0        \\
+$h=4$                 & 0       & $a_{8}$ & 0       & $a_{9}$  \\ \hline\hline
+$h_{0}^{g}$           & 1       & 4       & 3       & 4       \\
+$n_{0}^{g}$           & 1       & 4       & 2       & 3        \\
+\end{tabular}
+\end{center}
+
+The compress scattering matrix will then contain the following information:
+  \begin{displaymath}
+    \sigma_{\ell,c}=\left(\sigma_{\ell}^{h^{1}\to 1},\sigma_{\ell}^{h^{1}-1\to 1},
+    \ldots,\sigma_{\ell}^{h^{1}-n_{1}+1\to 1},\sigma_{\ell}^{h^{2}\to
+    2},\ldots,\sigma_{\ell}^{h^{G}-n_{G}+1\to G}\right)
+  \end{displaymath}
+which for the example above leads to
+  \begin{displaymath}
+    \sigma_{\ell,c}=\left(a_{1},a_{8},a_{6},
+                     a_{3},a_{2},a_{7},a_{4},a_{9},0,a_{5}\right)
+  \end{displaymath}
+As a result $\sigma_{\ell}^{h\to g}$ can be
+reconstructed using 
+\begin{displaymath}
+\sigma_{\ell}^{h\to g} = \left\{
+\begin{array}{lll}
+0 & \textrm{if} & h > h_{\ell}^{g}\\
+0 & \textrm{if} & h < h_{\ell}^{g}-n_{\ell}^{g}+1\\
+\sigma_{\ell,c}^{k} & \textrm{otherwise} & k=\sum_{h=1}^{g-1} n_{\ell}^{h} +
+h_{\ell}^{g}-h+1
+\end{array} \right.
+\end{displaymath}
+
+Finally, we will also save the total scattering cross section vector of order
+$\ell$ which is defined as 
+  \begin{displaymath}
+    \sigma_{\ell,s}^{h}=\sum_{g=1}^{G} \sigma_{\ell}^{h\to g}
+  \end{displaymath}
+In the case where only the order $\ell=0$ moment of scattering cross section is non
+vanishing (isotropic scattering) the following records can be found on the
+isotopic directory.
+
+\begin{DescriptionEnregistrement}{Optional scattering records}{7.0cm}
+\label{tabl:tabiso5}
+\RealEnr
+ {SIGS00\blank{6}}{$G$}{b}
+ {The isotropic component ($\ell=0$) of the multigroup total scattering cross
+  section
+  $\sigma_{0,s}^{g}$}
+\IntEnr
+  {IJJS00\blank{6}}{$G$}
+  {Highest energy group number for which 
+   the isotropic component of the scattering cross section to group $g$ does not
+   vanish, $h_{0}^{g}$}
+\IntEnr
+  {NJJS00\blank{6}}{$G$}
+  {Number of energy groups for which 
+   the isotropic component of the scattering cross section to group $g$ does not
+   vanish, $n_{0}^{g}$}
+\RealEnr
+  {SCAT00\blank{6}}{$\sum_{g=1}^{G} n_{0}^{g}$}{b}
+  {Compressed isotropic component of the scattering matrix
+   $\sigma_{0,c}^{k}$}
+\OptDirVar
+  {\listedir{subiso}}{$I_{\rm part}\ge 1$}
+  {Set of sub-directories containing scattering information towards a companion particle. \listedir{subiso}
+  is the name of the companion particle (set to {\tt N}, {\tt G}, {\tt B}, {\tt C} or {\tt P}). This information
+  is used to construct coupled sets of cross sections.}
+\end{DescriptionEnregistrement}
+
+If the scattering cross section is
+expanded to order $L>1$ in Legendre polynomials, additional set of scattering
+records similar to those described above will be presentin the cross section directory.
+The first four characters and last 6 characters in the names of
+these records will again be identical to those described above while character 5
+and 6 will differ from level to level. For example, the order
+$\ell=5$ compressed scattering matrix will be identified by
+\texttt{SCAT05\blank{6}} while for order 
+$\ell=50$ we will use \texttt{SCAT50\blank{6}}.
+
+\vskip 0.2cm
+
+The {\tt STRD} cross sections are normalized in such a way to permit the
+calculation of a diffusion coefficient using the following formula:
+
+\begin{equation}
+D^g={\displaystyle 1\over\displaystyle 3 \ \sum_i N_i \ \sigma_{{\rm strd},i}^g}
+\end{equation}
+
+\noindent where $N_i$ is the isotopic density of isotope $i$ and $\sigma_{{\rm strd},i}^g$
+is the {\tt STRD} cross section of isotope $i$ in energy group $g$. The sum is
+performed over {\sl all} isotopes present in the mixture. The {\tt STRD} cross
+sections for isotope $i$ are defined as
+
+\begin{eqnarray}
+\sigma_{{\rm strd},i}^g&=&{1\over (\mu^g)^2} \ {\left<\phi \right>_g \over 3
+\left<(\Sigma_1-\Sigma_{\rm s1}){\cal J}\right>_g} \ (\sigma_{1,i}^g-\sigma_{{\rm
+s1},i}^g) \ \
+\ {\rm if \ a \ streaming \ model \ is \ used} \\
+&=&{1\over (\mu^g)^2} \ {\left<\phi \right>_g^2 \over 3 \left< D \phi \right>_g
+\left<(\Sigma_0-\Sigma_{\rm s1})\phi\right>_g} \ (\sigma_{0,i}^g-\sigma_{{\rm
+s1},i}^g) \ \
+\ {\rm if \ no \ streaming \ model \ used}
+\end{eqnarray}
+\noindent where
+
+\begin{description}
+\item [$\phi^g$] fundamental flux
+\item [${\cal J}^g$] fundamental current
+\item [$\mu^g$] SPH equivalence factor
+\item [$\Sigma_0^g$] $\phi$--weighted macroscopic total cross section of the
+mixture
+\item [$\Sigma_1^g$] ${\cal J}$--weighted macroscopic total cross section of the
+mixture
+\item [$\Sigma_{\rm s1}^g$] macroscopic $P_1$ scattering cross section of the
+mixture (${\cal J}$--weighted
+if a streaming model is used; $\phi$--weighted if no streaming model used)
+\item [$D^g$] diffusion coefficient
+\item [$\sigma_{0,i}^g$] $\phi$--weighted microscopic total cross section for
+isotope $i$
+\item [$\sigma_{1,i}^g$] ${\cal J}$--weighted microscopic total cross section for
+isotope $i$
+\item [$\sigma_{{\rm s1}.i}^g$] microscopic $P_1$ scattering cross section for
+isotope $i$ (${\cal J}$--weighted
+if a streaming model is used; $\phi$--weighted if no streaming model used)
+\end{description}
+
+\vskip 0.2cm
+
+On the other hand the so-called directional cross
+section {\tt STRD\blank{1}X}, {\tt STRD\blank{1}Y}
+and {\tt STRD\blank{1}Z} are obtained in such a way that
+
+\begin{equation}
+D_k^g={\displaystyle 1\over\displaystyle 3 \ \sum_i N_i \ \sigma_{{\rm strd},k,i}^g}
+\ ; \ \ \ k=x,\ y \ {\rm or} \ z \ \ \ .
+\end{equation}
+
+\vskip 0.2cm
+
+For example, for an isotope with only total and scattering cross sections, we will find the
+following records on the cross section directory.
+
+\begin{DescriptionEnregistrement}{Example of cross section records}{7.5cm}
+\RealEnr
+  {NTOT0\blank{7}}{$G$}{b}
+  {The multigroup total cross section $\sigma^{g}$}
+\RealEnr
+ {SIGS00\blank{6}}{$G$}{b}
+ {The isotropic component ($\ell=1$)of the multigroup total scattering cross
+  section
+  $\sigma_{0,s}^{g}$}
+\IntEnr
+  {IJJS00\blank{6}}{$G$}
+  {Highest energy group number for which 
+   the isotropic component of the scattering cross section to group $g$ does not
+   vanishes, $h_{0}^{g}$}
+\IntEnr
+  {IJJS00\blank{3}}{$G$}
+  {Highest energy group number for which the first order perturbation in
+   the isotropic component of the scattering cross section to group $g$ does not
+   vanishes, $h_{0,1}^{g}$}
+\IntEnr
+  {NJJS00\blank{6}}{$G$}
+  {Number of energy groups for which 
+   the isotropic component of the scattering cross section to group $g$ does not
+   vanishes, $n_{0}^{g}$}
+\RealEnr
+  {SCAT00\blank{6}}{$\sum_{g=1}^{G} n_{0}^{g}$}{b}
+  {Compressed isotropic component of the scattering matrix
+   $\sigma_{0,c}^{k}$}
+\RealEnr
+ {SIGS01\blank{6}}{$G$}{b}
+ {The linearly anisotropic component ($\ell=1$) 
+  of the multigroup total scattering cross section 
+  $\sigma_{1,s}^{g}$}
+\IntEnr
+  {IJJS01\blank{6}}{$G$}
+  {Highest energy group number for which 
+   the linearly anisotropic component of the scattering cross section
+   to group $g$ does not vanishes,
+   $h_{1}^{g}$}
+\IntEnr
+  {NJJS01\blank{6}}{$G$}
+  {Number of energy groups for which 
+   the linearly anisotropic component of the scattering cross section 
+   to group $g$ does not vanishes,
+   $n_{1}^{g}$}
+\RealEnr
+  {SCAT01\blank{6}}{$\sum_{g=1}^{G} n_{1}^{g}$}{b}
+  {Compressed linearly anisotropic component of the scattering matrix
+   $\sigma_{1,c}^{k}$}
+\end{DescriptionEnregistrement}
+
+Note that most of these cross sections are not required to perform a cell
+calculation. In fact, in a typical transport calculation, only
+$\sigma^{g}$, $\sigma_{tc}^{g}$, $\nu\sigma_{f}^{g}$, $\chi^{g}$ and the
+isotropic and linearly anisotropic scattering matrix are
+used. For burnup calculations, depending on the depletion chain prescribed,
+the following cross sections may be required:
+$\sigma_{f}^{g}$, $\sigma_{c}^{g}$, $\sigma_{(n,2n)}^{g}$, $\sigma_{(n,3n)}^{g}$,
+$\sigma_{(n,4n)}^{g}$, $\sigma_{(n,p)}^{g}$, $\sigma_{(n,\alpha)}^{g}$.
+Finally, when editing isotopic cross sections, all the cross sections types in
+the library will be processed.
+
+\vskip 0.15cm
+
+A final note on the use of the transport correction and the homogenized and
+directional transport cross section. In DARGON, the transport correction cross
+section is used to correct the total and isotropic scattering cross
+section using the relations
+\begin{eqnarray*}
+\sigma_{c}^{g}       &=& \sigma^{g}         -\sigma_{tc}^{g}\\
+\sigma_{c,0}^{g\to g}&=& \sigma_{0}^{g\to g}-\sigma_{tc}^{g}
+\end{eqnarray*}
+
+\goodbreak
+
+\subsubsection{The probability table directory {\tt PT-TABLE} in \dir{isotope}}\label{sect:pt-table}
+
+Physical probability tables ($I_{\rm proc}=1$) are obtained from a least-square fit of the
+self-shielded cross sections against dilution. Mathematical probability tables ($I_{\rm proc}\ge 3$) are obtained from
+Autolib data using the CALENDF formalism.
+Resonance spectrum expansion (RSE) information ($I_{\rm proc}=6$) is obtained from Autolib data using a singular value decomposition (SVD) of the
+form $\shadowA=\shadowU \shadowW \shadowV^\top$ where
+\begin{description}
+\item[$\shadowA$:] snapshot flux matrix of size $N_{{\rm ufg},g}\times N_{\rm dil}$ recovered from the Draglib or Apollo2 file,
+\item[$\shadowU$:] first orthogonal SVD matrix of size $N_{{\rm ufg},g}\times K_g$,
+\item[$\shadowW$:] singular-value diagonal matrix of size $K_g\times K_g$,
+\item[$\shadowV$:] second orthogonal SVD matrix of size $N_{\rm dil}\times K_g$
+\end{description}
+\noindent where $N_{{\rm ufg},g}$ is the number of ultra-fine groups in coarse group $g$, $N_{\rm dil}$ is the number of snapshot ultra-fine group
+flux distributions in coarse group $g$ (corresponding to the number of dilutions) and $K_g$ is the SVD rank in coarse group $g$.
+
+\begin{DescriptionEnregistrement}{Probability tables or RSE tables in \dir{isotope}}{7.5cm}
+\OptDirlEnr
+  {GROUP-PT\blank{4}}{$G$}{$I_{\rm proc}\ne 6$}
+  {List of energy-group sub-directories. Each component of the list is a directory containing
+  the probability-table information associated with a specific group. See table~\ref{table:pt}.}
+\OptDirlEnr
+  {GROUP-RSE\blank{3}}{$G$}{$I_{\rm proc}= 6$}
+  {List of energy-group sub-directories. Each component of the list is a directory containing
+  the resonance spectrum expansion information associated with a specific coarse group. See table~\ref{table:rse}.}
+\OptDirVar
+  {\listedir{isotope2}}{$I_{\rm proc}= 6$}
+  {Set of sub-directories containing subgroup projection for {\sl isotope2} cross section information with
+  respect of {\sl isotope} base points for the RSE method. Subgroup projection of scattering cross sections is present for all
+  resonant isotopes, even for {\sl isotope2} $\equiv$ {\sl isotope}. Subgroup projection of total cross sections is
+  present only for {\sl isotope2} $\neq$ {\sl isotope}. See table~\ref{table:spmrse}.}
+\IntEnr
+  {NOR\blank{9}}{$G$}
+  {Order $K_g$ of the probability table or of the resonance spectrum expansion tables in each energy group $g$.
+  If $I_{\rm proc}= 6$, the RSE rank $K_g \le N_{\rm dil}$ where $N_{\rm dil}$ is the number of dilutions.}
+\IntEnr
+  {NDEL\blank{8}}{$1$}
+  {Number of delayed neutron precursor groups for this resonant isotope.}
+\OptRealEnr
+  {SVD-EPS\blank{5}}{$1$}{$I_{\rm proc}= 6$}{~}
+  {Rank accuracy of the SVD.}
+\end{DescriptionEnregistrement}
+
+\vskip -0.4cm
+
+\begin{DescriptionEnregistrement}{Group-dependent non-RSE directories in \dir{isotope}}{7.5cm}\label{table:pt}
+\RealEnr
+  {PROB-TABLE\blank{2}}{$12,N_{\rm part}$}{~}
+  {Probability tables. $N_{\rm part}$ is the total number of reactions
+   represented by probability tables. 12 is the maximum allowed order of a
+   probability table.}
+\OptRealEnr
+  {SIGQT-SIGS\blank{2}}{$K_g$}{$I_{\rm proc}=4$}{b}
+  {Probability table in secondary slowing-down cross section.}
+\OptRealEnr
+  {SIGQT-SLOW\blank{2}}{$K_g,K_g$}{$I_{\rm proc}=4$}{b}
+  {Slowing-down correlated weight matrix.}
+\OptRealVar
+  {\listedir{isotope2}}{$K_g,L_g$}{*}{1}
+  {Set of records, each containing the correlated weights
+  between the current total xs and the total xs of {\sl isotope2}. $L_g$ is the
+  order of the probability table for {\sl isotope2}. (*) This data is optional
+  and is provided only if $I_{\rm proc}\ge 3$ and if the mutual self-shielding
+  effect is to be taken into account.}
+\IntEnr
+  {ISM-LIMITS\blank{2}}{$2,L$}
+  {Minimum (index 1) and maximum (index 2) secondary group for each Legendre
+   order of the scattering matrices}
+\end{DescriptionEnregistrement}
+
+\vskip -0.4cm
+
+\begin{DescriptionEnregistrement}{Group-dependent RSE directories in \dir{isotope}}{7.5cm}\label{table:rse}
+\DbleEnr
+  {RSE-TABLE\blank{3}}{$N_{\rm part}, K_g$}{~}
+  {Resonance spectrum expansion (RSE) table $\shadowP_g$. $N_{\rm part}$ is the total number of flux and reactions
+  represented by RSE tables and $K_g$ is the RSE rank (equal to the number of base points). The table is obtained as
+  $$\shadowP_g=\shadowX_g \shadowV_g \shadowW_g^{-1} \shadowT_g$$
+  \noindent where $\shadowX_g$ is a $N_{\rm part} \times N_{\rm dil}$ double precision matrix containing dilution-dependent
+  homogeneous flux and effective cross sections in group $g$, as recovered from the Draglib or Apollo2 file.}
+\DbleEnr
+  {SIGT\_V\blank{6}}{$K_g$}{~}
+  {Double precision vector corresponding to the base points in microscopic total cross sections. These
+  values are the eigenvalues of the linear transformation. These base points are located in the following diagonal matrix:
+  $$\left[{\rm diag}(\sigma^*_{k,g})\right]=\shadowT_g^\top \shadowU_g^\top \left[{\rm diag}(\sigma^{*(m)}_g)\right] \shadowU_g \shadowT_g$$
+  \noindent where $\left[{\rm diag}(\sigma^{*(m)}_g)\right]$ is a $N_{{\rm ufg},g} \times N_{{\rm ufg},g}$ diagonal matrix containing UFG microscopic total cross section values.}
+\DbleEnr
+  {WEIGHT\_V\blank{4}}{$K_g$}{~}
+  {Double precision weight vector $$\bff(\omega)_g={1\over{u_g-u_{g-1}}} \bff(1)^\top \shadowU_g \shadowT_g$$
+  \noindent where $\bff(1)^\top$ is a row vector of ones used to sum over indices $m$ of the UFG mesh.}
+\DbleEnr
+  {GAMMA\_V\blank{5}}{$K_g$}{~}
+  {Double precision gamma vector $$\bff(\gamma)_g=\bff(1)^\top \left[{\rm diag}(\Delta u_g^{(m)})\right] \shadowU_g \shadowT_g .$$}
+\IntEnr
+  {ISM-LIMITS\blank{2}}{$2,L$}
+  {Minimum (index 1) and maximum (index 2) secondary group for each Legendre
+   order of the scattering matrices}
+\end{DescriptionEnregistrement}
+
+\vskip -0.4cm
+
+\begin{DescriptionEnregistrement}{Subgroup projection of {\sl isotope2} for the RSE method}{7.5cm}\label{table:spmrse}
+\OptDirlEnr
+  {SIGT\_M\blank{6}}{$G$}{*}
+  {Set of matrices representing the {\sl subgroup projection} of {\sl isotope2} microscopic total cross sections on {\sl isotope} base
+  points in group $g$. Each matrix of size $K_g \times K_g$ is defined as
+  $$\left[\sigma^{*b/a}_{k,\ell,g}\right]=\shadowT_g^\top \shadowU_g^\top \left[{\rm diag}(\sigma^{*b(m)}_g)\right] \shadowU_g \shadowT_g$$
+  \noindent where $\left[{\rm diag}(\sigma^{*b(m)}_g)\right]$ is a $N_{{\rm ufg},g} \times N_{{\rm ufg},g}$ diagonal matrix containing UFG microscopic total cross section values for {\sl isotope2}.
+  (*) This data is optional and is provided only if {\sl isotope2} is resonant and if {\sl isotope2} $\neq$ {\sl isotope}.}
+\DirlEnr
+  {SCAT\_M\blank{6}}{$n_{\rm pos}$}
+  {Set of matrices representing the {\sl subgroup projection} of {\sl isotope2} microscopic scattering cross sections on {\sl isotope} base
+  points in group $g$. Each matrix of size $K_g \times K_h$ is defined as
+  $$\left[\sigma^{*b/a}_{k,\ell,g\leftarrow h}\right]=\shadowT_g^\top \shadowU_g^\top \left[\sigma^{*b(m\leftarrow n)}_{{\rm s},g \leftarrow h}\right] \shadowU_h \shadowT_h$$
+  \noindent where $\left[\sigma^{*b(m\leftarrow n)}_{{\rm s},g \leftarrow h}\right]$ is a $N_{{\rm ufg},g} \times N_{{\rm ufg},h}$ matrix containing UFG microscopic scattering cross section values for {\sl isotope2}. Here, $n_{\rm pos}$ is the total number of scattering double precision matrices taking into account self-scattering and out-of-group scattering. Record {\sl isotope} (i. e., {\sl isotope2} $\equiv$ {\sl isotope} and $a\equiv b$) is always present.}
+\IntEnr
+  {NJJS00\blank{6}}{$G$}
+  {Bandwidth $n_{{\rm njj},g}$ of records {\tt SCAT\_M} for {\sl isotope2}. $n_{\rm pos}=\sum_g n_{{\rm njj},g}$.}
+\end{DescriptionEnregistrement}
+\eject
-- 
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