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+\subsubsection{The {\tt EXCELT:} tracking module}\label{sect:EXCELLData}
+
+The {\tt EXCELT:} module provides an implementation of the collision probability (PIJ) method or of the method of characteristics (MOC).
+The calling specification for this module is:
+
+\begin{DataStructure}{Structure \dstr{EXCELT:}}
+\dusa{TRKNAM} $[$ \dusa{TRKFIL} $]$
+\moc{:=} \moc{EXCELT:} $[$ \dusa{TRKNAM} $]$ $[$ \dusa{TRKFIL} $]$ 
+\dusa{GEONAM} \moc{::}  \dstr{desctrack} \dstr{descexcel}
+\end{DataStructure}
+
+\noindent  where
+\begin{ListeDeDescription}{mmmmmmm}
+
+\item[\dusa{TRKNAM}] {\tt character*12} name of the \dds{tracking} data
+structure that will contain region volume and surface area vectors in
+addition to region identification pointers and other tracking information.
+If \dusa{TRKNAM} also appears on the RHS, the previous tracking 
+parameters will be applied by default on the current geometry.
+
+\item[\dusa{TRKFIL}] {\tt character*12} name of the sequential binary tracking
+file  used to store the tracks lengths. If \dusa{TRKFIL} does not appear, the keyword
+\moc{XCLL} is set automatically. If the user wants to use a tracking file,
+\dusa{TRKFIL} is required for the \moc{EXCELT:} module, either on the LHS, on the RHS or on both sides. In
+the case where \dusa{TRKFIL} appears on both LHS and RHS, the existing tracking
+file is modified by the module while if \dusa{TRKFIL} appears only on the RHS,
+the existing tracking file is read but not modified.
+
+\item[\dusa{GEONAM}] {\tt character*12} name of the \dds{geometry} data
+structure.
+
+\item[\dstr{desctrack}] structure describing the general tracking data (see
+\Sect{TRKData})
+
+\item[\dstr{descexcel}] structure describing the transport tracking data
+specific to \moc{EXCELT:}.
+
+\end{ListeDeDescription}
+
+\vskip 0.15cm
+
+The \moc{EXCELT:} specific tracking data in \dstr{descexcel} is defined as
+
+\begin{DataStructure}{Structure \dstr{descexcel}}
+$[$ \moc{ANIS} \dusa{nanis} $]$ \\
+$[~\{$ \moc{ONEG} $|$ \moc{ALLG} $[$ \moc{BATCH} \dusa{nbatch} $]~|$ \moc{XCLL} $\}~]$ \\
+$[~\{$ \moc{TREG}  $|$ \moc{TMER} $\}~]$ \\
+$[$ $\{$ \moc{PISO} $|$ \moc{PSPC} $[$ \moc{CUT} \dusa{pcut} $]$ $\}$ $]$ \\
+$[~[$ \moc{QUAB} \dusa{iquab} $]~[~\{$ \moc{SAPO} $|$ \moc{HEBE} $|$ \moc{SLSI} $[$ \dusa{frtm} $]~\}~]~]$ \\
+$[$ $\{$ \moc{PRIX} $|$  \moc{PRIY} $|$ \moc{PRIZ} $\}$ \dusa{denspr} $]$ \\
+$[$ $\{$ \moc{LCMD} $|$ \moc{OPP1} $|$ \moc{OGAU} $|$ \moc{GAUS} $|$ \moc{CACA} $|$ \moc{CACB} $\}~[$ \dusa{nmu} $]~]$ \\
+$[$ \moc{TRAK}  $\{$  \moc{TISO} \dusa{nangl} $[$ \dusa{nangl\_z} $]$ \dusa{dens} $[$ \dusa{dens\_z} $]~[$ \moc{CORN} 
+\dusa{pcorn} $]$  $[$ \moc{SYMM} \dusa{isymm} $|$ \moc{NOSY} $]$ $|$ \\
+\moc{TSPC} $[$ \moc{MEDI}  $]$ \dusa{nangl} \dusa{dens} $|$ \moc{HALT} $\}$ $]$ \\
+{\tt ;}
+\end{DataStructure}
+
+\noindent
+where
+
+\begin{ListeDeDescription}{mmmmmmmm}
+
+\item[\moc{ANIS}] keyword to specify the order of scattering anisotropy. 
+
+\item[\dusa{nanis}] order of anisotropy in transport calculation.
+A default value of 1 represents isotropic (or transport-corrected) scattering while a value of 2
+correspond to linearly anisotropic scattering. When anisotropic scattering is considered, user should pay attention to the following points:
+\begin{itemize}
+\item the usage of \moc{DIAG}, \moc{SYME}, \moc{SSYM} keywords in the definition of the geometry is forbidden. Indeed, in \moc{EXCELT:}/\moc{NXT:} tracking procedures, the geometry is ``unfolded'' according to these symmetries : this is incompatible with the integration of the anisotropic moments of the flux; \\
+\item the angular quadratures should be selected paying attention to the restrictions mentioned in this manual in order to ensure the particle conservation.
+\end{itemize}
+
+\item[\moc{ONEG}] keyword to specify that the tracking is read before computing each group-dependent collision
+probability or algebraic collapsing matrix (default value if \dusa{TRKFIL} is set). The tracking file is
+read in each energy group if the method of characteristics (MOC) is used.
+
+\item[\moc{ALLG}] keyword to specify that the tracking is read once and the collision
+probability or algebraic collapsing matrices are computed in many energy groups.  The tracking file is
+read once if the method of characteristics (MOC) is used.
+ 
+\item[\moc{XCLL}] keyword to specify that the tracking is computed {\sl on-demand} (it is not stored on a file) and the
+collision probability matrices are computed in many energy groups. The tracking
+file \dusa{TRKFIL} should {\sl not} be provided (default value if \dusa{TRKFIL} is not set).
+
+\item[\moc{BATCH}] keyword to specify the number of tracks processed by each core for each energy group. OpenMP parallelization is processing each energy group on a different core. The default value is \dusa{nbatch} $=1$.
+
+\item[\dusa{nbatch}] the number of tracks processed by each core. Usually, a value \dusa{nbatch} $\ge 100$ is recommended.
+
+\item[\moc{TREG}] keyword to specify that the normalization procedure of the integration lines activated by keywords \moc{RENO}
+or \moc{REND} in Sect.~\ref{sect:TRKData} is to be performed with respect of the fine volumes as specified in the {\tt KEYFLX} record
+of the tracking object. This is the default option.
+
+\item[\moc{TMER}] keyword to specify that the normalization procedure of the integration lines activated by keywords \moc{RENO}
+or \moc{REND} in Sect.~\ref{sect:TRKData} is to be performed with respect of the {\sl merged volumes} as specified in the {\tt KEYMRG} record
+of the tracking object.
+
+\item[\moc{PISO}] keyword to specify that a collision probability calculation
+with isotropic reflection boundary conditions is required. It is the default
+option if a \moc{TISO} type integration is chosen. To obtain accurate
+transmission probabilities for the isotropic case it is recommended that the
+normalization options in the \moc{ASM:} module be used.
+
+\item[\moc{PSPC}] keyword to specify that  a collision probability calculation
+with specular reflection boundary conditions required; this is the default
+option if a \moc{TSPC} type integration is chosen. This calculation is only
+possible if the file was initially constructed using the \moc{TSPC} option. 
+
+\item[\moc{CUT}] keyword to specify the input of cutting parameters for the
+specular integration.
+
+\item[\dusa{pcut}] real value representing the maximum error allowed on the
+exponential function used for specular collision probability calculations.
+Tracks will be cut at a length such that the error in the probabilities
+resulting from this reduced track will be of the order of \dusa{pcut}. By
+default, there is no cutting of the tracks and \dusa{pcut}=0.0. If this option
+is used in an entirely reflected case, it is preferable to use the \moc{NORM}
+command in the \moc{ASM:} module.
+
+\item[\moc{QUAB}] keyword to specify the number of basis point for the
+numerical integration of each micro-structure in cases involving double
+heterogeneity (Bihet).
+
+\item[\dusa{iquab}] the number of basis point for the numerical integration of
+the collision probabilities in the micro-volumes using the  Gauss-Jacobi
+formula. The values permitted are: 1 to 20, 24, 28, 32 or  64. The default value
+is \dusa{iquab}=5. If \dusa{iquab} is negative, its absolute value will be used in the She-Liu-Shi approach to determine the
+split level in the tracking used to compute the probability collisions.
+
+\item[\moc{SAPO}] use the Sanchez-Pomraning double-heterogeneity model.\cite{sapo}
+
+\item[\moc{HEBE}] use the Hebert double-heterogeneity model (default option).\cite{BIHET}
+
+\item[\moc{SLSI}] use the She-Liu-Shi double-heterogeneity model without shadow effect.\cite{She2017}
+
+\item[\dusa{frtm}] the minimum microstructure volume fraction used to compute the size of the equivalent cylinder in She-Liu-Shi approach. The default value is \dusa{frtm} $=0.05$.
+
+\item[\moc{PRIX}] keyword to specify that a prismatic tracking is considered for a 3D geometry invariant along the $x-$ axis. In this case, the 3D geometry is projected in the $y-z$ plane and a 2D tracking on the projected geometry is performed. This capability is limited to the non-cyclic method of characteristics solver for the time being and a subsequent call to \moc{MCCGT:} is mandatory.
+
+\item[\moc{PRIY}] keyword to specify that a prismatic tracking is considered for a 3D geometry invariant along the $y-$ axis. In this case, the 3D geometry is projected in the $z-x$ plane and a 2D tracking on the projected geometry is performed. This capability is limited to the method of characteristics solver for the time being and a subsequent call to \moc{MCCGT:} is mandatory.
+
+\item[\moc{PRIZ}] keyword to specify that a prismatic tracking is considered for a 3D geometry invariant along the $z-$ axis. In this case, the 3D geometry is projected in the $x-y$ plane and a 2D tracking on the projected geometry is performed. This capability is limited to the method of characteristics solver for the time being and a subsequent call to \moc{MCCGT:} is mandatory.
+
+\item[\dusa{denspr}] real value representing the linear track density (in cm$^{-1}$) to be used for the inline contruction of 3D tracks from 2D tracking when a prismatic tracking is considered.
+
+\item[\moc{LCMD}] keyword to specify that optimized (McDaniel--type) polar integration angles are to be
+selected for the polar quadrature when a prismatic tracking is considered.\cite{LCMD} This is the default option. The conservation is ensured only for isotropic scattering.
+
+\item[\moc{OPP1}] keyword to specify that $P_1$ constrained optimized (McDaniel--type) polar integration angles are to be selected for the polar quadrature when a prismatic tracking is considered.\cite{LeTellierpa} The conservation is ensured only for isotropic and linearly anisotropic scattering.
+
+\item[\moc{OGAU}] keyword to specify that Optimized Gauss polar integration angles are to be
+selected for the method of characteristics.\cite{LCMD,LeTellierpa} The conservation is ensured up to $P_{\dusa{nmu}-1}$ scattering.
+
+\item[\moc{GAUS}] keyword to specify that Gauss-Legendre polar integration angles are to be selected for the polar quadrature when a prismatic tracking is considered. The conservation is ensured up to $P_{\dusa{nmu}-1}$ scattering.
+
+\item[\moc{CACA}] keyword to specify that CACTUS type equal weight polar integration angles are to be
+selected for the polar quadrature when a prismatic tracking is considered.\cite{CACTUS} The conservation is ensured only for isotropic scattering.
+
+\item[\moc{CACB}] keyword to specify that CACTUS type uniformly distributed integration polar angles
+are to be selected for the polar quadrature when a prismatic tracking is considered.\cite{CACTUS} The conservation is ensured only for isotropic scattering.
+
+\item[\dusa{nmu}] user-defined number of polar angles. By default, a value consistent with \dusa{nangl} is computed by the code. For \moc{LCMD}, \moc{OPP1}, \moc{OGAU} quadratures, \dusa{nmu} is limited to 2, 3 or 4.
+
+\item[\moc{TRAK}] keyword to specify the tracking parameters to be used. 
+
+\item[\moc{TISO}] keyword to specify that isotropic tracking parameters will
+be supplied. This is the default tracking option for cluster geometries.
+
+
+\item[\moc{TSPC}] keyword to specify that specular tracking parameters will be
+supplied.
+
+\item[\moc{MEDI}] keyword to specify that instead of selecting the angles
+located at the end of each angular interval, the angles located in the middle of
+these intervals are selected. This is particularly useful if one wants to avoid
+tracking angles that are parallel to the $X-$ or $Y-$axis as its is the case
+when the external region of a \moc{CARCEL} geometry is voided.
+
+\item[\dusa{nangl}] angular quadrature parameter. For applications involving
+3--D cells, the choices are  \dusa{nangl}=2, 4, 8, 10, 12, 14 or 16; these
+angular quadratures  $EQ_{n}$ present a rotational symmetry about the three
+cartesian axes. For 2--D isotropic  applications, any value of  \dusa{nangl} $\ge 2$ may
+be used; equidistant angles will be selected. For 2--D specular applications the
+input value must be of the form $p+1$ where $p$ is a prime number (for example
+$p$=7, 11, etc.); the choice of \dusa{nangl} = 8, 12, 14, 18, 20, 24, or 30 are
+allowed. For cluster type geometries the default value is \dusa{nangl}=10 for
+isotropic cases and \dusa{nangl}=12 for specular cases.
+
+\item[\dusa{nangl\_z}] angular quadrature parameter in the axial $Z$ direction. Used only
+with \dusa{HEXZ} and \dusa{HEXCELZ} geometries.
+
+\item[\dusa{dens}] real value representing the density of the integration
+lines (in $cm^{-1}$ for 2--D cases and $cm^{-2}$ for 3--D cases). This choice of
+density along the plan perpendicular to each angle depends on the geometry of
+the cell to be analyzed. If there are zones of very small volume, a high line
+density is essential. This value will be readjusted by \moc{EXCELT:}. In the case
+of the analysis of a cluster type geometry the default value of this parameter
+is $5/r_{m}$ where $r_{m}$ is the minimum radius of the pins or the
+minimum thickness of an annular ring in the geometry. If the selected value of \dusa{dens}
+is too small, some volumes or surfaces may not be tracked.
+
+\item[\dusa{dens\_z}] real value representing the density of the integration
+lines in the axial $Z$ direction. Used only with \dusa{HEXZ} and \dusa{HEXCELZ} geometries.
+
+\item[\moc{CORN}] keyword to specify that the input of the parameters used to
+treat the corners for the isotropic integration.
+
+\item[\dusa{pcorn}] maximum distance (cm) between a line and the intersection
+of $n\ge 2$ external surfaces where track redistribution will take place. Track
+redistribution will take place if a line comes close to the intersection of
+$n\ge 2$ external surfaces. In this case the line will be replicated $n$ times,
+each of these lines being associated with a different external surface, while
+its weight is reduced by a factor of $1/n$. This allows for a better
+distribution of tracks which are relatively close to $n$ external surfaces. By
+default, there is no treatment of the corners and \dusa{pcorn}=0.0.
+
+\item[\moc{SYMM}] keyword to specify that the geometry has a rotation
+symmetry.
+
+\item[\dusa{isymm}] integer value describing the rotation symmetry of the
+geometry. The fixed default of this parameter is 1.
+
+\item[\moc{NOSY}] \moc{EXCELT:} automatically try to take into account
+geometric symmetries in order to reduce the number of tracks and the CPU
+time. The \moc{NOSY} keyword desactivates this automatic capability.
+
+\item[\moc{HALT}] keyword to specify that the program is to be stopped after
+the analysis of the geometry, without the explicit tracking being performed.
+
+\end{ListeDeDescription}
+\eject