source: trunk/documents/UserDoc/DocBookUsersGuides/PhysicsReferenceManual/latex/hadronic/theory_driven/CrossSection/HECrossSectionModelAlgorithm.tex @ 1345

\subsection{High energy MC cross section algorithm.}

\hspace{1.0em}To obtain total (see Eq. $(\ref{GM7})$) and elastic 
(see Eq. $(\ref{GM8})$) hadron-nucleus or nucleus-nucleus
 cross section at given initial energy  we have to integrate the nucleon
 profile function $\Gamma(\vec{B},s)= 1-S(\vec{B},s)$.
 This is done by the Monte Carlo averaging procedure \cite{Shabelski90}, 
 \cite{ZSU84}
  to obtain the $S$-matrix values using Eq. $(\ref{GM9})$. These values
  depend on the squared total c.m.  energy of the colliding
$(i,j)$ pair  $s_{ij}=(p_{i}+p_{j})^2$, where 
  $p_{i}$ and $p_{j}$ are the particle $4$-momenta, 
respectively. Performing the Monte Carlo averaging one has to pick up 
projectile and target nucleons
 randomly
according to the weight functions $T([\vec{b}^{A}_{i}])$ and
$T([\vec{b}^{B}_{j}])$, respectively.
 The last functions represent
probability densities to find sets of the nucleon impact parameters
$[\vec{b}^{A}_{i}]$, where $i=1,2,...,A$ and $[\vec{b}^{B}_{j}]$, where
$j=1,2,...,B$. 
Then by integration over $\vec{B}$ we  find the total and elastic 
cross sections. To obtain the elastic differential cross section from 
the Eqs. $(\ref{GM2})$ and $(\ref{GM3})$ we have at first to
perform the back Fourier transform of the nucleon profile function (see 
Eq. $(\ref{GM6})$).