[1208] | 1 | \subsection{High energy MC cross section algorithm.} |
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| 2 | |
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| 3 | \hspace{1.0em}To obtain total (see Eq. $(\ref{GM7})$) and elastic |
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| 4 | (see Eq. $(\ref{GM8})$) hadron-nucleus or nucleus-nucleus |
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| 5 | cross section at given initial energy we have to integrate the nucleon |
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| 6 | profile function $\Gamma(\vec{B},s)= 1-S(\vec{B},s)$. |
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| 7 | This is done by the Monte Carlo averaging procedure \cite{Shabelski90}, |
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| 8 | \cite{ZSU84} |
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| 9 | to obtain the $S$-matrix values using Eq. $(\ref{GM9})$. These values |
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| 10 | depend on the squared total c.m. energy of the colliding |
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| 11 | $(i,j)$ pair $s_{ij}=(p_{i}+p_{j})^2$, where |
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| 12 | $p_{i}$ and $p_{j}$ are the particle $4$-momenta, |
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| 13 | respectively. Performing the Monte Carlo averaging one has to pick up |
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| 14 | projectile and target nucleons |
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| 15 | randomly |
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| 16 | according to the weight functions $T([\vec{b}^{A}_{i}])$ and |
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| 17 | $T([\vec{b}^{B}_{j}])$, respectively. |
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| 18 | The last functions represent |
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| 19 | probability densities to find sets of the nucleon impact parameters |
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| 20 | $[\vec{b}^{A}_{i}]$, where $i=1,2,...,A$ and $[\vec{b}^{B}_{j}]$, where |
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| 21 | $j=1,2,...,B$. |
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| 22 | Then by integration over $\vec{B}$ we find the total and elastic |
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| 23 | cross sections. To obtain the elastic differential cross section from |
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| 24 | the Eqs. $(\ref{GM2})$ and $(\ref{GM3})$ we have at first to |
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| 25 | perform the back Fourier transform of the nucleon profile function (see |
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| 26 | Eq. $(\ref{GM6})$). |
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