1 | \section{Stopped particle absorption simulation.} |
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2 | |
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3 | \subsection{Mechanism of the stopped particle absorption by a nucleus.} |
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4 | \hspace{1.0em} |
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5 | An absorption of a stopped $\pi^{-}$-meson, $K^{-}$-meson and $\bar{p}$ |
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6 | by a nucleus procceeds in several |
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7 | steps \cite{IKP94}: |
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8 | \begin{enumerate} |
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9 | \item A particle is captured by the Coulomb fiels of a nucleus forming a pionic |
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10 | or a kaonic or $\bar{p}$-atom; |
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11 | \item Such atom de-excites through the emission of Auger-electrons and $X$-rays; |
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12 | \item A stopped particle from the atomic orbit is captured by nucleus ( |
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13 | by a pair or more of intranuclear nucleons in the case of a stopped pion or |
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14 | by reaction on a quasifree nucleon producing a pion and $\Lambda$ or |
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15 | $\Sigma$ hyperon in the case of a stopped kaon or |
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16 | by annihilation on a quasifree nucleon in the case of $\bar{p}$-capture); |
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17 | \item Rescatterings of fast nucleons and pions produced in a stopped |
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18 | particle absorption (hadron |
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19 | kinetics); |
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20 | \item Decay of excited residual nucleus (nucleus deexcitation). |
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21 | \end{enumerate} |
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22 | |
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23 | Thus the absorption processes for the stopped pion, kaon and antiproton are |
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24 | similar. However, there are some absorption |
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25 | peculiarities for each type of particles. |
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26 | |
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27 | \subsection{Absorption of stopped $\pi^{-}$ by nucleus.} |
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28 | \hspace{1.0em} It is simulated by the kinetic model. |
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29 | As follows from calculations within the framework of the optical |
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30 | model \cite{INC76} with the Kisslinger potential \cite{Kiss55} |
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31 | the capture a pion from an orbit of atom takes place at |
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32 | radius $r$ in the |
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33 | nuclear surface and absorption probability $P_{abs}(r)$ can be approximated by |
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34 | \begin{equation} |
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35 | \label{SAS1} P_{abs}(r) = P_0 \exp{[-0.5(\frac{r-R_{\pi}}{D_{\pi}})^2]}, |
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36 | \end{equation} |
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37 | where parameters of the Gaussian distribution $R_{\pi} \approx R_{1/2}$, |
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38 | where $R_{1/2}$ is the half-density radius, and $D_{\pi}$ |
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39 | for different nuclei can be found |
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40 | in \cite{IKP94}. |
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41 | |
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42 | The absorption of the pion is considered as the $s$-wave (non-resonant) |
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43 | absorption mainly by the the simplest cluster consisting of two nucleon |
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44 | $(np)$ or $(pp)$. |
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45 | |
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46 | Once a pion has been absorbed by a nucleon pair, the pion mass is converted |
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47 | into kinetic energy of nucleon. Each nucleon has the energy $E_N = m_{\pi}/2$ |
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48 | in the center of mass pair. In the center of mass nucleons flay away in |
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49 | opposite direction isotropically. |
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50 | The inital momentum of pair is taken as a sum of nucleon Fermi momenta. |
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51 | |
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52 | \subsection{Absorption of stopped $K^{-}$ by nucleus.} |
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53 | \hspace{1.0em} It is simulated in the kinetic model framework. |
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54 | In this case the absorption probability was choosen the same as in |
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55 | annhihilation of the stopped antiprotons. |
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56 | |
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57 | \subsection{Annihilation of stopped $\bar{p}$ by nucleus.} |
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58 | In this case the absorption probability was also given by equation of |
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59 | (\ref{SAS1}) with the values of $R_{\bar{p}} = R_{\pi}$ and dispertion $D^2 = |
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60 | 1$\ fm$^2$ \cite{INC82}. |
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61 | |
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62 | The annhihilation of antiproton on a quasifree nucleon is modelled via the |
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63 | annihilation of a diquark-antidiquark with subsequent fragmentation of the |
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64 | meson string as it was done in the parton string model. |
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