1 | %\subsection{The transport algorithm \editor{Gunter}} |
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2 | |
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3 | %\begin{verbatim} |
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4 | %- choose impact |
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5 | %- find collisions |
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6 | %- loop { propagate to next in time collision |
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7 | %- do collision |
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8 | %- check Pauli |
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9 | %- OK |
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10 | %\end{verbatim} |
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11 | |
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12 | For the primary particle an impact parameter is chosen random in a |
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13 | disk outside the nucleus perpendicular to a vector passing through the |
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14 | center of the nucleus coordinate system an being |
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15 | parallel to the momentum direction. |
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16 | Using a straight line trajectory, the distance of closest approach |
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17 | $d_i^{min}$ |
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18 | to each target nucleon $i$ and the corresponding time-of-flight $t_i^d$ |
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19 | is calculated. In this calculation the momentum of the target nucleons |
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20 | is ignored, i.e. the target nucleons do not move. The interaction cross |
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21 | section ${\sigma}_i$ with target nucleons is calculated using total inclusive |
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22 | cross-sections described below. For calculation of the cross-section the |
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23 | momenta of the nucleons are taken into account. |
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24 | The primary particle may interact with those target nucleons where the distance of closest |
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25 | approach $d_i^{min}$ is smaller than |
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26 | $d_i^{min} < \sqrt{\frac{\sigma_i}{\pi}}$. These candidate interactions |
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27 | are called collisions, and these collisions are stored ordered by time-of-flight $t_i^d$. |
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28 | In the case no collision is found, a new impact |
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29 | parameter is chosen. |
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30 | |
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31 | The primary particle is tracked the time-step given by the time to the |
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32 | first collision. As long a particle is outside the nucleus, that is a radius of |
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33 | the outermost nucleon plus $3fm$, particles travel along |
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34 | straight line trajectories. Particles entering the nucleus have their |
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35 | energy corrected for Coulomb effects. Inside the nucleus particles are |
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36 | propagated in the scalar nuclear field. The equation of motion in the field |
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37 | is solved for a given time-step using a Runge-Kutta integration method. |
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38 | |
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39 | At the end of the step, the primary and the nucleon interact suing the |
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40 | scattering term. The resulting secondaries are checked for the Fermi |
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41 | exclusion principle. If any of the two particles has a momentum below |
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42 | Fermi momentum, the interaction is suppressed, and the original primary |
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43 | is tracked to the next collision. In case interaction is allowed, the |
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44 | secondaries are treated like the primary, that is, all possible |
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45 | collisions are calculated like above, with the addition that these new |
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46 | primary particles may be short-lived and may decay. A decay is treated like others |
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47 | collisions, the collision time being the time until the decay of the particle. |
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48 | All secondaries are tracked until they leave the nucleus, or |
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49 | the until the cascade stops. |
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50 | |
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51 | |
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52 | |
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53 | |
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