[1208] | 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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