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Celeritas
0.5.0-56+6b053cd
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Celeritas
0.5.0-56+6b053cd
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Sample delta ray energy for the muon Bethe-Bloch ionization model. More...
#include <MuBBEnergyDistribution.hh>
Public Types | |
Type aliases | |
| using | Energy = units::MevEnergy |
| using | Mass = units::MevMass |
Public Member Functions | |
| CELER_FUNCTION | MuBBEnergyDistribution (ParticleTrackView const &particle, Energy electron_cutoff, Mass electron_mass) |
| Construct with incident and exiting particle data. | |
| template<class Engine > | |
| CELER_FUNCTION Energy | operator() (Engine &rng) |
| CELER_FUNCTION Energy | min_secondary_energy () const |
| Minimum energy of the secondary electron [MeV]. | |
| CELER_FUNCTION Energy | max_secondary_energy () const |
| Maximum energy of the secondary electron [MeV]. | |
| template<class Engine > | |
| CELER_FUNCTION auto | operator() (Engine &rng) -> Energy |
| Sample secondary electron energy. | |
Sample delta ray energy for the muon Bethe-Bloch ionization model.
8 This samples the energy according to the muon Bethe-Bloch model, as described in the Geant4 Physics Reference Manual release 11.2 section 11.1. At the higher energies for which this model is applied, leading radiative corrections are taken into account. The differential cross section can be written as
\[ \sigma(E, \epsilon) = \sigma_{BB}(E, \epsilon)\left[1 + \frac{\alpha}{2\pi} \log \left(1 + \frac{2\epsilon}{m_e} \log \left(\frac{4 m_e E(E - \epsilon}{m_{\mu}^2(2\epsilon + m_e)} \right) \right) \right]. \]
\( \sigma_{BB}(E, \epsilon) \) is the Bethe-Bloch cross section, \( m_e \) is the electron mass, \( m_{\mu} \) is the muon mass, \( E \) is the total energy of the muon, and \( \epsilon = \omega + T \) is the energy transfer, where \( T \) is the kinetic energy of the electron and \( \omega \) is the energy of the radiative gamma (which is neglected).
As in the Bethe-Bloch model, the energy is sampled by factorizing the cross section as \( \sigma = C f(T) g(T) \), where \( f(T) = \frac{1}{T^2} \) and \( T \in [T_{cut}, T_{max}] \). The energy is sampled from \( f(T) \) and accepted with probability \( g(T) \).
1.9.1