Ionization¶
Models¶
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class MollerBhabhaInteractor¶
Perform Moller (e-e-) and Bhabha (e+e-) scattering.
This interaction, part of the ionization process, is when an incident electron or positron ejects an electron from the surrounding matter.
Note
This performs the same sampling routine as in Geant4’s G4MollerBhabhaModel class, as documented in section 10.1.4 of the Geant4 Physics Reference (release 10.6).
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template<class EnergySampler>
class MuHadIonizationInteractor¶ Perform the discrete part of the muon or hadron ionization process.
This simulates the production of delta rays by incident muons or hadrons. The same basic sampling routine is used by multiple models, but the energy of the secondary is sampled from a distribution unique to the model.
Note
This performs the same sampling routine as in Geant4’s
G4BetheBlochModel,G4MuBetheBlochModel,G4BraggModel, andG4ICRU73QOModel, as documented in the Geant4 Physics Reference Manual release 11.2 sections 11.1 and 12.1.5.
Distributions¶
The exiting energy distribution from most of these ionization models are sampled using external helper distributions.
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class BetheBlochEnergyDistribution¶
Sample the energy of the delta ray for muon or hadron ionization.
This samples the energy according to the Bethe-Bloch model, as described in the Geant4 Physics Reference Manual release 11.2 section 12.1.5. The Bethe-Bloch differential cross section can be written as
and factorized as\[ \difd{\sigma}{T} = 2\pi r_e^2 mc^2 Z \frac{z_p^2}{\beta^2}\frac{1}{T^2} \left[1 - \beta^2 \frac{T}{T_{max}} + s \frac{T^2}{2E^2} \right] \]with \( T \in [T_{cut}, T_{max}] \), where \( f(T) = \frac{1}{T^2} \), \( g(T) = 1 - \beta^2 \frac{T}{T_max} + s \frac{T^2}{2 E^2} \), \( T \) is the kinetic energy of the electron, \( E \) is the total energy of the incident particle, and \( s \) is 0 for spinless particles and 1 otherwise. The energy is sampled from \( f(T) \) and accepted with probability \( g(T) \).\[ \difd{\sigma}{T} = C f(T) g(T) \]
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class BraggICRU73QOEnergyDistribution¶
Sample the energy of the delta ray for muon or hadron ionization.
This samples the energy according to the Bragg and ICRU73QO models, as described in the Geant4 Physics Reference Manual release 11.2 section 11.1.
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class BhabhaEnergyDistribution¶
Helper class for
MollerBhabhaInteractor.Sample the exiting energy fraction for Bhabha scattering.
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class MollerEnergyDistribution¶
Helper class for
MollerBhabhaInteractor.Sample the exiting energy fraction for Moller scattering.
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class MuBBEnergyDistribution¶
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
\( \sigma_{BB}(E, \epsilon) \) 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).\[ \sigma(E, \epsilon) = \sigma_{BB}(E, \epsilon)\left[1 + \frac{\alpha}{2\pi} \log \left(1 + \frac{2\epsilon}{m_e} \log \left(\frac{4 m_e E(E - \epsilon}{m_{\mu}^2(2\epsilon + m_e)} \right) \right) \right]. \]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 \( g(T) \).