 |
Celeritas 0.6.0-rc.2.12+develop.263d2fcc
|
|
Celeritas 0.6.0-rc.2.12+develop.263d2fcc
|
Calculate the Landau-Pomeranchuk-Migdal (LPM) suppression functions. More...
#include <LPMCalculator.hh>
Classes | |
| struct | LPMFunctions |
| Evaluated LPM suppression functions default to "low energy" values. More... | |
Public Member Functions | |
| CELER_FUNCTION | LPMCalculator (MaterialView const &material, ElementView const &element, bool dielectric_suppression, units::MevEnergy gamma_energy) |
| Construct with LPM data, material data, and photon energy. | |
| CELER_FUNCTION LPMFunctions | operator() (real_type epsilon) |
| Compute the LPM suppression functions. | |
Calculate the Landau-Pomeranchuk-Migdal (LPM) suppression functions.
The LPM effect is the suppression of low-energy photon production due to electron multiple scattering [landau-limits-1953], (migdal-brems-1956) . At high energies and in high density materials, the cross sections for pair production and bremsstrahlung are reduced. The differential cross sections accounting for the LPM effect are expressed in terms of the LPM suppression functions \( \xi(s) \), \( G(s) \), and \( \phi(s) \).
Here \( \epsilon \) is the ratio of the electron (or positron) energy to the photon energy, \( \epsilon = E / k \). As \( \epsilon \to 0 \), the suppression factors all approach unity.
The suppression variable \( s' \) is
\[ s' = \sqrt{\frac{E_\textrm{LPM} k}{8 E \abs{E - k}}} \quad , \]
where \( k < E \) for bremsstrahlung and \( E < k \) for pair production, and
\[ E_\textrm{LPM} \sim 61.5 L \frac{\mathrm{TeV}}{\mathrm{cm}} \]
is approximately the energy (using the radiation length L ) above which the LPM effect is significant.
Calculations of \( \xi(s') \) and \( s = \frac{s'}{\sqrt{\xi(s')}} \) are functional approximations from Eq. 21 in stanev-lpm-1982 .
G4eBremsstrahlungRelModel::ComputeLPMfunctions and G4PairProductionRelModel::GetLPMFunctions . 
1.9.8