celeritas::TsaiScreeningCalculator Class Reference

Thomas-Fermi screening functions from Tsai. More...

#include <ScreeningFunctions.hh>

Public Types
Type aliases
using	result_type = BhwlScreeningFactors
using	Mass = units::MevMass
using	InvEnergy = RealQuantity< UnitInverse< units::Mev > >

Public Member Functions
CELER_FUNCTION	TsaiScreeningCalculator (Mass gamma_factor, Mass epsilon_factor)
	Construct with gamma and epsilon factors.
CELER_FUNCTION result_type	operator() (InvEnergy delta) const
	Calculate screening function from energy transfer.

Detailed Description

Thomas-Fermi screening functions from Tsai.

This calculates atomic screening factors given by tsai-1974 Eq. 3.30-31, as part of the relativistic bremsstrahlung cross section calculation. This model is valid for \( Z \ge 5 \).

The calculator argument is the fraction

\[ \delta = \frac{k}{E(k - E)} \equiv \frac{2\delta_\mathrm{Tsai}}{m_e} \]

where \(E\) is the kinetic plus rest mass energy of the electron and \(k\) is the photon energy. (For Bremsstrahlung, the electron is incident and photon is exiting.)

The calculated screening functions are:

\[ \begin{aligned} \varphi_1(\gamma) &= 20.863 - 2 \ln \left( 1 + (0.55846\gamma)^2 \right) - 4 \left( 1 - 0.6 \exp(-0.9\gamma) - 0.4 \exp(-1.5\gamma) \right), \\ \varphi_2(\gamma) = \varphi_1(\gamma) - \frac{2}{3} \left( 1 + 6.5\gamma + 6\gamma^2 \right)^{-1}, \\ \psi_1(\epsilon) &= 28.340 - 2 \ln \left( 1 + (3.621\epsilon)^2 \right) - 4 \left( 1 - 0.7 \exp(-8\epsilon) - 0.3 \exp(-29.2\epsilon) \right), \psi_2(\epsilon) &= \psi_1(\epsilon) - \frac{2}{3} \left( 1 + 40\epsilon + 400\epsilon^2 \right)^{-1}. \end{aligned} \]

Here,

\[ \begin{aligned} \gamma &= \frac{100 m_e k}{E (k - E) Z^{1/3}} \\ \epsilon &= \frac{100 m_e k}{E (k - E) Z^{2/3}} \end{aligned} \]

from which we extract input factors precalculated in celeritas::RelativisticBremModel:

\[ f_\gamma = \frac{100 m_e}{Z^{1/3}} \]

and

\[ f_\epsilon = \frac{100 m_e}{Z^{2/3}} \]

See also

RBDiffXsCalculator

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The documentation for this class was generated from the following file:

• ScreeningFunctions.hh