Method

Let:

$\{d\sigma (E,T)dT\}$

be the differential cross-section for the ejection of an electron with kinetic energy T by an incident $e\pm$ of total energy E moving in a medium of density $\rho$ .

The variable DCUTE in common /GCCUTS/ is the kinetic energy cut-off for the generated $\delta$ -rays. Below this threshold the soft electrons ejected are simulated as continuous energy loss by the incident $e\pm$ , and above it they are explicitly generated.

The mean value of the energy lost by the incident $e\pm$ to the soft $\delta$ -rays is: $E$_soft(E,DCUTE)= ∫₀^DCUTE{d σ(E,T)dT}T &sp;dT

whereas the total cross-section for the ejection of an electron of energy $T\; >\; DCUTE$ is: $\sigma (E,DCUTE)=\; \int$_DCUTE^T_Max{d σ(E,T)dT}&sp;dT

where $T$_Max is the maximum energy transferable to the free electron: $T$_Max=

$E-m$
$(E-m)/2$

$.$

where m is the electron mass. The method of calculation of the continuous energy loss and the total cross-section are explained below. [PHYS331] deals with the explicit simulation of the $\delta$ -rays.

• Continuous energy loss
• Total cross-sections