Method

In GEANT, $\delta$ -rays are generated only above a threshold energy $T$_cut which corresponds to the variable DCUTE for electrons and positrons, DCUTM for all other charged particles. The total cross-section for the production of a $\delta$ -ray electron of kinetic energy $T\; >\; T$_cut= DCUTE, DCUTM by a particle of kinetic energy E is: $\sigma (E,T$_cut) = ∫_Tcut^T_max{d σ(E,T)dT}dT

where $T$_max is the maximum energy transferable to the free electron: $T$_max={2m(γ²-1)1+2γ{mM}+ ({mM})²}

The energy lost in ionising collisions producing $\delta$ -rays below $T$_cut

are included in the continuous energy loss. The mean value of the energy lost due to these soft collisions is: $E$_loss(E,T_cut) = ∫₀^T_cutT {d σ(E,T)dT}dT

where m is the electron mass and M is the mass of the incident particle.

In this chapter, the method of calculation of the continuous energy loss and the total cross-section are explained. The generation of $\delta$ -rays is explained in chapter [PHYS331].

• Continuous energy loss
• Total cross-section