Cross-section, energy loss and range tables

Cross-sections, energy loss $dE/dx$ and range $R(E$_kin)

are tabulated for all materials which enter in the definition of a tracking medium by the routine GPHYSI. The values of the energy for which the tabulated quantities are calculated are stored in the common /GCMULO/ (see [BASE030]). To evaluate one of the tabulated quantities for a particle of kinetic energy $E$₀ , a linear interpolation is used. Let i be such that:

$E$_i< E₀≤E_i+1

The integer variable IEKBIN in common /GCTRACK/ is equal to i during tracking and its value is recomputed by the routine GEKBIN when the energy of the particle changes. If the quantity Y has been tabulated so that $Y$_i= Y(E_i) then the value $Y$₀= Y(E₀) is calculated as:

$Y$₀= Y_i+ {E₀-E_iE_i+1-E_i}( Y_i+1-Y_i)= Y_i( 1 - {E₀-E_iE_i+1-E_i}) +Y_i+1{E₀-E_iE_i+1-E_i}

Inside the code the following quantities are used:

$GEKRAT=\; \{E$₀-E_iE_i+1-E_i}&sp;GEKRT1= ( 1 - {E₀-E_iE_i+1-E_i})

where GEKRAT is in common /GCTRAK/ and GEKRT1 is a local variable recomputed when needed.