Subroutines

CALL GFLUCT (DEMEAN,DE*)

DEMEAN

( REAL) average energy loss according to the energy loss tables;

DE

( REAL) actual energy loss.

GFLUCT selects the method to sample the fluctuations around the mean energy loss DEMEAN and returns the energy loss DE in the current step.

If $\delta$ -rays are not produced ( DRAY=0), it calls GLANDG when the current particle and material parameters are in the validity range of Landau theory, GVAVIV when in the range of Vavilov theory, or performs a Gaussian sampling. For fluctuations in small steps GLANDZ is called.

If $\delta$ -rays are produced ( DRAY=1), it calls GLANDZ which, the cut for the $\delta$ -ray production being set, does sampling from restricted formula.

GFLUCT is called from the tracking routines GTELEC, GTHADR and GTMUON when the LOSS flag is set to 1, 2 or 3.

CALL GLANDG (YRAN*)

YRAN

( REAL) random variable distributed according to the Landau distribution;

GLANDG samples from the Landau distribution. It is called from GFLUCT.

GVAVIVVALUE = GVAVIV(RKAPPA,BETA2,RAN)

RKAPPA

( REAL) $\kappa$ parameter of the Vavilov distribution (see below);

BETA2

( REAL) $\beta 2$ of the particle;

RAN

( REAL) random number uniformly distributed in ]0,1[.

GVAVIV samples samples the variable $\lambda =\; \lambda$_v/κ- lnκ , sometimes called the Landau $\lambda$ , where $\lambda$_v is distributed according to the Vavilov distribution. For more details see below. It is called from GFLUCT.

CALL GLANDZ (Z,STEP,P,E,DEDX,DE*,POTI,POTIL)

Z

( REAL) atomic number of the medium;

STEP

( REAL) step size in cm;

P

( REAL) momentum of the particle in GeV $c-1$ ;

E

( REAL) total energy of the particle in GeV;

DEDX

( REAL) average energy loss in the step according to the energy loss tables;

DE

( REAL) actual energy loss in the step;

POTI

( REAL) average ionisation potential for the medium;

POTIL

( REAL) logarithm of the average ionisation potential.

GLANDZ gives the energy loss DE for the current particle with energy E and momentum P in a material of atomic number Z where the average energy loss is DEDX and the current step length STEP. It is called from GFLUCT for restricted Landau fluctuations when $\delta$ -rays are produced or to sample the fluctuations in thin layers (with or without $\delta$ -ray production).