Energy threshold for delta-ray production

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| Geant 3.10  |               GEANT User's Guide              | PHYS333  ##
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Author(s) : M.Maire Submitted: 30.05.86 Origin : Same Revised: 04.06.93

Subroutines

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           |CALL GDRPRT (IPART,IMATE,STEP) |
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This routine is used to inspect the values of relevant parameters linked with the utilisation of Landau fluctuations or delta-rays generation in the tracking. It prints the value of some relevant parameters (see [PHYS332]): T ,z,k and the regime for fluctuations. max

IPART
GEANT particle number;
IMATE
GEANT material number;
STEP
step in cm;

The user should be aware that this routine has no action on the GEANT system. It is just an utility in order to help the user to take a decision, for instance via the routine GSTPAR [CONS 210].

Method

When a charged particle is moving in a medium, there are two ways to simulate the energy loss by ionization.

The first way consists of calculating the mean value of the energy loss (dE/dx) with the full Bethe-Bloch equation and to simulate the fluctuations around this mean value from a Landau distribution [PHYS332]. In GEANT this method is selected by the flag ILOSS >= 2

The second way consists of taking account of the fluctuations by generating explicitly the delta-rays above a given threshold (DCUTE for electrons, DCUTM for others particles) [PHYS330, 430]. In this case the mean value of energy loss must be computed from a restricted energy loss formula (1), and both dE/dx and the number of delta-rays produced are function of this cut: DRCUT.

Recommendations

Concerning the distribution of the energy loss by the incident particle, the two methods are equivalent if the total number of delta-rays generated along the trajectory is statistically sufficient, i.e. a few ten along the full trajectory of the particle in the given medium.

For a relativistic particle, the number of delta-rays produced per cm can be estimated by [bib-PDGB]:

    ((dN)/ (dx))# ((D)/(a)).((rhoZ)/ (A)).((1)/(DRCUT))                (1)

where

2
D=
0.307 MeV.cm /g
rho=
density of the medium
Z,A=
atomic number and atomic weight of the medium
DRCUT=
energy threshold for emitted delta-rays.

This formula holds for electrons/positrons as well as for other particles. The number of delta-rays produced must be sufficient in order to give a Landau distribution of the energy loss by the incident particle, but not too large as the timing for tracking such delta-rays will increase dramatically without any improvement of the energy loss distribution. It is the responsability of the user to estimate the number of delta-rays produced per cm that he would like, according to the considerations above. Then the routine GDRCUT returns the corresponding energy threshold DRCUT computed from formula (1). It is recommended to use this value for DCUTE and DCUTM in the current medium. However, the GEANT tables for cross-sections are not guaranteed below ELOW=10 keV. Therefore, DRCUT cannot be smaller than ELOW. Usually, in a non-dense material like gas, the number of emitted delta-rays for DRCUT=10 keV will not be sufficient to ensure a correct energy loss distribution. In that case the explicit delta-ray generation is not recommended and the Landau fluctuations must be used instead [PHYS 332]. The routine GDRCUT takes care of such cases.

Default values in GEANT3

(See BASE 040 Section 4.)

In order to avoid double counting, there is an automatic protection in the code: if ILOSS=2 one cannot change the default values of delta-rays generation

The table below summarizes the different cases.

       ##---------##-----------------------------------------------
       ##         ##                                              |
       ##         ##-Default-para##ters-for-delta-ray-generation--+
       ##         ##  Landau ON  ##           Landau OFF          |
       ##         ##   LOSS=2    ##            LOSS=1             |
       ##         ##  (default)   |                               |
       ##  IDRAY  ##------0-------+--------------2----------------+
       ##         ##     4       ##                               |
       ##  DCUTE   |   10 GeV    ##            CUTELE             |
       ##          |     4       ##                               |
       ##--DCUTM--##---10-GeV----##------------CUTELE-------------+
       ##         ##
       ##         ##
                                  

For more information see also GEANT3 routines : GDRELA, GDRSGA, GLANDO, GSTPAR.