Recommendations

The full energy loss fluctuations or the restricted fluctuations complemented by the production of $\delta$ -rays give equivalent results if the number of $\delta$ -rays generated is sufficient, e.g. a few tens along the full trajectory of the particle in the medium.

For a relativistic particle, the number of delta-rays produced per cm can be estimated integrating the cross section provided in []: $\{dNdx\}\approx \{D2\}\{\rho ZA\}\{Z$_inc²DRCUT}

where

D

0.307 MeV $cm2$ $g-1$ ;

$\rho$

density of the medium;

Z,A

atomic number and atomic weight of the medium;

$Z$_inc

charge of the particle;

DRCUT

energy threshold for emitted delta-rays.

On the other hand, the distribution of the energy lost by a particle does not necessarily correspond to the distribution of the energy deposited by the same particle in the medium traversed. This is particularly true for light or thin materials where $\delta$ -rays can escape into the next material.

It is the responsibility of the user to estimate the number of $\delta$ -rays per cm that are needed, according to the considerations above. Then the correct value for DRCUT should be set with the help of GDRPRT. It is recommended to use the same value for DCUTE and DCUTM. As the GEANT tables for cross-sections are not generated below EKMIN, DRCUT cannot be smaller than EKMIN. The value of EKMIN can be changed via the ERAN data record, and its default value is 10 keV.

In a light material like gas, the number of emitted $\delta$ -rays for DRCUT =10 keV may not be sufficient to ensure a correct energy loss distribution. If the user is mainly interested in the energy lost by the particle, no discrete $\delta$ -ray should be produced setting ILOSS =2 (see [PHYS332]).

In case the user is more interested in a precise simulation of the energy deposited, then the explicit $\delta$ -ray generation should be tried.

As far as thin materials are concerned ( ), the default in GEANT is to use the Urbán model. Comparison with experimental data have shown that this model gives very good results, and it is considerably faster than both the ASHO and the PAI models. Users should understand well their setup and their results before they try with different models, which, in principle, should give very similar results.