Method

When a charged particle traverses a portion of matter, it interacts with the electrons and the nuclei of the atoms. Most of these interactions are electromagnetic (quasi-) elastic collisions in which the incoming particle loses energy in the laboratory reference frame. The amount of energy loss in a thickness of material t is subject to two sources of fluctuations. The number of collisions can fluctuate, and at the same time the energy lost in each collision varies statistically. Both distributions are characterised by a Poissonian-like behaviour. We can distinguish between collisions where the energy transferred to the atomic electrons is enough to extract them from the atoms (ionisation with production of $\delta$ -rays) and collisions where the atomic structure is excited, without a complete ionisation (excitation). It has to be noted that the energy transferred to the nuclei is usually negligible. Momentum conservation considerations show that the ratio of the energy transferred to electrons to the energy transferred to nucleus in Coulomb interactions is of the order of $m$_eZ A^-1m_p^-1 .

Several theories have been proposed to describe this important mechanism in the transport of charged particles. The main difference of these theories is in the greater or lesser detail with which the scattering centres are described. The detail of these theories as they are implemented in GEANT can be found in [PHYS332], [PHYS334] for energy loss fluctuations and in [PHYS430], [PHYS431] for energy loss.

In general, the greater the thickness of the layer traversed in terms of the number of atoms encountered, the larger is the number of collisions. In this case a detailed description of the atomic structure may be irrelevant to account for the form of the fluctuation. Landau and Vavilov have proposed theories in this region and these are implemented in GEANT.

When the thickness of the material is such that the number of collisions becomes smaller, the detailed nature of the atomic structure becomes important in determining the fluctuations of the energy loss. In this case the coupling of the various atomic energy levels to the to the Coulomb field must be taken into account.

When simulating the energy loss by ionisation, the average path-length between collisions is a function of the cross section $\sigma (E)$ . This cross section becomes very large when $E\; \to 0$ , so that it is necessary to establish a threshold energy below which the process is described in a condensed way. Above this threshold, ionisations are described in a detailed way, with the production of $\delta$ -rays. Thus, when a charged particle is moving in a medium, there are in general two ways to simulate the energy loss by ionisation:

1. calculate the average value the energy loss via the full Bethe-Bloch equation. This takes into account $\delta$ -rays generation. The fluctuations are then explicitly introduced via an appropriate distribution. In GEANT this method is selected by the value ILOSS = 2 which is controlled by the LOSS data record.
2. explicitly generate the $\delta$ -rays above a given threshold ( DCUTE for electrons, DCUTM for others particle). In this case the average energy loss is computed from a restricted formula and both the value of the energy loss and the number of $\delta$ -rays produced are function of the threshold cut (hereafter DRCUT). In GEANT this method is selected by the value ILOSS = 1 which is controlled by the LOSS data record.

• Validity ranges for the different models
• Recommendations
• Default values in GEANT