Slowing down and range of a beam of particles

To analyze the many effects taking place when a beam of particles passes through a medium, two types of problems must be solved: first of all, one needs to know the cross-sections for the interactions between the test particles (t.p.) and the field particles (f.p.); then, one must solve the transport equations, in terms of energy, position and time. Much effort has been put into calculating cross-sections, even through very sophisticated quantum-mechanical models. However, often these cross sections have been used within otherwise very scanty transport models, mostly the well known 'continuous slowing down approximation'. The errors embedded in such transport models make such detailed cross-section calculations unjustified. Besides, for slow particles, the effects of the thermal agitation and chemical bonding of the atoms in the target need to be taken into account to compute properly the range and the stopping power. In the present work a simple but more realistic transport model is described, that brings out the importance of phenomena that are completely disregarded by the continuous slowing down approximation, like energy straggling for slow particles. A BGK kernel and realistic collision frequencies can be used in this model, particularly for meaningful comparison with experimental results.