New projected range algorithm as derived from transport equations

Abstract

A new PRojected RAnge ALgorithm — further referred to as PRAL — was presented at two earlier conferences: PRAL as derived from an angular diffusion model (Albany 1980), and a more plausible direct derivation (Sidney 1981). This algorithm is distinguished from other projected range calculations by (i) being simpler and faster on the computer, (ii) readily allowing approximate analytic solutions, (iii) taking into account higher energy loss moments, e.g. nuclear and electronic straggling, and (iv) dealing with all mass ratiosM ₂/M ₁ in the same manner, and hence allowing to treat any chemically composed target materials, e.g. alloys, metal oxides, -hydrides, new semiconductor materials, etc. — Since results of PRAL show good agreement with presently available results from transport equations (backward Boltzmann equations), it was suspected that both approaches are equivalent. This indeed is proved in the present paper by deriving PRAL from the Boltzmann equation.