Extension and applications of switching model: Range theory, multiple scattering model of Goudsmit–Saunderson, and lateral spread treatment of Marwick–Sigmund

The switching model (PSM) developed in the previous paper is extended to obtain an “extended switching model (ESM). In the ESM, the mixt electronic-and-nuclear energy-loss region, in addition to the electronic and nuclear energy-loss regions in PSM, is taken into account analytically and appropriately. This model is combined with a small-angle multiple scattering range theory considering both nuclear and electronic stopping effects developed by Marwick–Sigmund and Valdes–Arista to formulate a improved range theory. The ESM is also combined with the multiple scattering theory with non-small angle approximation by Goudsmit–Saunderson. Furthermore, we applied ESM to lateral spread model of Marwick–Sigmund. Numerical calculations of the entire distribution functions including one of the mixt region are roughly and approximately possible. However, exact numerical calculation may be impossible. Consequently, several preliminary numerical calculations of the electronic, mixt, and nuclear regions are performed to examine their underlying behavior with respect to the incident energy, the scattering angle, the outgoing projectile intensity, and the target thickness. We show the numerical results not only of PSM and but also of ESM. Both numerical results are shown in the present paper for the first time. Since the theoretical relations are constructed using reduced variables, the calculations are made only on the case of C colliding on C. •Involving energy loss effects (nuclear, electronic, and mixt of them) in one simple formula.•Numerical results previous switching model and extended switching model for the first time.•Combined small angle multiple scattering and range in target matter.•Introducing energy loss effects into Goudsmit‒Saundersonʼs multiple scattering theory.•Introducing energy loss effects and applied switching model into lateral spread model of Marwick–Sigmund.