Mass scaling laws due to isotopic effects in the energy loss of He2+colliding with H, D, and T

Abstract

Total, electronic, and nuclear energy loss as well as stopping cross sections are calculated for He${}^{2+}$ ions incident on atomic hydrogen, deuterium, and tritium at low to intermediate energies by means of an ab initio, nonadiabatic approach for solving the Schr\odinger equation incorporating coupled electron and nuclear dynamics. Comparison of this ab initio treatment with classical nuclear stopping cross-section formulations obtained from Coulomb and screened potential models, and an ab initio theory, allows us to deduce scaling laws that incorporate the different target masses (target isotopic effect). We provide a discussion on the range of validity of the use of classical trajectories. We verify that the nuclear energy loss is a universal function of the center-of-mass (c.m.) scattering angle. The scattering angle in the c.m. system shows a dependence on the projectile charge due to a strong isotopic effect on the charge-transfer cross section. In the case of a Coulombic interaction, that dependence disappears, and leads to a formulation based only on the c.m. collision energy for the nuclear stopping cross section. Due to the small electron capture cross section for He${}^{2+}$ on H, D, and T in the low-energy region, it is shown that the effective charge model that assumes neutralization of the projectile does not apply to the energy loss of He${}^{2+}$ ions in the calculation of stopping cross sections. Thus, for this system, there is no influence of the charge exchange isotope effect of the target in the nuclear stopping cross section of the projectile. In the electronic energy loss, such an isotopic effect is present through Stueckelberg oscillations, but its contribution is small. Furthermore, the electronic stopping cross section shows a threshold effect that results from the minimum momentum transfer necessary to produce an electronic excitation in the target. Finally, the nuclear stopping cross section has a universal behavior as a function of the c.m. collision energy, and care must be taken when comparing ionic systems stopping cross-section results to those of neutral systems as obtained by effective charge models.