Charge Asymmetry in the Dependence of Stopping on Impact Parameter

Abstract

The charge asymmetry effects in the dependence of electronic energy loss on impact parameter are studied theoretically. Allowance for some corrections to the calculations made in terms of the first-order perturbation theory is shown to result in a dependence of stopping on projectile charge sign. Corrections for binding-energy variations and for Coulomb deflection are allowed for in the case of stopping on inner shells of atoms. A correction for electron cloud polarization is allowed for in the case of valence electrons. Particular calculations are carried out in case of proton and antiproton stopping by Si atoms. The antiproton energy loss proves to exceed the proton energy loss in case of low values of impact parameters, and vice versa in case of high values of impact parameters. As the projectile velocity increases, all the corrections decrease, thereby resulting in that the impact parameter dependences of the proton and antiproton stoppings become in practice identical.

Correlated model atom in a time-dependent external field: Sign effect in the energy shift

“…However, this sign effect (∝ −Λω 2 0 /v 2 ) is opposite to the Barkas effect (∝ Z 1 Ω 2 0 /v 3 ) found earlier [5,6] in the dipole limit with charge-conjugated particles Z 1 = ±1. In agreement with Fermi's forecast [2], our theoretical result signals the importance of a quantum mechanical treatment for fast "close collisions" with consideration (ω 0 = 0) of the binding effect [11,12]. Such, reversed Barkas effect was predicted earlier using data sets from OBELIX experiments at CERN with swift (v ≃ 5 − 6) protons and antiprotons moving in gaseous He, i.e., in a target of compact inert atoms [43].…”

“…We left a more detailed investigation of the energy shift, by using an impact parameter dependent estimation for the collisional time T c (b, v, r 0 ), for a future study. Such a study, combined with estimations for the distant (large impact parameter) range, where the polarization-related energy shift generated by a dipole-like field may be important [11], is highly desirable for an interacting system. Furthermore, one should keep in mind that contributions from the nuclear-stopping and electronic-stopping are evidently correlated [49].…”

“…There the precise knowledge of the biological effectiveness is vital. Clearly, close collisions with binding-effect [11,12], but without the annihilation process, could be important.…”

Angular dependence of energy loss in proton-helium collisions

“…For relatively high projectile velocities v, i.e. , v &) v" the typical electron orbital velocities in the target atom, calculations in firstorder Born approximation are assumed to provide a good description [3][4][5]. However, for intermediate velocities (v=v, ) one has to apply numerical solutions of the time-dependent Schrodinger equation that go beyond perturbative treatments [6,7].…”

Electronic stopping based on atomic and solid-state wavefunctions

“…may be adopted for the relative stopping power and good values can be obtained if it is normalized to the homogeneous electron gas dE/dx value. This corresponds to F(v,p) c&v,P) P (15) in eq (10) and relatively accurate results are expected if the constant c,,(v,P> is obtained from a density-functional projectile potential using the phase-shift method. l6 Nevertheless, this scaling should be used with some caution for higher incident energies, where interband transitions and the above discussed fluctuations of the projectile potential come into play.…”