Integral and differential alignment of atomic inner-shell vacancies in the semiclassical approximation

Abstract

The semiclassical approximation (SCA) is used to obtain general expressions for the statistical tensors describing the polarisation state of vacancies in inner shells of atoms produced by fast proton or ion impact. The asymptotic behaviour of alignment is examined in the range of high impact parameters. The restrictions imposed on the statistical tensors by the symmetry of the experiment and by the additional symmetry introduced by the various SCA versions are discussed. The integral and differential alignment of vacancies in the L and M shells of atoms is calculated systematically allowing for the Coulomb deflection of ions by the target nucleus. The deflection is allowed for by a tangential approximation of hyperbolic trajectory. The atom is described by the Hartree-Slater self-consistent-field model. The results of the calculation are compared with the experimental and calculated data published elsewhere. The effect of the screening of nuclear charge of an ion by its electrons on the differential alignment is investigated.

Charge asymmetry effects in inner-shell alignment induced by ion-atom collisions

“…In the region v/v2v <0.3 the difference between the proton-and antiproton-induced alignments and cross sections increases with decreasing velocity. The dependence of the alignment tensor components on the impact parameter is similar to that obtained earlier for higher velocities [6,8]. The Azo component is negative and large at small impact parameters b and diminishes with increasing b.…”

“…In the rectilinear approximation this component vanishes [8]. Its big value found here at small impact parameters is totally determined by the rotation of the quantization axis, i.e., by Coulomb deflection.…”

“…All necessary formulae, their derivation and discussion can be found in the paper by Kabachnik and Kondratyev [8]. The computer programs used in this work were the same as in the paper [8] except for the alterations discussed below.…”

“…The real impact parameter b and the velocity v of the ion are substituted by their effective values b~ff = ½ v(1 + b/beff) which respectively coincide with the impact parameter and the ion velocity at the point of closest approach. The approximation is known [19] to be justified for the impact parameters b > d and to describe well both the total ionisation cross sections [-20] and the differential and integral alignment [8]. It is obvious that this approximation partly describing the charge asymmetry effects should yield different results for protons and antiprotons.…”

“…The A22 component is also negative and close to zero at small impact parameters. Its absolute value grows with increasing b, determined mainly by the population of the substates with maximum projection of the angular momentum which are predominantly populated at large impact parameters (see [8]). The difference of the results for protons and antiprotons is not large, at least for b > 10 .2 a.u.…”