Note on the L-and M-shell ionization by heavy, charged particles

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

“…The SCA was used in the calculations. The Coulomb deflection of ions was allowed for by the tangential approximation of hyperbolic trajectory (Hansteen and Mosebekk 1969), which simplifies the calculations substantially and is fairly accurate (Kocbach 1974), as confirmed by the latest calculations for proton and a-particle scattering by lead with K-shell ionisation (Valluri et a1 1985). Our calculations of the integral and differential L,-subshell alignments (see below) have shown that the tangential approximation yields a good agreement with more accurate alignment calculations and may be used to analyse experimental data.…”

“…In this case the statistical tensors in the laboratory system ( X Y Z ) must satisfy the equality 6) , with the last component being of importance only if the detector is sensitive to circular polarisation of the x-rays. The conditions of symmetry with respect to time inversion and to mirror reflection relative to the ( X ' O Y ) plane are obviously satisfied by other SCA versions that disregard the ion energy loss for ionisation: tangential approximation (Hansteen and Mosebekk 1969), hyperbolic trajectory (Rose1 et a1 1982a), trajectory calculated making allowance for the electrons of the target atom (Trautmann et a1 1983) and broken trajectory (Andersen et a1 1976) (see figure l ( 6) ) . Therefore, all the above mentioned properties relate to the X'YZ' coordinate system.…”

“…In this case the integration (6) is made analytically, so ALM (q, s, b ) can be expressed as where P y ( x ) is the associated Legendre polynomial and J M ( x ) is the cylindrical Bessel function. The Coulomb scattering may then be included using the so called tangential approximation of hyperbolic trajectory (Hansteen and Mosebekk 1969). Such an approximation assumes that an incident ion moves rectilinear1 at an angle 8 / 2 with is the collision radius, E = p u 2 / 2 ) and constant velocity veff = f v ( 1 + b/ ben), which coincide respectively with the impact parameter and the ion velocity at the point of closest approach (see figure l(b)).…”

Classical description and calculation of ionization in collisions of 100 eV electrons and positrons with He and H2

“…Since the classical atom is unstable against autoionization when orbital electron-electron interactions are present, this interaction is ignored and each orbital electron is bound by an energy equal to the first ionization potential of helium. Thus, this model is largely analogous to the independent electron model (Hansteen andMosebek 1972, McGuire andWeaver 1977) concerning the resulting total ionization probabilities, but differing from it in that the particle trajectories will be influenced by the interaction of the projectile with both the orbital electrons.…”

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

“…The Coulomb deflection and acceleration corrections were introduced by use of the tangential line approximation [18]. In this approximation it is assumed that a real hyperbolic trajectory of an incident ion may be substituted by a rectilinear trajectory tangential to the hyperbolic one at the point of closest approach to the target nucleus.…”