Inelastic collisions of relativistic highly charged ions with atoms

Abstract

A general expression for the cross sections of inelastic collisions of fast (including relativistic) multicharged ions with atoms which is based on the genelazition of the eikonal approximation is derived. This expression is applicable for wide range of collision energy and has the standard nonrelativistic limit and in the ultrarelativistic limit coincides with the Baltz's exact solution [1] of the Dirac equation.As an application of the obtained result the following processes are calculated: the excitation and ionization cross sections of hydrogenlike atom; the single and double excitation and ionization of heliumlike atom; the multiply ionization of neon and argon atoms; the probability and cross section of K-vacancy production in the relativistic U 92+ − U 91+ collision. The simple analytic formulae for the cross sections of inelastic collisions and the recurrence relations between the ionization cross sections of different multiplicities are also obtained. Comparison of our results with the experimental data and the results of other calculations are given.

Projectile electron losses in the collisions with neutral targets: sudden-perturbation approximation

“…The eikonal phase in equation ( 18) corresponds to the excitation of the hydrogen-like atom projectile in the field of the neutral target. Therefore (unlike the case of target ionization, treated in [30,31]) the integral (over the impact parameter) in equation ( 17) is convergent for all values of the impact parameter and in the case of projectile ionization, after integration, γ -dependence in equation ( 18) disappears. This can be explained as follows.…”

“…Therefore under these assumptions equation (16) gives equation (15). Therefore equation ( 15) is applicable in the case of relativistic collisions, too, provided projectile electrons remain as non-relativistic before and after collision [30,31]. In this case, the eikonal phase in equation ( 15) is the same for relativistic and non-relativistic collisions.…”

“…First of all, it should be noted that in the case of target ionization (excitation) (as in [30,31]) when transitions in the target electron state occur under the influence of the projectile nucleus Coulomb field, the eikonal phase is the standard integral from the Coulomb potential and the integral over the impact parameter diverges at higher values of b. Therefore in this case the cutoff of the integral should be performed at some upper limit, b 0 and for b > b 0 one should use dipole approximation, the so-called Bethe asymptotics [30,31]. Namely, the Bethe asymptotics gives the logarithmic dependence on γ in the cross section.…”

“…In the case of the projectile ionization/excitation, the Coulomb field of the target is strongly screened and the static electric field (equation ( 12)) of the (neutral) target exponentially decreases at large impact parameters. This leads to the convergence of the integral in equation ( 13) and there is no need to use the Bethe asymptotics and matching procedure used in the case of the target ionization/excitation as it was done in [30,31], and therefore the cross does not contain the γ -dependence.…”

Finite-size projectile effects in relativistic ion-atom collisions

“…It is convenient to solve this problem using the relativistic eikonal approximation. The cross section for the transition of the heavy (relativistic) atom from a state |ψ i with energy E i to a state ψ f | with energy E f in the eikonal approximation has been derived recently (Khabibullaev et al 1998, Matveev et al 1999,…”