Relativistic calculations of differential ionization cross sections: Application to antiproton-hydrogen collisions

Abstract

A new relativistic method based on the Dirac equation for calculating fully differential cross sections for ionization in ion-atom collisions is developed. The method is applied to ionization of the atomic hydrogen by antiproton impact, as a non-relativistic benchmark. The fully differential, as well as various doubly and singly differential cross sections for ionization are presented. The role of the interaction between the projectile and the target nucleus is discussed. Several discrepancies in available theoretical predictions are resolved. The relativistic effects are studied for ionization of hydrogenlike xenon ion under the impact of carbon nuclei.

Doubly differential cross sections for ionization of lithium atom by protons and O8+ ions

“…In this paper, we have calculated the doubly differential cross sections for single ionization of lithium atom by 6 MeV protons and 1.5 MeV bare oxygen nuclei within the recently developed non-perturbative approach based on the Dirac equation [17]. The results of the calculations are compared with the predictions of other nonperturbative approaches, such as the TDCC [15] and CP [16], and the experimental data [8].…”

“…Having the set of expansion coefficients {C a (t, b)} at asymptotic time t → ∞, we extract information about active electron transitions during the collision. The transition amplitude to the state with a given energy ε, asymptotic momentum direction p = p/p = (θ e , φ e ), helicity µ s , and incoming spherical waves boundary conditions reads as [17] T…”

“…Here C jµ lm,sµs and g LM (j a µ a ; j b µ b ) are the Clebsh-Gordan and relativistic Gaunt coefficients [17], respectively; Y LM and j λ are the spherical harmonics and spherical Bessel functions of the first kind, respectively; G(r) and F (r) are the large and small radial components of the wave functions, respectively; ∆ jl is a phase shift. Thus, treating Eq.…”

“…In this contribution, we apply the relativistic nonperturbative approach of Ref. [17] to calculate doubly differential cross sections (DDCS) for single ionization of lithium atom by protons and bare oxygen nuclei.…”

“…2, we summarize the key points of the method developed in Ref. [17] and emphasize features of the lithium target description. In Sec.…”