Relativistic theory of the double photoionization of heliumlike atoms

Abstract

A fully relativistic calculation of the double photoionization of heliumlike atoms is presented. The approach is based on the partial-wave representation of the Dirac continuum states and accounts for the retardation in the electron-electron interaction as well as the higher-order multipoles of the absorbed photon. The electron-electron interaction is taken into account to the leading order of the perturbation theory. The relativistic effects are shown to become prominent already for the medium-Z ions, changing the shape and the asymptotic behavior of the photon energy dependence of the ratio of the double-to-single photoionization cross section.

Relativistic calculations of doubleK-shell-photoionization cross sections for neutral medium-Zatoms

“…This explains why we took great care in order to calculate σ ++ and σ + fully consistently, i.e., both to the leading order in perturbation theory with exactly the same screening potential in the Dirac equation (7). Importance of such consistency was implicitly acknowledged already in previous perturbation-theory calculations [15,22,23], where results were presented solely in terms of R, and not in terms of σ ++ . From the comparison in Tables I-III, we see that the difference between the CH 1 and CH 2 results (which we use for estimating the magnitude of the residual electron correlation effects) monotonically decreases with the increase of the nuclear charge.…”

“…The prefactor of Z 2 in the definition (10) ensures that the function R(ω/ω cr ) depend only weakly on the nuclear charge and the degree of ionization of atom (ion); this fact is often termed as the universal scaling law of double photoionization [26,27]. In our previous calculation for He-like ions [15], we demonstrated that this scaling holds exactly in the nonrelativistic limit and to the first order in perturbation theory, but is violated by the relativistic effects.…”

“…The general expression for the amplitude was derived in Ref. [15] by using the two-time Green's function method [17],…”

“…A general (numerical) scheme for the computation of double photoionization cross sections was developed in our previous investigation [15]. Similarly to that, the summation over…”

“…In a previous study of two of us [15], a calculation of the double photoionization was performed within a fully relativistic framework, for which the problem of gauge dependence does not arise as the formalism is gauge invariant from the very beginning. Large relativistic effects were demonstrated in that work, but results were reported only for the He-like ions.…”