About universal scalings in double K-shell photoionization

Abstract

We discuss the problem of the universal scalings in the double ionization of atomic K-shell electrons caused by absorption of a single photon. In particular, we envisage the following questions: Under which conditions and up to which accuracy the universal scalings are realized? Does it make sense to talk about different physical mechanisms in the double-ionization process? Finally, we present also the theoretical analysis of recent experimental measurements performed on neutral atoms. As a testing ground, QED perturbation theory is employed. PACS numbers: 32.80.Fb, 32.30.Rj The double K-shell photoionization (or the so-called double K-shell photoeffect) is the fundamental process, which is being persistently investigated already for more than three decades [1,2]. The extended interest in the problem is due to the fact that the two-electron ejection is exclusively caused by the correlation interactions. Accordingly, it serves as a testing ground for different theoretical approaches. The most of previous experimental measurements concerns with the energy behavior for the ratio of double-to-single photoionization cross sections in neutral helium [3,4,5,6]. The other atomic targets are investigated much less thoroughly. In view of the recent developments of novel synchrotron radiation sources, such experiments become feasible to perform in a wide range of photon energies [7,8,9,10,11]. Therefore, the theoretical study of the universal scalings is of particular importance, because it provides information about most generic features of the double-ionization process for a whole family of atomic systems.The problem of the double K-shell photoionization of helium-like ions allows for rigorous theoretical treatment within the framework of QED perturbation theory [12,13,14,15,16,17,18]. For moderate values of the nuclear charge Z, the bound K-shell electrons are characterized by the binding energy I = η 2 /(2m) and the average momentum η = mαZ, where α is the fine-structure constant and m is the electron mass ( = 1, c = 1). The incident photon is characterized by the momentum k and the energy ω = k. In the non-relativistic case, it is assumed that αZ ≪ 1 and ω ≪ m. Since the atomic nucleus is much heavier than the electron, the former can be represented as a source of the external field (the Furry picture). Accordingly, to zeroth approximation, the electrons are described by the Coulomb wave functions for the discrete and continuous spectra. The electron-electron interaction is mediated by the exchange of a different number of virtual photons. Mathematically, it is equivalent to the expansion with respect to the correlation parameter Z −1 , which exhibits fast convergence for any Z 1 [19]. To leading order, the amplitude of the double K-shell photoionization consists of two Feynman diagrams, which describe the electron-electron interactions in the initial and final states by the one-photon exchange (see Fig. 1).It is convenient to distinguish between the near-threshold energy domain (ω I 2K , where I 2K denotes the doub...

Relativistic theory of the double photoionization of heliumlike atoms

“…First, we confirm the known statement [31,32] that the nonrelativistic limit of the scaled ratio R(ω) ≡ Z 2 R(ω/ω cr ) is well described by a universal function that does not depend on the nuclear charge number. We will show later that this universal scaling is strongly violated by the relativistic effects.…”

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

“…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.…”

Photo-double-ionization of He-like and Be-like systems in excited states within an intermediate-energyR-matrix framework

“…For example, Mikhailov et al [21,22] and Hoszowska et al [23,24] applied this principle to photo-double-ionization of the K shell of neutral atoms and Wehlitz et al [25] and Bluett et al [26] applied it to scaling the energy in the ratio of double to single photoionzation of neutral atoms. It is interesting to examine how the photo-double-ionization cross sections for Be-like atoms and ions in the various excited states studied in this paper scale according to these principles since the screening effect of the 1s electrons should be accounted for.…”