Breakdown of the electric dipole approximation at Cooper minima in direct two-photon ionisation

Abstract

We predict breakdown of the electric dipole approximation at nonlinear Cooper minimum in direct two-photon K−shell atomic ionisation by circularly polarised light. According to predictions based on the electric dipole approximation, we expect that tuning the incident photon energy to the Cooper minimum in two-photon ionisation results in pure depletion of one spin projection of the initially bound 1s electrons, and hence, leaves the ionised atom in a fully oriented state. We show that by inclusion of electric quadrupole interaction, dramatic drop of orientation purity is obtained. The low degree of the remaining ion orientation provides a direct access to contributions of the electron-photon interaction beyond the electric dipole approximation in the two-photon ionisation of atoms and molecules. The orientation of the photoions can be experimentally detected either directly by a Stern-Gerlach analyzer, or by means of subsequent Kα fluorescence emission, which has the information about the ion orientation imprinted in the polarisation of the emitted photons. 2/113/11

Enhanced polarization transfer to the characteristic $Lα$ x-ray lines near the nonlinear Cooper minimum of two-photon ionization

“…In contrast, the results presented in Ref. [35] concentrate on a special case of two-photon ionization of s electrons by circularly polarized light near the nonlinear Cooper minimum. In this particular scenario, all electric dipole channels drop to zero, and hence, reveal the contributions of higher multipole orders.…”

“…For the two-photon ionization of a p 3/2 electron from a closed shell atom, the statistical tensor ρ kq takes the form (see [34,35] for details)…”

“…Cooper minimum in multi-photon ionization can be also noticed in earlier calculations, both in total cross sections [28][29][30] as well as in photoelectron angular distributions [31,32], however, no attention was paid to investigate it in detail. We recently demonstrated, that such Cooper minimum in multi-photon ionization processes can strongly influence the photoelectron angular distributions [33], or the magnetic sublevel populations of photoions [34,35]. In [34], it has also been shown, that in the case of two-photon ionization of atomic p electrons by circularly polarized light, the polarization transfer from the ionizing light to the atom is maximized at this nonlinear Cooper minimum.…”

Photoelectron Angular Distributions of Nonresonant Two-Photon Atomic Ionization Near Nonlinear Cooper Minima

“…What is more, the Cooper minimum can be found also in many-photon (nonlinear) ionization of atoms and appears between any two adjacent level resonances of the same angular momentum [31]. We have previously shown, that such a nonlinear Cooper minimum enhances the polarization transfer from incident to fluorescence photons [31], and in the case of two-photon K-shell ionization, can uniquely reveal multipole contributions in the two-photon ionization process [32]. Furthermore, we have demonstrated that the maximum of elliptical dichroism in photoelectron angular distributions appears near the nonlinear Cooper minimum [5].…”

Photoelectron Angular Distributions of Nonresonant Two-Photon Atomic Ionization Near Nonlinear Cooper Minima

“…What is more, the Cooper minimum can be found also in many-photon (nonlinear) ionization of atoms and appears between any two adjacent level resonances of the same angular momentum [32]. We have previously shown, that such a nonlinear Cooper minimum enhances the polarization transfer from incident to fluorescence photons [32], and in the case of two-photon K-shell ionization, can uniquely reveal multipole contributions in the two-photon ionization process [33]. Furthermore, we have demonstrated that the maximum of elliptical dichroism in photoelectron angular distributions appears near the nonlinear Cooper minimum [5].…”