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Journal of Physics B Atomic Molecular and Optical Physics

Photon photon angular correlations in the radiative recombination of bare high-Zions

A. Surzhykov, S. Fritzsche, Thomas St hlker

Published Aug 21, 2002• 38 citations
Publisher

Abstract

The radiative recombination of a free electron into excited states of bare, high- Z ions and the subsequent photon decay are studied in the framework of the density matrix theory. Emphasis is placed, in particular, on the angular correlation between the recombination and the decay photons. The general expression for the photon–photon angular correlation function is derived, based on Dirac's equation as appropriate for high- Z ions. Computations for the dependence of the photon–photon correlation function on the nuclear charge and the projectile energies are carried out for the capture into the 2p 3/2 level and the subsequent Lyman -α 1 (2p 3/2 → 1s 1/2 ) radiation.

DOI
10.1088/0953-4075/35/17/308

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The radiative recombination of a free electron into excited states of bare, high- Z ions and the subsequent photon decay are studied in the framework of the density matrix theory. Emphasis is placed, in particular, on the angular correlation between the recombination and the decay photons. The general expression for the photon–photon angular correlation function is derived, based on Dirac's equation as appropriate for high- Z ions. Computations for the dependence of the photon–photon correlation function on the nuclear charge and the projectile energies are carried out for the capture into the 2p 3/2 level and the subsequent Lyman -α 1 (2p 3/2 → 1s 1/2 ) radiation.
The two-photon decay of highly charged hydrogenlike ions is studied within the framework of second-order perturbation theory, based on Dirac's equation. Attention has been paid to the angle-angle correlations between the two emitted photons. In particular, the density matrix theory is applied in order to explore how these angle-angle correlations are affected by the alignment of the excited states of the ions. Detailed computations have been carried out for the $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transition in hydrogenlike uranium U91+{\mathrm{U}}^{91+}U91+ ions for different (degrees of) initial alignment. It is shown that the angular correlation function is very sensitive to the alignment of the 3d5∕23{d}_{5∕2}3d5∕2​ state, an effect which has to be accounted for in the analysis of all (future) two-photon decay experiments, for which the excited state of the ions is produced by relativistic ion-atom collisions.
The angular correlations in the two-photon decay of hydrogenlike ions are studied within the framework of second-order perturbation theory, based on Dirac's equation. Particular attention has been paid to the effects which arise from the higher (nondipole) terms in the expansion of the electron-photon interaction. It is shown that the photon-photon angular correlation function, which is found symmetric with respect to the angle $\ensuremath{\theta}=90\ifmmode^\circ\else\textdegree\fi{}$ in the electric dipole approximation, becomes asymmetric because of the nondipole contributions, and that this effect is enhanced as the nuclear charge ZZZ increases. Detailed computations on the photon-photon angular distribution have been carried out for the $2{s}_{1∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ and $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transitions in neutral hydrogen (H) as well as for hydrogenlike xenon (Xe53+)({\mathrm{Xe}}^{53+})(Xe53+) and uranium (U91+)({\mathrm{U}}^{91+})(U91+) ions, and are compared with previous nonrelativistic results by Au [Phys. Rev. A 14, 531 (1976)]).
The method for calculating the function of angular photon correlation and the angular distribution of photons emitted in the process of dielectronics recombination at any phase of a cascade of radiative and Auger transitions was presented. This method was developed incorporating the formalism of the spin density matrix and the kinetic Pauli equation as the basis. The calculations conducted revealed that the effect of alignment transfer in a cascade can have a strong impact on the shape of angular correlation of cascade photons.
The angular correlation of two Lyman-α photons generated by the linearly polarized single-photon absorption of H 2 (X 1 Σ g + ) followed by the neutral dissociation of the doubly excited Q 2 1 Π u (1) state has been theoretically investigated with the second-order correlation function in quantum optics. A strong angular correlation has been obtained even for the molecules randomly oriented in space, due to the complicated entanglement of two H(2p) atoms in the intermediate state. It has been revealed how the symmetry properties in the electronic state are transferred to the two-photon state and how they manifest themselves in the angular correlation function.