Parametrization of the angular correlation and degree of linear polarization in two-photon decays of hydrogen-like ions

TL;DR

This paper develops parametrized formulas for the angular correlation and linear polarization degree of photon pairs emitted in two-photon decays of hydrogen-like ions, considering relativistic effects and higher multipoles across the entire hydrogen isoelectronic sequence.

Contribution

It introduces a parametrization method for angular correlation and polarization in two-photon decays, including higher multipole effects, applicable to all hydrogen-like ions.

Findings

Coefficients depend on atomic number and photon energy sharing.

Higher multipole contributions significantly affect angular and polarization characteristics.

Results are provided for multiple transitions across the hydrogen isoelectronic sequence.

Abstract

The two-photon decay in hydrogen-like ions is investigated within the framework of second order perturbation theory and Dirac's relativistic equation. Special attention is paid to the angular correlation of the emitted photons as well as to the degree of linear polarization of one of the two photons, if the second is just observed under given angles. Expressions for the angular correlation and the degree of linear polarization are expanded in terms of $\cos\theta$-polynomials, whose coefficients depend on the atomic number and the energy sharing of the emitted photons. The effects of including higher (electric and magnetic) multipoles upon the emitted photon pairs beyond the electric-dipole approximation are also discussed. Calculations of the coefficients are performed for the transitions $2s_{1/2}\rightarrow1s_{1/2}$, $3d_{3/2}\rightarrow1s_{1/2}$ and $3d_{5/2}\rightarrow1s_{1/2}$, along the entire hydrogen isoelectronic sequence ($1\le Z \le 100$).