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

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 $\cosθ$-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 ($1\le Z \le 100$).