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arXiv · 1906.05144

A generating integral for the matrix elements of the Coulomb Green's function with the Coulomb wave functions

K. Dzikowski·O. D. Skoromnik
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Abstract

We analytically evaluate the generating integral $K_{nl}(\beta,\beta') = \int_{0}^{\infty}\int_{0}^{\infty} e^{-\beta r - \beta' r'}G_{nl} r^{q} r'^{q'} dr dr'$ and integral moments $J_{nl}(\beta, r) = \int_{0}^{\infty} dr' G_{nl}(r,r') r'^{q} e^{-\beta r'}$ for the reduced Coulomb Green's function $G_{nl}(r,r')$ for all values of the parameters $q$ and $q'$, when the integrals are convergent. These results can be used in second-order perturbation theory to analytically obtain the complete energy spectra and local physical characteristics such as electronic densities of multi-electron atoms or ions.

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K. Dzikowski, O. D. Skoromnik. 2019-06-12. A generating integral for the matrix elements of the Coulomb Green's function with the Coulomb wave functions. https://doi.org/10.1063/1.5119349

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