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arXiv · 0803.0801

Singular Hylleraas three-electron integrals

Krzysztof Pachucki·Mariusz Puchalski
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Abstract

Calculations of the leading quantum electrodynamics effects in few electron systems involve singular matrix elements of the inter-electronic distances of the form $1/r_i^3$ and $1/r_{ij}^3$. Integrals that result when the nonrelativistic wave function is represented with a Hylleraas basis representation are studied. Recursion relations for various powers of the electron coordinates and the master integrals are derived in a form suited for high precision numerical evaluations.

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Krzysztof Pachucki, Mariusz Puchalski. 2008-03-06. Singular Hylleraas three-electron integrals. https://doi.org/10.1103/physreva.77.032511

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