Singular Hylleraas three-electron integrals

Details Singular Hylleraas three-electron integrals Singular Hylleraas three-electron integrals

2008-03-06

arxiv.org/abs/0803.0801v1

Physics

Atomic Physics

20 pages, accepted for Phys. Rev. A

Scientific paper

10.1103/PhysRevA.77.032511

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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