Atomic Integrals Containing r23λ r31μ r12v

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Abstract
S states of atoms may be calculated to high precision by means of expansions containing correlation factors of the form r ij ν . Resulting integrals may be expressed as sums of auxiliary functions which are evaluated by algebraic methods. Explicit expressions, suitable for computer programing, are given for such integrals for three‐electron atoms; these include integrals containing correlation factors with linked indices, r 23 λ r 31 μ r 12 ν , with any set of (integral) values λ, μ, ν . Expressions are based on an expansion of r ij ν in terms of Legendre polynomials in cos θ ij ; coefficients of this expansion are represented by a conveniently evaluated formula and some numerical values are given. The expressions given here have been found quite convenient in preliminary calculations of lithium ground state.