On the evaluation of some three-body variational integrals

Abstract

Stable recursive relations are presented for the numerical computation of the integrals $$\int d{\mathbf{r}}_{1}d{\mathbf{r}}_2{r}_1^{l-1}{r}_2^{m-1}{r}_{12}^{n-1}\exp \{-\alpha r_1-\beta r_2-\gamma r_{12}\}$$ ($l$, $m$ and $n$ integer, $\alpha$, $\beta$ and $\gamma$ real) when the indices $l$, $m$ or $n$ are negative. Useful formulas are given for particular values of the parameters $\alpha$, $\beta$ and $\gamma$.

12 pages, 1 figure (PS) and 3 tables. Old figures 2 and 3 replaced by Tables I and III. A further table added. Paper enlarged giving some tips on the convergence of quadratures