1302.5996 (Alexei M. Frolov)

On the products of bipolar harmonics    [PDF]

Alexei M. Frolov

The products of the two and three bipolar harmonics ${\cal Y}^{\ell_1 \ell_2}_{LM}({\bf r}_{31}, {\bf r}_{32})$ are represented as the finite sums of powers of the three relative coordinates $r_{32}, r_{31}$ and $r_{21}$. The integrals of the products of the two and three bipolar harmonics in the basis of exponential functions such products are expressed as finite sums of the auxiliary three-particle integrals $\Gamma_{n,k,l}(\alpha, \beta, \gamma)$. The formulas derived in this study can be used to accelerate highly accurate computations of the rotationally excited (bound) states in arbitrary three-body systems.

View original: http://arxiv.org/abs/1302.5996