Integrals for Exponentially Correlated Four-Body Systems of General Angular Symmetry

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Abstract

This contribution considers the spatial integrals arising for Coulomb four-body systems when the basis wavefunctions include exponentials in all six interparticle coordinates and are also eigenfunctions of the orbital angular momentum. Integration over the Euler angles describing the overall rotation of the system leads to polynomials in the interparticle distances which are explicitly presented for a range of angular quantum numbers. Completion of the integrals can then be carried out using the known closed analytical formulas for fully correlated exponential wavefunctions. The present approach leads to a complete separation of the angular part of the integrals and avoids the introduction of the series expansions normally used in Hylleraas-type methods for these systems.