Hyperspherical harmonics as Sturmian orbitals in momentum space: a systematic approach to the few-body Coulomb problem

To exploit hyperspherical harmonics (including orthogonal transformations) as basis sets to obtain atomic and molecular orbitals, Fock projection into momentum space for the hydrogen atom is extended to the mathematical d-dim ensional case, higher than the physical case d=3. For a system of N particl es interacting through Coulomb forces, this method allows us to work both i n a d=3(N-1) dimensional configuration space (on eigenfunctions expanded on a Sturmian basis) and in momentum space (using a (d+1)-dimensional hypersp herical harmonics basis set). Numerical examples for three-body problems ar e presented. Performances of alternative basis sets corresponding to differ ent coupling schemes for hyperspherical harmonics have also been explicitly obtained for bielectronic atoms and H-2(+), (in the latter case, also in t he Born-Oppenheimer approximation extending th multicentre technique of Shi buya and Wulfman), Among the various generalizations and applications parti cularly relevant is the introduction of alternative expansions for multidim ensional plane waves, of use for the generalization of Fourier transforms t o many-electron multicentre problems. The material presented in this paper provides the starting point for numerical applications, which include vario us generalizations and hierarchies of approximation schemes, here briefly r eviewed.