HYPERSPHERICAL WAVE-FUNCTIONS WITH ORTHOGONAL AND PERMUTATIONAL SYMMETRY

Hyperspherical harmonic basis functions, expressed in terms of the Jac obi coordinates and belonging to well-defined irreducible representati ons of the orthogonal and symmetric groups, were recently introduced. The usefulness of these basis functions is presented and the two-body matrix elements between these functions an evaluated, using the variou s hyperspherical coefficients of fractional parentage. The appropriate rotation, necessary for this evaluation, is achieved by using the rot ational symmetry of these functions. Therefore, the representation mat rices of the orthogonal group are sufficient for the calculation of th e two-body matrix elements. Thus, the Raynal-Revai and the T coefficie nts are unnecessary. These results make this basis set suitable for fe w-body calculations in nuclear, atomic, and molecular physics, as well as for microscopic calculations of collective modes in nuclear physic s. [S1050-2947(97)02212-9].