Hyperspherical wave functions with orthogonal and permutational symmetry

Hyperspherical harmonic basis functions, expressed in terms of the Jacobi coordinates and belonging to well-defined irreducible representations 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 are evaluated, using the various hyperspherical coefficients of fractional parentage. The appropriate rotation, necessary for this evaluation, is achieved by using the rotational symmetry of these functions. Therefore, the representation matrices of the orthogonal group are sufficient for the calculation of the two-body matrix elements. Thus, the Raynal-Revai and the $T$ coefficients are unnecessary. These results make this basis set suitable for few-body calculations in nuclear, atomic, and molecular physics, as well as for microscopic calculations of collective modes in nuclear physics.