Hyperspherical functions with arbitrary permutational symmetry: Reverse construction

Abstract

An algorithm is formulated for the construction of hyperspherical functions with an arbitrary permutational symmetry. As proposed by Novoselsky and Katriel [Phys. Rev. A $49,$ 833 (1994)], we use a recursive procedure, introducing hyperspherical coefficients of fractional parentage (hscfps). These coefficients are the eigenvectors of the transposition class sum of the symmetric group in an appropriate basis. Utilizing a reversed-order set of the Jacobi coordinates we obtain a set of symmetrized basis functions well suited for few-body calculations as the evaluation of matrix elements of two-body and three-body forces involves the hscfps but no further rotation of the Jacobi coordinates. The results are applicable to the study of atomic, molecular and nuclear few-body problems. Numerical results for nuclear soft-core model potential are presented for 3, 4, and 5 body systems.