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 reversedorder set of the Jacobi coordinates we obtain a set of symmetrized basis functions well suited for fewbody calculations as the evaluation of matrix elements of twobody and threebody forces involves the hscfps but no further rotation of the Jacobi coordinates. The results are applicable to the study of atomic, molecular and nuclear fewbody problems. Numerical results for nuclear softcore model potential are presented for 3, 4, and 5 body systems.
 Publication:

Physical Review A
 Pub Date:
 February 1999
 DOI:
 10.1103/PhysRevA.59.1135
 Bibcode:
 1999PhRvA..59.1135B
 Keywords:

 31.15.Ja;
 03.65.Ge;
 02.20.Df;
 36.40.c;
 Hyperspherical methods;
 Solutions of wave equations: bound states;
 Atomic and molecular clusters