CONSTRUCTION OF HYPERSPHERICAL FUNCTIONS SYMMETRIZED WITH RESPECT TO THE ORTHOGONAL AND THE SYMMETRICAL GROUPS

We present a general recursive algorithm for the efficient constructio n of N-body wave functions that belong to a given irreducible represen tation (irrep) of the orthogonal group and are at the same time charac terized by a well-defined permutational symmetry. The main idea is to construct independently the hyperspherical functions with well defined orthogonal symmetry, and then reduce the irreps of the orthogonal gro up into the appropriate irreps of the symmetry group. The recursive al gorithm in both groups is similar-we diagonalize the appropriate secon d order Casimir operator. The algorithm is applied to the hyperspheric al functions, which are standard basis functions for N-body calculatio ns. The evaluation of one and two-body matrix elements, in this basis, requires the use of the various hyperspherical coefficients, which ar e given in this paper. We have encoded this algorithm and found it ver y efficient for calculating symmetrized hyperspherical functions. We f ound that, in our method, the number of coefficients of fractional par entages involved is reduced drastically compared to previous methods w hich do not use the orthogonal group. Therefore we are able to constru ct the symmetrized basis functions for N-body systems that are beyond the reach of the other approaches. (C) 1997 Academic Press.