The propagator method for elementary excitations is applied to three particles outside a closed shell. It is shown that the propagator contains no spurious contributions and that the overcompleteness of the basis has the advantage that coefficients of fractional parentage can be extracted.
Abstract A new procedure for large-scale calculations of the coefficients of fractional parentage (CFP) for many-particle systems is presented. The approach is based on a simple enumeration scheme for antisymmetric N particle states, and we suggest an efficient method for constructing the eigenvectors of two-particle transposition operator PN1,N in a subspace where N 1 and N 2 = N − N 1 nucleons basis states are already antisymmetrized. The main result of this paper is that according to permutation operators PN1,N eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.