Method simplifying calculation of coefficients of fractional parentage for translationally invariant shell-model

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 $P_{N_1 ,N}$ 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 $P_{N_1 ,N}$ eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.