Calculation of coefficients of fractional parentage for large-basis harmonic-oscillator shell model

Abstract

A new procedure for large-scale calculations of the coefficients of fractional parentage (CFPs) for a single j-orbit with isospin is presented, The approach is based on a simple enumeration scheme for antisymmetric A-particle states and an efficient method for constructing the eigenvectors of an idempotent matrix. We investigate the characteristics of the introduced CFP basis and the application of this procedure to the ab initio harmonic-oscillator shell-model approach. The results of CFP calculations for the j = 1/ 2,...,41/2 orbits are presented (the full sets of one-particle and two-particle CFPs up to the j = 9/2 orbit are obtained). The new computer code for calculation of the CFPs proves to be very quick, efficient, and numerically stable and produces results possessing only small numerical uncertainties.