Many-Particle Configurations in a Central Field

Closed formulas are obtained for the fractional parentage coefficients of $j-j$ coupled configurations of three and four equivalent particles. In states of low seniority, these formulas can be used to simplify the calculation of familiar types of matrix elements. Some extension is made to the study of more complex configurations. In particular, it is shown that near the ground state the energy level spectrum of an even-even nucleus should be independent of the number of particles in the unfilled shell.