Total number of $J$ levels for identical particles in a single-$j$ shell using coefficients of fractional parentage

Abstract

Analytical expressions of the total number of $J$ levels for three and four fermions in a nuclear $j^n$ shell are provided. The formulas were derived using a combination of sum rules for coefficients of fractional parentage, and "unusual" identities, i.e. which do not contain the weighting factor $(2J+1)$ involving $6j$ and $9j$ symbols.

submitted to Phys. Rev. C

References in corpus (7)

• Partial Dynamical Symmetries in the g9/2 Shell-Progress and Puzzles
• Relations Between Coefficients of Fractional Parentage
• Number of Spin $I$ States of Identical Particles
• Lowest Eigenvalues of Random Hamiltonians
• New Relations for Coefficients of Fractional Parentage--the Redmond Recursion Formula with Seniority
• Number of spin-J states and odd-even staggering for identical particles in a single-j shell
• Relations for Four Nucleons in a Single j Shell-using 9j Symbols to get rid of 9j Symbols

Cited by in corpus (2)

• Exact expressions for the number of levels in single-\textit{j} orbits for three, four and five fermions
• Distribution of the total angular momentum in relativistic configurations