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… Click to show full 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.
               
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