Special 6j and 9j symbols for a single-j shell

TL;DR

This paper introduces general formulas for 6j and 9j angular momentum coupling coefficients relevant to fermions in a single-j shell, extending beyond specific known cases.

Contribution

It provides the first general expressions for 6j and 9j symbols in the context of single-j shell fermion interactions, broadening their applicability.

Findings

Derived explicit formulas for 6j and 9j coefficients

Applicable to arbitrary angular momenta in single-j shells

Facilitates calculations in J-pairing interactions

Abstract

In this Brief Report, we propose general expressions for 6j and 9j coefficients arising in the study of the J-pairing interaction of identical fermions in a single-j shell. In the literature such coefficients are available only for a number of given angular momenta.