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In this work, new recursion relations for the number of spin-J states foridentical particles in a single-j shell are presented. Such relations areobtained using the generating-function technique, which enables one to exhibitan odd-even staggering in the spin distribution of an even number of fermionsin a single-j shell: the number of states with an even value of J is largerthan the number of states with an odd value of J. An analytical expression ofthe excess of states with an even value of J is provided, and its asymptoticbehavior for large values of j is discussed.

Number of spin-J states and odd-even staggering for identical particles in a single-j shell