J-pairing interaction, number of states, and nine-j sum rules of four identical particles
Y. M. Zhao, A. Arima
Abstract
In this paper we study J-pairing Hamiltonian and find that the sum of eigenvalues of spin I states equals sum of norm matrix elements within the pair basis for four identical particles such as four fermions in a single-j shell or four bosons with spin l. We relate number of states to sum rules of nine-j coefficients. We obtained sum rules for nine-j coefficients <(jj)J,(jj)K:I| (jj)J, (jj)K:I> and <(ll)J,(ll)K:I| (ll)J, (ll)K:I> summing over (1) even J and K, (2) even J and odd K, (3) odd J and odd K, and (4) both even and odd J,K, where j is a half integer and l is an integer.
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