Phys. Rev. C 72, 054307 (2005) [8 pages]J-pairing interaction, number of states, and nine-j sum rules of four identical particlesReceived 30 August 2005; published 16 November 2005 We study the J-pairing Hamiltonian and find that the sum of eigenvalues of spin-I states equals the sum of the 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 the 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 even K, (2) even J and odd K, (3) odd J and odd K, and (4) both even and odd values for J and K, where j is a half integer and l is an integer. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevC.72.054307
DOI:
10.1103/PhysRevC.72.054307
PACS:
05.30.Fk, 05.45.-a, 21.60.Cs, 24.60.Lz
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