J-pairing interaction, number of states, and nine-j sum rules of four identical particles

Journal Article · Tue Nov 01 00:00:00 EST 2005 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PhysRevC.72.054307· OSTI ID:20699112

Zhao, Y M ^[1]; Arima, A ^[2]

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1. Department of Physics, Shanghai Jiao Tong University, Shanghai 200240 (China)
2. Science Museum, Japan Science Foundation, 2-1 Kitanomaru-koen, Chiyodaku, Tokyo 102-0091 (Japan)

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.

• OSTI ID: 20699112
• Journal Information: Physical Review. C, Nuclear Physics, Vol. 72, Issue 5; Other Information: DOI: 10.1103/PhysRevC.72.054307; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2813
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOSONS
EIGENFUNCTIONS
EIGENVALUES
FERMIONS
HAMILTONIANS
MATRIX ELEMENTS
NUCLEAR STRUCTURE
PAIRING INTERACTIONS
SHELL MODELS
SPIN
STATISTICAL MODELS
SUM RULES