Classification of states of single-$j$ fermions with $J$-pairing interaction

Details Classification of states of single-$j$ fermions with $J$-pairing interaction Classification of states of single-$j$ fermions with $J$-pairing interaction

2004-04-16

arxiv.org/abs/nucl-th/0404042v2

Phys.Rev. C70 (2004) 034306

Physics

Nuclear Physics

Nuclear Theory

to be published in Physical Review C

Scientific paper

10.1103/PhysRevC.70.034306

In this paper we show that a system of three fermions is exactly solvable for the case of a single-$j$ in the presence of an angular momentum-$J$ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six-$j$ symbols. It is also found that the "non-integer" eigenvalues of three fermions with angular momentum $I$ around the maximum appear as "non-integer" eigenvalues of four fermions when $I$ is around (or larger than) $J_{\rm max}$ and the Hamiltonian contains only an interaction between pairs of fermions coupled to spin $J=J_{\rm max}=2j-1$. This pattern is also found in five and six fermion systems. A boson system with spin $l$ exhibits a similar pattern.

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