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

Abstract

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) $J_{\max }$ and the Hamiltonian contains only an interaction between pairs of fermions coupled to spin $J=J_{\max }=2j-1$. This pattern is also found in five and six fermion systems. A boson system with spin $l$ exhibits a similar pattern.

arXiv commentto be published in Physical Review C

References in corpus (2)

• General pairing interactions and pair truncation approximations for fermions in a single-j shell
• Number of states with fixed angular momentum for identical fermions and bosons

Cited by in corpus (10)

• Alternate proof of the Rowe-Rosensteel proposition and seniority conservation
• Alternate Derivation of Ginocchio-Haxton relation [(2j+3)/6]
• $J$-pairing interaction, number of states, and nine-$j$ sum rules of four identical particles
• Number of states for nucleons in a single-$j$ shell
• Isospin relations for four nucleons in a single j shell
• Companion problems in quasispin and isospin
• New Relations for Coefficients of Fractional Parentage--the Redmond Recursion Formula with Seniority
• Special 6j and 9j symbols for a single-j shell
• Total number of $J$ levels for identical particles in a single-$j$ shell using coefficients of fractional parentage
• Number of spin-J states and odd-even staggering for identical particles in a single-j shell