dorsal/arxiv
View SchemaClassification of states of single-$j$ fermions with $J$-pairing interaction
| Authors | Y. M. Zhao, A. Arima |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0404042 |
| URL | https://arxiv.org/abs/nucl-th/0404042 |
| DOI | 10.1103/PhysRevC.70.034306 |
| Journal | Phys.Rev. C70 (2004) 034306 |
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) $J_{\rm max}$ 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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"abstract": "In this paper we show that a system of three fermions is exactly solvable for\nthe case of a single-$j$ in the presence of an angular momentum-$J$ pairing\ninteraction. On the basis of the solutions for this system, we obtain new sum\nrules for six-$j$ symbols. It is also found that the \"non-integer\" eigenvalues\nof three fermions with angular momentum $I$ around the maximum appear as\n\"non-integer\" eigenvalues of four fermions when $I$ is around (or larger than)\n$J_{\\rm max}$ and the Hamiltonian contains only an interaction between pairs of\nfermions coupled to spin $J=J_{\\rm max}=2j-1$. This pattern is also found in\nfive and six fermion systems. A boson system with spin $l$ exhibits a similar\npattern.",
"arxiv_id": "nucl-th/0404042",
"authors": [
"Y. M. Zhao",
"A. Arima"
],
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"doi": "10.1103/PhysRevC.70.034306",
"journal_ref": "Phys.Rev. C70 (2004) 034306",
"title": "Classification of states of single-$j$ fermions with $J$-pairing interaction",
"url": "https://arxiv.org/abs/nucl-th/0404042"
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