dorsal/arxiv
View Schema$J$-pairing interaction, number of states, and nine-$j$ sum rules of four identical particles
| Authors | Y. M. Zhao, A. Arima |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0508018 |
| URL | https://arxiv.org/abs/nucl-th/0508018 |
| DOI | 10.1103/PhysRevC.72.054307 |
| Journal | Phys.Rev. C72 (2005) 054307 |
Abstract
In this paper we study $J$-pairing Hamiltonian and find that the sum of eigenvalues of spin $I$ states equals sum of 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 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 $K$, (2) even $J$ and odd $K$, (3) odd $J$ and odd $K$, and (4) both even and odd $J,K$, where $j$ is a half integer and $l$ is an integer.
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"abstract": "In this paper we study $J$-pairing Hamiltonian and find that the sum of\neigenvalues of spin $I$ states equals sum of norm matrix elements within the\npair basis for four identical particles such as four fermions in a single-$j$\nshell or four bosons with spin $l$. We relate number of states to sum rules of\nnine-$j$ coefficients. We obtained sum rules for nine-$j$ coefficients\n$\u003c(jj)J,(jj)K:I| (jj)J, (jj)K:I\u003e$ and $\u003c(ll)J,(ll)K:I| (ll)J, (ll)K:I\u003e$ summing\nover (1) even $J$ and $K$, (2) even $J$ and odd $K$, (3) odd $J$ and odd $K$,\nand (4) both even and odd $J,K$, where $j$ is a half integer and $l$ is an\ninteger.",
"arxiv_id": "nucl-th/0508018",
"authors": [
"Y. M. Zhao",
"A. Arima"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.72.054307",
"journal_ref": "Phys.Rev. C72 (2005) 054307",
"title": "$J$-pairing interaction, number of states, and nine-$j$ sum rules of four identical particles",
"url": "https://arxiv.org/abs/nucl-th/0508018"
},
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