dorsal/arxiv
View SchemaNew results for the missing quantum numbers labeling the quadrupole and octupole boson basis
| Authors | A. Gheorghe, A. A. Raduta |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0405065 |
| URL | https://arxiv.org/abs/nucl-th/0405065 |
| DOI | 10.1088/0305-4470/37/45/013 |
| Journal | J.Phys. A37 (2004) 10951-10958 |
Abstract
The many $2^k$-pole boson states, $|N_kv_k\alpha_k I_kM_k>$ with $k=2,3$, realize the irreducible representation (IR) for the group reduction chains $SU(2k+1)\supset R_{2k+1}\supset R_3\supset R_2$. They have been analytically studied and widely used for the description of nuclear systems. However, no analytical expression for the degeneracy $d_v(I)$ of the $R_{2k+1}$'s IR, determined by the reduction $R_{2k+1}\supset R_3$, is available. Thus, the number of distinct values taken by $\alpha_k$ has been so far obtained by solving some complex equations. Here we derive analytical expressions for the degeneracy $d_v(I)$ characterizing the octupole and quadrupole boson states, respectively. The merit of this work consists of the fact that it completes the analytical expressions for the $2^k$-pole boson basis.
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"abstract": "The many $2^k$-pole boson states, $|N_kv_k\\alpha_k I_kM_k\u003e$ with $k=2,3$,\nrealize the irreducible representation (IR) for the group reduction chains\n$SU(2k+1)\\supset R_{2k+1}\\supset R_3\\supset R_2$. They have been analytically\nstudied and widely used for the description of nuclear systems. However, no\nanalytical expression for the degeneracy $d_v(I)$ of the $R_{2k+1}$\u0027s IR,\ndetermined by the reduction $R_{2k+1}\\supset R_3$, is available. Thus, the\nnumber of distinct values taken by $\\alpha_k$ has been so far obtained by\nsolving some complex equations. Here we derive analytical expressions for the\ndegeneracy $d_v(I)$ characterizing the octupole and quadrupole boson states,\nrespectively. The merit of this work consists of the fact that it completes the\nanalytical expressions for the $2^k$-pole boson basis.",
"arxiv_id": "nucl-th/0405065",
"authors": [
"A. Gheorghe",
"A. A. Raduta"
],
"categories": [
"nucl-th"
],
"doi": "10.1088/0305-4470/37/45/013",
"journal_ref": "J.Phys. A37 (2004) 10951-10958",
"title": "New results for the missing quantum numbers labeling the quadrupole and octupole boson basis",
"url": "https://arxiv.org/abs/nucl-th/0405065"
},
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