dorsal/arxiv
View SchemaEffective three-body interactions in the alpha-cluster model for the ^{12}C nucleus
| Authors | S. I. Fedotov, O. I. Kartavtsev, A. V. Malykh |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0509021 |
| URL | https://arxiv.org/abs/nucl-th/0509021 |
| DOI | 10.1140/epja/i2005-10165-4 |
| Journal | Eur.Phys.J. A26 (2005) 201-207 |
Abstract
Properties of the lowest $0^{+}$ states of $^{12}\mathrm{C}$ are calculated to study the role of three-body interactions in the $\alpha$-cluster model. An additional short-range part of the local three-body potential is introduced to incorporate the effects beyond the $\alpha$-cluster model. There is enough freedom in this potential to reproduce the experimental values of the ground-state and excited-state energies and the ground-state root-mean-square radius. The calculations reveal two principal choices of the two-body and three-body potentials. Firstly, one can adjust the potentials to obtain the width of the excited $0_2^+$ state and the monopole $0_2^+ \to 0_1^+ $ transition matrix element in good agreement with the experimental data. In this case, the three-body potential has strong short-range attraction supporting a narrow resonance above the $0_2^+$ state, the excited-state wave function contains a significant short-range component, and the excited-state root-mean-square radius is comparable to that of the ground state. Next, rejecting the solutions with an additional narrow resonance, one finds that the excited-state width and the monopole transition matrix element are insensitive to the choice of the potentials and both values exceed the experimental ones.
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"abstract": "Properties of the lowest $0^{+}$ states of $^{12}\\mathrm{C}$ are calculated\nto study the role of three-body interactions in the $\\alpha$-cluster model. An\nadditional short-range part of the local three-body potential is introduced to\nincorporate the effects beyond the $\\alpha$-cluster model. There is enough\nfreedom in this potential to reproduce the experimental values of the\nground-state and excited-state energies and the ground-state root-mean-square\nradius. The calculations reveal two principal choices of the two-body and\nthree-body potentials. Firstly, one can adjust the potentials to obtain the\nwidth of the excited $0_2^+$ state and the monopole $0_2^+ \\to 0_1^+ $\ntransition matrix element in good agreement with the experimental data. In this\ncase, the three-body potential has strong short-range attraction supporting a\nnarrow resonance above the $0_2^+$ state, the excited-state wave function\ncontains a significant short-range component, and the excited-state\nroot-mean-square radius is comparable to that of the ground state. Next,\nrejecting the solutions with an additional narrow resonance, one finds that the\nexcited-state width and the monopole transition matrix element are insensitive\nto the choice of the potentials and both values exceed the experimental ones.",
"arxiv_id": "nucl-th/0509021",
"authors": [
"S. I. Fedotov",
"O. I. Kartavtsev",
"A. V. Malykh"
],
"categories": [
"nucl-th"
],
"doi": "10.1140/epja/i2005-10165-4",
"journal_ref": "Eur.Phys.J. A26 (2005) 201-207",
"title": "Effective three-body interactions in the alpha-cluster model for the ^{12}C nucleus",
"url": "https://arxiv.org/abs/nucl-th/0509021"
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