dorsal/arxiv
View SchemaPairing Matrix Elements and Pairing Gaps with Bare, Effective and Induced Interactions
| Authors | F. Barranco, P. F. Bortignon, R. A. Broglia, G. Colo', P. Schuck, E. Vigezzi, X. Vinas |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0502076 |
| URL | https://arxiv.org/abs/nucl-th/0502076 |
| DOI | 10.1103/PhysRevC.72.054314 |
| Journal | Phys.Rev. C72 (2005) 054314 |
Abstract
The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential $v_{low-k}$ is studied in the semiclassical approximation for the case of a typical finite, superfluid nucleus ($^{120}$Sn). It is found that the matrix elements of $v_{low-k}$ follow closely those of $v_{Gogny}$ on a wide range of energy values around the Fermi energy $e_F$, those associated with $v_{low-k}$ being less attractive. This result explains the fact that around $e_F$ the pairing gap $\Delta_{Gogny}$ associated with the Gogny interaction (and with a density of single-particle levels corresponding to an effective $k$-mass $m_k\approx 0.7 m$) is a factor of about 2 larger than $\Delta_{low-k}$,being in agreement with $\Delta_{exp}$= 1.4 MeV. The exchange of low-lying collective surface vibrations among pairs of nucleons moving in time-reversal states gives rise to an induced pairing interaction $v_{ind}$ peaked at $e_F$. The interaction $(v_{low-k}+ v_{ind})Z_{\omega}$ arising from the renormalization of the bare nucleon-nucleon potential and of the single-particle motion ($\omega-$mass and quasiparticle strength $Z_{\omega}$) due to the particle-vibration coupling leads to a value of the pairing gap at the Fermi energy $\Delta_{ren}$ which accounts for the experimental value.
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"abstract": "The dependence on the single-particle states of the pairing matrix elements\nof the Gogny force and of the bare low-momentum nucleon-nucleon potential\n$v_{low-k}$ is studied in the semiclassical approximation for the case of a\ntypical finite, superfluid nucleus ($^{120}$Sn). It is found that the matrix\nelements of $v_{low-k}$ follow closely those of $v_{Gogny}$ on a wide range of\nenergy values around the Fermi energy $e_F$, those associated with $v_{low-k}$\nbeing less attractive. This result explains the fact that around $e_F$ the\npairing gap $\\Delta_{Gogny}$ associated with the Gogny interaction (and with a\ndensity of single-particle levels corresponding to an effective $k$-mass\n$m_k\\approx 0.7 m$) is a factor of about 2 larger than $\\Delta_{low-k}$,being\nin agreement with $\\Delta_{exp}$= 1.4 MeV. The exchange of low-lying collective\nsurface vibrations among pairs of nucleons moving in time-reversal states gives\nrise to an induced pairing interaction $v_{ind}$ peaked at $e_F$. The\ninteraction $(v_{low-k}+ v_{ind})Z_{\\omega}$ arising from the renormalization\nof the bare nucleon-nucleon potential and of the single-particle motion\n($\\omega-$mass and quasiparticle strength $Z_{\\omega}$) due to the\nparticle-vibration coupling leads to a value of the pairing gap at the Fermi\nenergy $\\Delta_{ren}$ which accounts for the experimental value.",
"arxiv_id": "nucl-th/0502076",
"authors": [
"F. Barranco",
"P. F. Bortignon",
"R. A. Broglia",
"G. Colo\u0027",
"P. Schuck",
"E. Vigezzi",
"X. Vinas"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.72.054314",
"journal_ref": "Phys.Rev. C72 (2005) 054314",
"title": "Pairing Matrix Elements and Pairing Gaps with Bare, Effective and Induced Interactions",
"url": "https://arxiv.org/abs/nucl-th/0502076"
},
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