dorsal/arxiv
View SchemaPairing of fermions in atomic traps and nuclei
| Authors | H. Heiselberg |
|---|---|
| Categories | |
| ArXiv ID | physics/0304005 |
| URL | https://arxiv.org/abs/physics/0304005 |
| DOI | 10.1103/PhysRevA.68.053616 |
| Journal | Phys.Rev. A68 (2003) 053616 |
Abstract
Pairing gaps for fermionic atoms in harmonic oscillator traps are calculated for a wide range of interaction strengths and particle number, and compared to pairing in nuclei. Especially systems, where the pairing gap exceeds the level spacing but is smaller than the shell splitting $\hbar\omega$, are studied which applies to most trapped Fermi atomic systems as well as to finite nuclei. When solving the gap equation for a large trap with such multi-level pairing, one finds that the matrix elements between nearby harmonic oscillator levels and the quasi-particle energies lead to a double logarithm of the gap, and a pronounced shell structure at magic numbers. It is argued that neutron and proton pairing in nuclei belongs to the class of multi-level pairing, that their shell structure follows naturally and that the gaps scale as $\sim A^{-1/3}$ - all in qualitative agreement with odd-even staggering of nuclear binding energies. Pairing in large systems are related to that in the bulk limit. For large nuclei the neutron and proton superfluid gaps approach the asymptotic value in infinite nuclear matter: $\Delta\simeq 1.1$ MeV.
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"abstract": "Pairing gaps for fermionic atoms in harmonic oscillator traps are calculated\nfor a wide range of interaction strengths and particle number, and compared to\npairing in nuclei. Especially systems, where the pairing gap exceeds the level\nspacing but is smaller than the shell splitting $\\hbar\\omega$, are studied\nwhich applies to most trapped Fermi atomic systems as well as to finite nuclei.\nWhen solving the gap equation for a large trap with such multi-level pairing,\none finds that the matrix elements between nearby harmonic oscillator levels\nand the quasi-particle energies lead to a double logarithm of the gap, and a\npronounced shell structure at magic numbers. It is argued that neutron and\nproton pairing in nuclei belongs to the class of multi-level pairing, that\ntheir shell structure follows naturally and that the gaps scale as $\\sim\nA^{-1/3}$ - all in qualitative agreement with odd-even staggering of nuclear\nbinding energies. Pairing in large systems are related to that in the bulk\nlimit. For large nuclei the neutron and proton superfluid gaps approach the\nasymptotic value in infinite nuclear matter: $\\Delta\\simeq 1.1$ MeV.",
"arxiv_id": "physics/0304005",
"authors": [
"H. Heiselberg"
],
"categories": [
"physics.atom-ph",
"cond-mat.supr-con",
"nucl-th",
"physics.gen-ph"
],
"doi": "10.1103/PhysRevA.68.053616",
"journal_ref": "Phys.Rev. A68 (2003) 053616",
"title": "Pairing of fermions in atomic traps and nuclei",
"url": "https://arxiv.org/abs/physics/0304005"
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