dorsal/arxiv
View SchemaComparison of the Effective Interaction to Various Orders in Different Mass Regions
| Authors | M. Hjorth-Jensen, H. Muether, A. Polls, E. Osnes |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9509006 |
| URL | https://arxiv.org/abs/nucl-th/9509006 |
| DOI | 10.1088/0954-3899/22/3/006 |
| Journal | J.Phys.G22:321-330,1996 |
Abstract
The convergence of the perturbation expansion for the effective interaction to be used in shell-model calculations is investigated as function of the mass number $A$, from $A=4$ to $A=208$. As the mass number increases, there are more intermediate states to sum over in each higher-order diagram which contributes to the effective interaction. Together with the fact that the energy denominators in each diagram are smaller for larger mass numbers, these two effects could largely enhance higher-order contributions to the effective interaction, thereby deteriorating the order-by-order convergence of the effective interaction. This effect is counterbalanced by the short range of the nucleon-nucleon interaction, which implies that its matrix elements are weaker for valence single-particle states in ``large'' nuclei with large mass number as compared to those in light nuclei. These effects are examined by comparing various mean values of the matrix elements. It turns out that the contributions from higher-order terms remain fairly stable as the mass number increases from $A=4$ to $A=208$. The implications for nuclear structure calculations are discussed.
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"abstract": "The convergence of the perturbation expansion for the effective interaction\nto be used in shell-model calculations is investigated as function of the mass\nnumber $A$, from $A=4$ to $A=208$. As the mass number increases, there are more\nintermediate states to sum over in each higher-order diagram which contributes\nto the effective interaction. Together with the fact that the energy\ndenominators in each diagram are smaller for larger mass numbers, these two\neffects could largely enhance higher-order contributions to the effective\ninteraction, thereby deteriorating the order-by-order convergence of the\neffective interaction. This effect is counterbalanced by the short range of the\nnucleon-nucleon interaction, which implies that its matrix elements are weaker\nfor valence single-particle states in ``large\u0027\u0027 nuclei with large mass number\nas compared to those in light nuclei. These effects are examined by comparing\nvarious mean values of the matrix elements. It turns out that the contributions\nfrom higher-order terms remain fairly stable as the mass number increases from\n$A=4$ to $A=208$. The implications for nuclear structure calculations are\ndiscussed.",
"arxiv_id": "nucl-th/9509006",
"authors": [
"M. Hjorth-Jensen",
"H. Muether",
"A. Polls",
"E. Osnes"
],
"categories": [
"nucl-th"
],
"doi": "10.1088/0954-3899/22/3/006",
"journal_ref": "J.Phys.G22:321-330,1996",
"title": "Comparison of the Effective Interaction to Various Orders in Different Mass Regions",
"url": "https://arxiv.org/abs/nucl-th/9509006"
},
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