dorsal/arxiv
View SchemaShell-model Hamiltonians from Density Functional Theory
| Authors | Y. Alhassid, G. F. Bertsch, L. Fang, B. Sabbey |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0512031 |
| URL | https://arxiv.org/abs/nucl-th/0512031 |
| DOI | 10.1103/PhysRevC.74.034301 |
| Journal | Phys. Rev. C 74 (2006) 034301 |
Abstract
The density functional theory of nuclear structure provides a many-particle wave function that is useful for static properties, but an extension of the theory is necessary to describe correlation effects or other dynamic properties. Here we propose a procedure to extend the theory by mapping the properties of the self-consistent mean-field Hamiltonian onto an effective shell-model Hamiltonian with two-body interactions. In this initial study, we consider the sd-shell nuclei Ne-20, Mg-24, Si-28, and Ar-36. Our first application is in the framework of the USD shell-model Hamiltonian, using its mean-field approximation to construct an effective Hamiltonian and partially recover correlation effects. We find that more than half of the correlation energy is due to the quadrupole interaction. We then follow a similar procedure but using the SLy4 Skyrme energy functional as our starting point and truncating the space to the spherical $sd$ shell. The constructed shell-model Hamiltonian is found to satisfy minimal consistency requirements to reproduce the properties of the mean-field solution. The quadrupolar correlation energies computed with the mapped Hamiltonian are reasonable compared with those computed by other methods.
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"abstract": "The density functional theory of nuclear structure provides a many-particle\nwave function that is useful for static properties, but an extension of the\ntheory is necessary to describe correlation effects or other dynamic\nproperties. Here we propose a procedure to extend the theory by mapping the\nproperties of the self-consistent mean-field Hamiltonian onto an effective\nshell-model Hamiltonian with two-body interactions. In this initial study, we\nconsider the sd-shell nuclei Ne-20, Mg-24, Si-28, and Ar-36. Our first\napplication is in the framework of the USD shell-model Hamiltonian, using its\nmean-field approximation to construct an effective Hamiltonian and partially\nrecover correlation effects. We find that more than half of the correlation\nenergy is due to the quadrupole interaction. We then follow a similar procedure\nbut using the SLy4 Skyrme energy functional as our starting point and\ntruncating the space to the spherical $sd$ shell. The constructed shell-model\nHamiltonian is found to satisfy minimal consistency requirements to reproduce\nthe properties of the mean-field solution. The quadrupolar correlation energies\ncomputed with the mapped Hamiltonian are reasonable compared with those\ncomputed by other methods.",
"arxiv_id": "nucl-th/0512031",
"authors": [
"Y. Alhassid",
"G. F. Bertsch",
"L. Fang",
"B. Sabbey"
],
"categories": [
"nucl-th",
"cond-mat.mes-hall"
],
"doi": "10.1103/PhysRevC.74.034301",
"journal_ref": "Phys. Rev. C 74 (2006) 034301",
"title": "Shell-model Hamiltonians from Density Functional Theory",
"url": "https://arxiv.org/abs/nucl-th/0512031"
},
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