dorsal/arxiv
View SchemaRelativistic Hartree approach including both positive- and negative-energy bound states
| Authors | G. Mao, H. Stöcker, W. Greiner |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9903041 |
| URL | https://arxiv.org/abs/nucl-th/9903041 |
| DOI | 10.1142/S0218301399000288 |
| Journal | Int. J. Mod. Phys. E8, 389-416 (1999). |
Abstract
We develop a relativistic model to describe the bound states of positive energy and negative energy in finite nuclei at the same time. Instead of searching for the negative-energy solution of the nucleon's Dirac equation, we solve the Dirac equations for the nucleon and the anti-nucleon simultaneously. The single-particle energies of negative-energy nucleons are obtained through changing the sign of the single-particle energies of positive-energy anti-nucleons. The contributions of the Dirac sea to the source terms of the meson fields are evaluated by means of the derivative expansion up to the leading derivative order for the one-meson loop and one-nucleon loop. After refitting the parameters of the model to the properties of spherical nuclei, the results of positive-energy sector are similar to that calculated within the commonly used relativistic mean field theory under the no-sea approximation. However, the bound levels of negative-energy nucleons vary drastically when the vacuum contributions are taken into account. It implies that the negative-energy spectra deserve a sensitive probe to the effective interactions in addition to the positive-energy spectra.
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"abstract": "We develop a relativistic model to describe the bound states of positive\nenergy and negative energy in finite nuclei at the same time. Instead of\nsearching for the negative-energy solution of the nucleon\u0027s Dirac equation, we\nsolve the Dirac equations for the nucleon and the anti-nucleon simultaneously.\nThe single-particle energies of negative-energy nucleons are obtained through\nchanging the sign of the single-particle energies of positive-energy\nanti-nucleons. The contributions of the Dirac sea to the source terms of the\nmeson fields are evaluated by means of the derivative expansion up to the\nleading derivative order for the one-meson loop and one-nucleon loop. After\nrefitting the parameters of the model to the properties of spherical nuclei,\nthe results of positive-energy sector are similar to that calculated within the\ncommonly used relativistic mean field theory under the no-sea approximation.\nHowever, the bound levels of negative-energy nucleons vary drastically when the\nvacuum contributions are taken into account. It implies that the\nnegative-energy spectra deserve a sensitive probe to the effective interactions\nin addition to the positive-energy spectra.",
"arxiv_id": "nucl-th/9903041",
"authors": [
"G. Mao",
"H. St\u00f6cker",
"W. Greiner"
],
"categories": [
"nucl-th"
],
"doi": "10.1142/S0218301399000288",
"journal_ref": "Int. J. Mod. Phys. E8, 389-416 (1999).",
"title": "Relativistic Hartree approach including both positive- and negative-energy bound states",
"url": "https://arxiv.org/abs/nucl-th/9903041"
},
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