dorsal/arxiv
View SchemaOn the Coulomb and higher-order sum rules in the relativistic Fermi gas
| Authors | P. Amore, R. Cenni, T. W. Donnelly, A. Molinari |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9610005 |
| URL | https://arxiv.org/abs/nucl-th/9610005 |
| DOI | 10.1016/S0375-9474(97)00028-6 |
| Journal | Nucl.Phys. A615 (1997) 353-372 |
Abstract
Two different methods for establishing a space-like Coulomb sum rule for the relativistic Fermi gas are compared. Both of them divide the charge response by a normalizing factor such that the reduced response thus obtained fulfills the sum rule at large momentum transfer. To determine the factor, in the first approach one exploits the scaling property of the longitudinal response function, while in the second one enforces the completeness of the states in the space-like domain via the Foldy-Wouthuysen transformation. The energy-weighted and the squared-energy-weighted sum rules for the reduced responses are explored as well and the extension to momentum distributions that are more general than a step-function is also considered. The two methods yield reduced responses and Coulomb sum rules that saturate in the non-Pauli-blocked region, which can hardly be distinguished for Fermi momenta appropriate to atomic nuclei. Notably the sum rule obtained in the Foldy-Wouthuysen approach coincides with the well known non-relativistic one. Only at quite large momentum transfers (say 1 GeV/c) does a modest softening of the Foldy-Wouthuysen reduced response with respect to that obtained in the scaling framework show up. The two responses have the same half-width to second order in the Fermi momentum expansion. However, when distributions extending to momenta larger than that at the Fermi surface are employed, then in both methods the Coulomb sum rule saturates only if the normalizing factors are appropriately modified to account for the high momentum components of the nucleons.
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"abstract": "Two different methods for establishing a space-like Coulomb sum rule for the\nrelativistic Fermi gas are compared. Both of them divide the charge response by\na normalizing factor such that the reduced response thus obtained fulfills the\nsum rule at large momentum transfer. To determine the factor, in the first\napproach one exploits the scaling property of the longitudinal response\nfunction, while in the second one enforces the completeness of the states in\nthe space-like domain via the Foldy-Wouthuysen transformation. The\nenergy-weighted and the squared-energy-weighted sum rules for the reduced\nresponses are explored as well and the extension to momentum distributions that\nare more general than a step-function is also considered. The two methods yield\nreduced responses and Coulomb sum rules that saturate in the non-Pauli-blocked\nregion, which can hardly be distinguished for Fermi momenta appropriate to\natomic nuclei. Notably the sum rule obtained in the Foldy-Wouthuysen approach\ncoincides with the well known non-relativistic one. Only at quite large\nmomentum transfers (say 1 GeV/c) does a modest softening of the\nFoldy-Wouthuysen reduced response with respect to that obtained in the scaling\nframework show up. The two responses have the same half-width to second order\nin the Fermi momentum expansion. However, when distributions extending to\nmomenta larger than that at the Fermi surface are employed, then in both\nmethods the Coulomb sum rule saturates only if the normalizing factors are\nappropriately modified to account for the high momentum components of the\nnucleons.",
"arxiv_id": "nucl-th/9610005",
"authors": [
"P. Amore",
"R. Cenni",
"T. W. Donnelly",
"A. Molinari"
],
"categories": [
"nucl-th"
],
"doi": "10.1016/S0375-9474(97)00028-6",
"journal_ref": "Nucl.Phys. A615 (1997) 353-372",
"title": "On the Coulomb and higher-order sum rules in the relativistic Fermi gas",
"url": "https://arxiv.org/abs/nucl-th/9610005"
},
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