dorsal/arxiv
View SchemaLight-Front Nuclear Physics: Mean Field Theory for Finite Nuclei
| Authors | P. G. Blunden, M. Burkardt, G. A. Miller |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9906012 |
| URL | https://arxiv.org/abs/nucl-th/9906012 |
| DOI | 10.1103/PhysRevC.60.055211 |
| Journal | Phys.Rev. C60 (1999) 055211 |
Abstract
A light-front treatment for finite nuclei is developed from a relativistic effective Lagrangian (QHD1) involving nucleons, scalar mesons and vector mesons. We show that the necessary variational principle is a constrained one which fixes the expectation value of the total momentum operator $P^+$ to be the same as that for $P^-$. This is the same as minimizing the sum of the total momentum operators: $P^-+P^+$. We obtain a new light-front version of the equation that defines the single nucleon modes. The solutions of this equation are approximately a non-trivial phase factor times certain solutions of the usual equal-time Dirac equation. The ground state wave function is treated as a meson-nucleon Fock state, and the meson fields are treated as expectation values of field operators in that ground state. The resulting equations for these expectation values are shown to be closely related to the usual meson field equations. A new numerical technique to solve the self-consistent field equations is introduced and applied to $^{16}$O and $^{40}$Ca. The computed binding energies are essentially the same as for the usual equal-time theory. The nucleon plus momentum distribution (probability for a nucleon to have a given value of $p^+$) is obtained, and peaks for values of $p^+$ about seventy percent of the nucleon mass. The mesonic component of the ground state wave function is used to determine the scalar and vector meson momentum distribution functions, with a result that the vector mesons carry about thirty percent of the nuclear plus-momentum. The vector meson momentum distribution becomes more concentrated at $p^+=0$ as $A$ increases.
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"abstract": "A light-front treatment for finite nuclei is developed from a relativistic\neffective Lagrangian (QHD1) involving nucleons, scalar mesons and vector\nmesons. We show that the necessary variational principle is a constrained one\nwhich fixes the expectation value of the total momentum operator $P^+$ to be\nthe same as that for $P^-$. This is the same as minimizing the sum of the total\nmomentum operators: $P^-+P^+$. We obtain a new light-front version of the\nequation that defines the single nucleon modes. The solutions of this equation\nare approximately a non-trivial phase factor times certain solutions of the\nusual equal-time Dirac equation. The ground state wave function is treated as a\nmeson-nucleon Fock state, and the meson fields are treated as expectation\nvalues of field operators in that ground state. The resulting equations for\nthese expectation values are shown to be closely related to the usual meson\nfield equations. A new numerical technique to solve the self-consistent field\nequations is introduced and applied to $^{16}$O and $^{40}$Ca. The computed\nbinding energies are essentially the same as for the usual equal-time theory.\nThe nucleon plus momentum distribution (probability for a nucleon to have a\ngiven value of $p^+$) is obtained, and peaks for values of $p^+$ about seventy\npercent of the nucleon mass. The mesonic component of the ground state wave\nfunction is used to determine the scalar and vector meson momentum distribution\nfunctions, with a result that the vector mesons carry about thirty percent of\nthe nuclear plus-momentum. The vector meson momentum distribution becomes more\nconcentrated at $p^+=0$ as $A$ increases.",
"arxiv_id": "nucl-th/9906012",
"authors": [
"P. G. Blunden",
"M. Burkardt",
"G. A. Miller"
],
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"hep-ph"
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"doi": "10.1103/PhysRevC.60.055211",
"journal_ref": "Phys.Rev. C60 (1999) 055211",
"title": "Light-Front Nuclear Physics: Mean Field Theory for Finite Nuclei",
"url": "https://arxiv.org/abs/nucl-th/9906012"
},
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