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The relativistic mean-field equations of the atomic nucleus

Rota Nodari, Simona (2012), The relativistic mean-field equations of the atomic nucleus, Reviews in Mathematical Physics, 24, 4, p. 41 pages. http://dx.doi.org/10.1142/S0129055X12500080

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00553265/fr/
Date
2012
Journal name
Reviews in Mathematical Physics
Volume
24
Number
4
Publisher
World Scientific
Pages
41 pages
Publication identifier
http://dx.doi.org/10.1142/S0129055X12500080
Metadata
Show full item record
Author(s)
Rota Nodari, Simona cc
Abstract (EN)
In nuclear physics, the relativistic mean-field theory describes the nucleus as a system of Dirac nucleons which interact via meson fields. In a static case and without nonlinear self-coupling of the $\sigma$ meson, the relativistic mean-field equations become a system of Dirac equations where the potential is given by the meson and photon fields. The aim of this work is to prove the existence of solutions of these equations. We consider a minimization problem with constraints that involve negative spectral projectors and we apply the concentration-compactness lemma to find a minimizer of this problem. We show that this minimizer is a solution of the relativistic mean-field equations considered.
Subjects / Keywords
system of Dirac; atomic nucleus; relativistic mean-field equations

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