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
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00553265/fr/
Journal nameReviews in Mathematical Physics
MetadataShow full item record
Author(s)Rota Nodari, Simona
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 / Keywordssystem of Dirac; atomic nucleus; relativistic mean-field equations
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Symmetric ground states for a stationary relativistic mean-field model for nucleons in the nonrelativistic limit Esteban, Maria J.; Rota Nodari, Simona (2012) Article accepté pour publication ou publié