Symmetric ground states for a stationary relativistic mean-field model for nucleons in the nonrelativistic limit

Maria J. Esteban (1) , Simona Rota Nodari (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LJLL - Laboratoire Jacques-Louis Lions

In this paper we consider a model for a nucleon interacting with the $\omega$ and $\sigma$ mesons in the atomic nucleus. The model is relativistic, but we study it in the nuclear physics nonrelativistic limit, which is of a very different nature from the one of the atomic physics. Ground states with a given angular momentum are shown to exist for a large class of values for the coupling constants and the mesons' masses. Moreover, we show that, for a good choice of parameters, the very striking shapes of mesonic densities inside and outside the nucleus are well described by the solutions of our model.

Mots clés: ground state; symmetric ground state; relativistic; nucleons; nuclear physics; mean-field model

Domaines: Equations aux dérivées partielles [math.AP]

Maria J. Esteban, Simona Rota Nodari. Symmetric ground states for a stationary relativistic mean-field model for nucleons in the nonrelativistic limit. Reviews in Mathematical Physics, 2012, 24 (10), pp.1250025. ⟨hal-00692134v2⟩