Ground States for a Stationary Mean-Field Model for a Nucleon

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 variational problem related to a model for a nucleon interacting with the $\omega$ and $\sigma$ mesons in the atomic nucleus. The model is relativistic, and we study it in a nuclear physics nonrelativistic limit, which is of a very different nature than the nonrelativistic limit in the atomic physics. Ground states are shown to exist for a large class of values for the parameters of the problem, which are determined by the values of some physical constants.

Mots clés: ground states; variational methods; relativistic; nuclear physics; mean-field model

Domaines: Equations aux dérivées partielles [math.AP]

Maria J. Esteban, Simona Rota Nodari. Ground States for a Stationary Mean-Field Model for a Nucleon. Annales Henri Poincaré, 2013, 14 (5), pp 1287-1303. ⟨10.1007/s00023-012-0211-y⟩. ⟨hal-00723553⟩