Symmetric Excited States for a Mean-Field Model for a Nucleon

Loïc Le Treust (1) , Simona Rota Nodari (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

In this paper, we consider a stationary 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. By a shooting method, we prove the existence of infinitely many solutions with a given angular momentum. These solutions are ordered by the number of nodes of each component.

Domaines: Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]

Loïc Le Treust, Simona Rota Nodari. Symmetric Excited States for a Mean-Field Model for a Nucleon. Journal of Differential Equations, 2013, 255, pp.3536-3563. ⟨10.1016/j.jde.2013.07.041⟩. ⟨hal-00755608⟩