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

In this paper we consider a model for a nucleon interacting with the $ω$ and $σ$ 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.