SYMMETRIC GROUND STATES FOR A STATIONARY RELATIVISTIC MEAN-FIELD MODEL FOR NUCLEONS IN THE NON-RELATIVISTIC LIMIT

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 non-relativistic 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.