  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.
