  In the present paper, we study the semi-classical approximation of a
Yukawa-coupled massive Dirac-Klein-Gordon system with some general nonlinear
self-coupling. We prove that for a constrained coupling constant there exists a
family of ground states of the semi-classical problem, for all $\hbar$ small,
and show that the family concentrates around the maxima of the nonlinear
potential as $\hbar\to0$. Our method is variational and relies upon a delicate
cutting off technique. It allows us to overcome the lack of convexity of the
nonlinearities.
