  A very rich phase diagram has recently been found in CeCu$_{2}$Si$_{2}$ from
high pressure experiments where, in particular, a transition between an
intermediate valence configuration and an integral valent heavy fermion state
has been observed. We show that such a valence transition can be understood in
the framework of the periodic Anderson model. In particular, our results show a
breakdown of a mixed-valence state which is accompanied by a drastic change in
the \textit{f} occupation in agreement with experiment. This valence transition
can possibly be interpreted as a collapse of the large Fermi surface of the
heavy fermion state which incorporates not only the conduction electrons but
also the localized \textit{f} electrons. The theoretical approach used in this
paper is based on the novel projector-based renormalization method (PRM). With
respect to the periodic Anderson model, the method was before only employed in
combination with the basic approximations of the well-known slave-boson
mean-field theory. In this paper, the PRM treatment is performed in a more
sophisticated manner where both mixed as well as integral valent solutions have
been obtained. Furthermore, we argue that the presented PRM approach might be a
promising starting point to study the competing interactions in
CeCu$_{2}$Si$_{2}$ and related compounds.
