  We investigate the symmetric Periodic Anderson Model (PAM) on a
three-dimensional cubic lattice with nearest-neighbor hopping and hybridization
matrix elements. Using Gutzwiller's variational method and the Hubbard-III
approximation (which corresponds to the exact solution of an appropriate
Falicov-Kimball model in infinite dimensions) we demonstrate the existence of a
quantum critical point at zero temperature. Below a critical value $V_c$ of the
hybridization (or above a critical interaction $U_c$) the system is an {\em
insulator} in Gutzwiller's and a {\em semi-metal} in Hubbard's approach,
whereas above $V_c$ (below $U_c$) it behaves like a metal in both
approximations. These predictions are compared with the density of states of
the $d$- and $f$-bands calculated from Quantum Monte Carlo and NRG
calculations. Our conclusion is that the half-filled symmetric PAM contains a
{\em metal-semimetal transition}, not a metal-insulator transition as has been
suggested previously.
