  The magnetic and non-magnetic ground states of the periodic Anderson model
with Coulomb interaction between $f$-electrons on the nearest-neighbour(NN)
sites are investigated using a variational method, which gives exact
calculation of the expectation values in the limit of infinite dimensions. It
is shown that for a critical value of NN Coulomb interactions the magnetic
ground state of the periodic Anderson model in the Kondo regime is unstable.
Factors in terms of the physical processes responsible for instability of the
magnetic ground state are also discussed. Our study indicates the importance of
the NN Coulomb interactions for correlated two band models.
