  The saturation properties of the nuclear matter taking pion correlations into
account is studied. We construct a Bogoliubov transformations for the pion pair
operators and calculate the energy associated with the pion pairs. The pion
dispersion relation is investigated. We next study the correlation energy due
to one pion exchange in nuclear matter and neutron matter at random phase
approximation using the generator coordinate method. The techniques of the
charged pion correlations are discussed in the neutron matter calculations. We
observe that there is no sign of the pion condensation in this model.
