  We use the X-boson method to study the heavy fermion superconductivity
employing an extension of the periodic Anderson model in the $ U = \infty $
limit with a nearest neighbor attractive interaction between the localized $ f
$-electrons and we show that higher values of the hybridization parameter
implies in lower values associated to the maximum of the superconducting
critical temperature $ T_{c} $, indicating that the real charge transfer
between bands tends to destabilizes the Cooper pairing. Moreover, we show that
superconductivity are constrained to the vicinity of a range of occupations
where the $ f $-band density of states at the Fermi level $ \rho_{f} (\mu) $
have sufficiently high values, though superconductivity was found both for
configurations where the system present intermediate valence and heavy fermion
behavior, as experimentally observed. Finally, as the total occupation is
raised and for increased hybridization parameter $ V $ there is a transition
insulator-superconductor, which is related to the existence of a hybridization
gap that cannot be obtained by the slave-boson method.
