  We study local moment formation in the presence of superconducting
correlations among the f-electrons in the periodic Anderson model. Local
moments form if the Coulomb interaction U>U_cr. We find that U_cr is
considerably stronger in the presence of superconducting correlations than in
the non-superconducting system. Our study is done for various values of the
f-level energy and electronic density. The smallest critical U_cr values occur
for the case where the number of f- electrons per site is equal to one. In the
presence of d-wave superconducting correlations we find that local moment
formation presents a quantum phase transition as function of pressure. This
quantum phase transition separates a region where local moments and d-wave
superconductivity coexist from another region characterized by a
superconducting ground state with no local moments. We discuss the possible
relevance of these results to experimental studies of the competition between
magnetic order and superconductivity in CeCu_2Si_2.
