  We study the influence of superconductivity on the formation of the localized
magnetic moment for a single-level quantum impurity embedded in an s-wave
Bardeen-Cooper-Schrieffer (BCS) superconducting medium, modeled by
single-impurity Anderson Hamiltonian. We have combined Bogoliubov
transformation with Green's function method within self-consistent Hartree-Fock
Mean Field approximation to analyze the conditions necessary in metal (in the
superconducting) for the formation of the magnetic moment at the impurity site
for the low-frequency limit $|\omega|<<\Delta_{sc}$ as well as for the finite
superconducting gap $\Delta_{sc}$. We have compared these results with other
theoretical results and with the single-level quantum impurity embedded in the
normal metallic host. Further we analyze the electronic spectral density of the
quantum impurity embedded in superconducting host with the finite
superconducting gap to study the sub-gap states as a function of impurity
parameters.
