  We numerically investigate the Spin Density Functional theory for
superconductors (SpinSCDFT) and the approximated exchange-correlation
functional, derived and presented in the preceding paper I. As a test system we
employ a free electron gas featuring an exchange-splitting, a phononic pairing
field and a Coulomb repulsion. SpinSCDFT results are compared with Sarma, the
Bardeen Cooper and Schrieffer theory and with an Eliashberg type of approach.
We find that the spectrum of the superconducting Kohn-Sham SpinSCDFT system is
not in agreement with the true quasi particle structure. Therefore, starting
from the Dyson equation, we derive a scheme that allows to compute the many
body excitations of the superconductor and represents the extension to
superconductivity of the G0W0 method in band structure theory. This
superconducting G0 W0 method vastly improves the predicted spectra.
