  More than fifty years old "Anderson's theorem" suggests disorder-independent
pair-amplitude and critical temperature at low to moderate strength of
disorders. In spite of the extension of this paradigm and several subsequent
theoretical proposals, mechanism for the superconductor-insulator transition
(SIT) at large disorder is still an open problem. The understanding of
experimental data at intermediate disorder is also lacking. Here, we proceed
beyond "Anderson's theorem" by calculating disorder-averaged two-point
pair-amplitude fluctuations. We find this correlation to be finite and
long-ranged, activating scattering of quasiparticles in the novel "Cooper"
channel. Without invoking any further parameter, this mechanism quantitatively
predicts several testable properties: reduction of pair-amplitude at zero
temperature; reduction of temperature, T_\Delta, at which pair-amplitude
vanishes; suppression and broadening of coherence peak; and decrease of
hard-gap in quasiparticle density of states, with the increase of disorder. We
interpret old and new data at intermediate disorder in light of our
predictions. The robustness of this theory will hopefully provide insight to
unravel the true mechanism for SIT.
