The BCS theory has conceptual and numerical difficulties. We have previously overhauled it with a new scheme of phonon-mediated electron pairing that can be expressed analytically in terms of an empirical pairing survival rate factor, S(q) = 0 or 1/2, depending on phonon momentum, q. Now we evaluate S(q) numerically entirely from experimental data on normal state electrical resistivity and on superconducting tunnelling conductance. The empirical and numerical S(q) are reassuringly close in aluminium and lead and particularly so in two other cases, niobium and tantalum.
Zheng, X. H., & Walmsley, D. G. (2016). BCS theory has to be overhauled: reassurance from numerical survival rate. Solid state communications, 237-238, 42-48. https://doi.org/10.1016/j.ssc.2016.03.026