Comparison of Heine-Abarenkov and alternative pseudopotentials for electron-phonon interaction in aluminium, lead, lithium and calcium

Applying the Heine-Abarenkov pseudopotential to aluminium and lead in both the superconducting and normal states, Carbotte and coworkers have set a challenging standard befitting the status of the classic BCS superconductor theory. Upholding the same standard and equipped with the technique of numerical inversion, we have extracted alternative pseudopotentials from experimental data with minimal prejudgement that might cloud the physics. The two potentials are broadly consistent in the superconducting state but distinctly different in the normal state. This is an urgent issue requiring confirmation or refutation in the context of the current search for high temperature conventional superconductivity.