Kohn anomaly energy in conventional superconductors equals twice the energy of the superconducting gap: How and why?

Kohn anomaly occurs in metals as a weak but discernible kink in the phonon spectrum around 2k_F arising out of screened Coulombic interaction. Over the years this has been observed in a number of normal metallic systems. As a major surprise however, the recent neutron spin-echo experiments on elemental (conventional) superconductors Pb and Nb reveal a very important and striking relation that Kohn (anomaly) energy equals twice the energy of the superconducting gap. In this paper we explore the microscopic origin of this novel phenomenon and discuss its implication to the standard model BCS Theory.