Description
Abstract
Cooper pairs are bound entities with attractive interaction provided by the virtual exchange of a phonon between two electrons. Phonon energy is ℏω_D where ω_D is the Debye frequency of a given super-conductor. The corresponding Debye temperature θ_D is related to ℏω_D via the relation kθ_D=ℏω_D. Since the electrons in a Cooper pair are separated by a finite distance (r) called the size of the Cooper pair, there is finite Coulomb repulsion energy (Ec) between the electrons in a Cooper pair. For the Cooper pair to be bound and stable, ℏω_D>E_C. It is well known that the electron - electron interaction is screened out exponentially at a distance larger than the Thomas - Fermi radius, rs. Keeping this in mind, a modified Coulomb law for the electron – electron Coulomb interaction in the Cooper pair is proposed. The calculated values for the modified Coulomb energy (Em) are compared with the phonon energy ℏω_D and it is found that ℏω_D>E_C. for most of the BCS type (conventional) superconductors for which calculations are done in this manuscript.
