Superexchange and superconductivity: A possible correlation

We analyze the possibility of pair formation between conduction electrons in a metal via exchange interactions with electrons of the atomic cores, in analogy with the phenomenon of "superexchange" between unpaired ($d$) electrons on two paramagnetic cations via electrons of a closed-shell anion in insulating solids. The matrix elements for the scattering of a pair state of conduction electrons with opposite momenta and $z$ components of spin, into another pair state, are derived on the basis of a model, and evaluated by using simple orbital functions for the conduction and core electrons. An approximate solution for the energy gap at the Fermi level is obtained. The model is shown to incorporate the occurrence of itinerant-electron antiferromagnetic states in metals, recently discussed in the literature, under well-defined conditions. Applications are made to metals of the groups $\mathrm{I}A$ (Li to Cs), $\mathrm{II}A$ (Be to Ba), $\mathrm{III}A$ (Al to Tl), $\mathrm{IV}A$ (Sn and Pb), $\mathrm{I}B$ (Cu, Ag, and Au), and $\mathrm{II}B$ (Zn, Cd, and Hg). The results reproduce the observed trends regarding the occurrence, or absence, of superconductivity. The critical temperatures are of the correct order of magnitude. It is concluded that this mechanism, at least for the metals considered, can play a significant role in understanding Cooper-pair formation.