INSIGNIFICANCE OF VERTEX CORRECTIONS IN THE PLASMON MECHANISM OF SUPERCONDUCTIVITY AT LOW ELECTRON-CONCENTRATION - MIGDAL THEOREM IN THE ANTIADIABATIC REGION

Migdal's discussion to validate the neglect of vertex corrections in the adiabatic region, omega0 much less than E(F) (the Fermi energy), is examined at the opposite extreme, omega0 much greater than E(F), where omega0 is the characteristic energy of modes mediating the Cooper pair. Both analytical and numerical methods are employed to find whether the effect of vertex corrections is small in the low-density electron gas, if the modes are the plasmons. Calculated transition temperatures are compared with experimental ones of many exotic superconductors.