Insignificance of Vertex Corrections in the Plasmon Mechanism of Superconductivity at Low Electron Concentration: Migdal’s Theorem in the Antiadiabatic Region

Migdal’s discussion to validate the neglect of vertex corrections in the adiabatic region, ω₀≪E_F (the Fermi energy), is examined at the opposite extreme, ω₀≫E_F, where ω₀ 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.