Abstract
Migdal's discussion to validate the neglect of vertex corrections in the adiabatic region,ω 0 ≪ E F (the Fermi energy), is examined at the opposite extreme, ω 0 ≫ E F , where ω 0 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.
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