Possible experimentally observable effects of vertex corrections in superconductors

We calculate the effects of vertex corrections, of nonconstant density of s tates and of a (self-consistently determined) phonon self-energy for the Ho lstein model on a th;ee-dimensional cubic lattice. We replace vertex correc tions with a Coulomb pseudopotential mu(C)* adjusted to give the same T-c, and repeat the calculations, to see which effects are a distinct feature of vertex corrections. This allows us to determine directly observable effect s of vertex corrections on a variety of thermodynamic properties of superco nductors. To this end, we employ conserving approximations (in the local ap proximation) to calculate the superconducting critical temperatures, isotop e coefficients, superconducting gaps, free-energy differences, and thermody namic critical fields for a range of parameters. We find that the dressed v alue of lambda is significantly larger than the bare value. While vertex co rrections can cause significant changes in all the above quantities (even w hen the bare electron-phonon coupling is small), the changes can usually be well modeled by an appropriate Coulomb pseudopotential. The isotope coeffi cient proves to be the quantity that most clearly shows effects of vertex c orrections that can not be mimicked by a mu(C)*. [S0163-1829(98)05245-X].