  In this article we quantify the possible effects of the breakdown of Migdal's
theorem on the electron-phonon (e-p) coupling constant, on the critical
temperature and on the superconducting gap by examining different kinds of
superconducting materials either with low and high critical temperature. We use
the theoretical approach developed by Grimaldi, Pietronero and Strassler [PRB
52, 10516 & 10530 (1995)] on experimental data taken both from literature and
from our recent break-junction tunneling experiments in Bi_2Sr_2CaCu_2O_{8+x}
(BSCCO) [Physica C 275, 162 (1997) and cond-mat/9612220]. The results show that
a large violation of the Migdal's theorem (as in BSCCO) yields to a large
increase of the observed e-p coupling constant and, in a first approximation
and by direct solution of the Eliashberg equations, to large but different
increases of Tc and gap. The same theory gives no modifications when applied to
low-Tc conventional superconductors. In BSCCO, the renormalized values of the
e-p coupling constant and of the ratio 2Delta/kTc (1.85 and 4.98, respectively)
are compatible with a strong-coupling electron-phonon origin of
superconductivity.
