Using the strong coupling theory, the deviations from the BCS laws are calculated .for Pb under hydrostatic pressure. The strength of the electronphonon coupling is reduced under pressure and this is manifested in the temperature variation of the reduced gap edge, de Josephson current, and critical magnetic field, all of which tend toward the BCS values.In previous papers we have described in some detail the thermodynamic properties of Bio.lPbo.9,1 amorphous Bi and Ga, a and the intermetallic compound BizT1) These are all strong coupling materials and the finitetemperature Eliashberg 4 equations must be used to describe superconductivity in these materials. Deviations from the BCS 5 temperature variation are found to occur in all their properties, although for some the deviations are not large. Lead is perhaps the best known example of a strong coupling system. Measures of the coupling strength are the ratios 2Ao/k~T ~ and TJo~D, where A o is the zero-temperature gap, T~ is the critical temperature, k B is the Boltzmann constant, and c% is the maximum phonon energy (~Debye energy). For Pb, 2Ao/kBT ~ is found to be about 4.3, 6 as opposed to the BCS value of 3.52. Under hydrostatic pressure this ratio is observed to decrease. 7 This decrease has been interpreted as being due to a decrease in the strength of the electron-phonon coupling with pressure and hence a general tendency toward a BCS behavior. 8'9The present work is the finite-temperature generalization of the zerotemperature work of Carbotte and Vashishta 9 for the superconducting properties of Pb under hydrostatic pressure. Present solutions and results are much more accurate than those of Trofimenkoff and Carbotte 8 reported *
