Thermodynamic properties of the lead superconductor: The new value of the Coulomb pseudopotential

Abstract

In the framework of the Eliashberg approach, the selected thermodynamic properties of the lead superconductor are analyzed. The new value of the Coulomb pseudopotential ( μ ∗ ) is assumed, μ ∗ = 0.1295 . In particular, the wave function renormalization factor ( Z ) and the order parameter ( Δ ) for different values of the temperature are calculated. It is shown that the electron–phonon interaction strongly enhances the effective electron mass; [ | Z | ] max = 2.84 . Next are calculated: the free energy difference between the superconducting and the normal state ( Δ F ), the thermodynamical critical field ( H C ), the specific heat in the normal state ( C N ) and the specific heat in the superconducting state ( C S ). Finally, the ratios R 2 ≡ ( C S − C N ) / C N and R 3 ≡ ( T C C N ) / H C 2 are obtained. The numerical results have shown that R 2 = 2.6344 and R 3 = 0.1293 . The presented theoretical values of the ratios agree well with the experimental data.