Penetration of a magnetic field in a very strong coupling superconductor

We have calculated the absolute value and temperature dependence of the London penetration depth for several values of the strong-coupling index $\frac{T_c}{{\omega }_{\ln }}$ and find large characteristic differences between the weak coupling $\frac{T_c}{{\omega }_{\ln }}\sim 0$, conventional strong coupling $\frac{T_c}{{\omega }_{\ln }}\lesssim 0.25$, and very strong coupling $\frac{T_c}{{\omega }_{\ln }}\sim 1$ regimes. Our results do not depend sensitively on the value of Coulomb pseudopotential, nor on the shape of the electron-boson exchange spectral density, but depend mainly on the characteristic boson energy ${\omega }_{\ln }$.