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We consider a planar SIS-type Josephson junction between diffusivesuperconductors (S) through an insulating tunnel interface (I). We constructfully self-consistent perturbation theory with respect to the interfaceconductance. As a result, we find correction to the first Josephson harmonicand calculate the second Josephson harmonic. At arbitrary temperatures, wecorrect previous results for the nonsinusoidal current-phase relation inJosephson tunnel junctions, which were obtained with the help of conjecturedform of solution. Our perturbation theory also describes the difference betweenthe phases of the order parameter and of the anomalous Green functions.

Superconducting phases and the second Josephson harmonic in tunnel junctions between diffusive superconductors