Phonon singularities on volt-ampere curves of niobium point contacts

The volt-ampere curves and their second derivatives were studied for niobium point contacts at low temperatures in the voltage range corresponding to the characteristic phonon energies. It was found that while for the dirty contacts in the normal state no PC spectra of phonons could be detected, in the superconducting state there were singularities in the I–V curves corresponding to maxima either in the first or in the second derivatives. The singularities observed were due to the energy dependence of the excess current. We suppose that the origin of these singularities is due to the inelastic transitions of electrons between chemical potentials of Cooper pairs at both sides of the contact, which differ in energy by eV. These transitions are possible if ξ(0) ? d ≈ Λ_?, (ξ(0) being the coherence length; d, the contact diameter; $\text{Λ}{}_{\mathrm{?}}\text{= (l}{}_{\mathrm{i}}\text{·l}{}_{\mathrm{?}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where l_i and l_? being the elastic and inelastic electron mean free paths, respectively).