Relations between Superconductivity and Velocity of Sound

In the BCS-theory of superconductivity the ratio (Θ/T _c) of the Debye-temperature Θ and the transition temperature T _c of superconductors is represented as a function of properties of electrons and their interactions with phonons. The theorem of corresponding states and experimental results show, that superconductors of the periodic system of the elements divide into groups around the quadratic numbers z ² of the ratio (Θ/T _c)- The numbers are z = 3, 4, 7, 11, 18, 29 etc.

The sound velocities and frequencies used for the definition of the Debye-temperature are considered critically. Therefore a relation proved for liquids declaring that the velocity of sound is proportional to the space filling of atoms, is used for isotropic solids. The result is that the isotopic-effect is represented as a function of atomic volume, which is itself a function of the atomic mass. The relation is given by the well-known garland shaped curve relying the atomic volume to the atomic mass. Contradiction between experiment and theory disappear in the new representation without using a new mechanism of interaction between electrons and phonons.