Isotope effect and pressure coefficient of the superconducting transition temperature within the Eliashberg-theory

Abstract Isotope Effect and Pressure Coefficient of the Superconducting Transition Temperature within the Eliashberg-Theory Starting from the observation that both the mass of the ions and their volume control the phonon frequencies by stretching the phonon spectrum, the change of the Eliashberg-equations of the theory of superconductivity regarding these stretchings is considered. General expressions for the isotopic exponent and the pressure coefficient of the transition temperature are derived in which only derivatives of the transition temperature with respect to the fundamental parameters of the theory are involved. A comparison with experimental values shows that lead is not the metal with the highest transition temperature possible under the simple metals.