Abstract
Exact expression for the isotope-shift exponent and the pressure coefficient of the transition temperature are derived from the BCS gap equation for a density of states (DOS) with a van Hove singularity (VHS). The variations of these quantities with the shift of the Fermi level from the VHS and with [ital T][sub [ital c]] are discussed. The superconducting gap-to-[ital T][sub [ital c]] ratio (2[Delta][sub 0]/[ital T][sub [ital c]]) is also studied. The value of 2[Delta][sub 0]/[ital T][sub [ital c]] lies in the range from 3.53 to 4 for the DOS with a VHS at the Fermi level. A comparison of theoretical predictions with experimental results of high-[ital T][sub [ital c]] oxide systems are made. A qualitative good agreement is obtained for the pressure coefficient of [ital T][sub [ital c]].
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