ISOTOPE-SHIFT EXPONENT, PRESSURE COEFFICIENT OF T(C), AND THE SUPERCONDUCTING-GAP RATIO WITHIN THE VANHOVE SCENARIO

Exact expressions for the isotope-shift exponent and the pressure coef ficient of the transition temperature are derived from the BCS gap equ ation 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 T(c) are discussed. The superconducting-gap-to-T (c) ratio (2DELTA0/T(c)) is also studied. The value of 2DELTA0/T(c) li es in the range from 3.53 to 4 for the DOS with a VHS at the Fermi lev el. A comparison of theoretical predictions with experimental results of high-T(c) oxide systems is made. A qualitatively good agreement is obtained for the pressure coefficient of T(c).