Abstract

Some inequalities for the isotope coefficient, α, are derived from an exact expression obtained from the BCS gap equation for any arbitrary electronic density of states. It is shown that the effect of the mass dependence of the carrier concentration, n, within the van Hove scenario (VHS) can explain some anomalous features of α for La 2CuO 4 based superconductors, not explained by earlier theories based on VHS. These features are the asymmetry of α about the optimum concentration, n m , a minimum value of α above n m , and a value of α less than BCS value of 1 2 below n m .

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