ISOTOPE-SHIFT EXPONENT AND THE GAP RATIO FOR D-WAVE PAIRING WITHIN THE PHONON-MEDIATED MECHANISM

An exact analytical expression for the isotope-shift exponent is deriv ed for the d-wave pairing assuming a phonon-mediated interaction. The role of the orthorhombic distortion and second nearest-neighbor hoppin g on the transition temperature (T-c) and the isotope-shift exponent ( alpha) are studied. The temperature dependence of the gap parameter an d the doping dependence of the gap ratio are also investigated. It is found that introduction of second nearest-neighbor hopping increases T -c) as well as the gap ratio while decreases the minimum value of alph a. The variation of alpha with doping is qualitatively consistent with the experimental results of high-T-c oxide systems.