Calculation of the isotope effect inLa2−xMxCuO7−xandYBa2Cu3O7−x

We have calculated the transition temperature and the isotope shift for oxygen replacement for ${\mathrm{La}}_{2-x}{M}_x\mathrm{Cu}{\mathrm{O}}_4$ ($M=\mathrm{Sr},\mathrm{Ba}$) and $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$, based on the lattice-dynamical calculations of these compounds with shell models. It is found that the experimental value of $T_c$ and the isotope shift $\Delta T_c$ for ${\mathrm{La}}_{2-x}{M}_x\mathrm{Cu}{\mathrm{O}}_4$ can be accounted for on the basis of McMillan's strong-coupling equation for $T_c$, supporting the conclusion that ${\mathrm{La}}_{2-x}{M}_x\mathrm{Cu}{\mathrm{O}}_4$ is a strong-coupling BCS superconductor. In contrast, experimental values of $T_c$ for $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ cannot be obtained on this basis. It is argued that expressing isotope shifts in terms of isotopic mass exponents ${\alpha }_i$ is not a useful procedure for these multi-ionic compounds.