Possible isotope effect on the resonance peak formation in high- T c cuprates

Within effective $t\ensuremath{-}J$ Hamiltonian we analyze the influence of electronic correlations and electron-phonon interaction on the dynamical spin susceptibility in layered cuprates. We find an isotope effect on the resonance peak in the magnetic spin susceptibility $\mathrm{Im}\mathrm{}\ensuremath{\chi}(\mathbf{q},\ensuremath{\omega}),$ seen by inelastic neutron scattering. It results from both the electron-phonon coupling and the electronic correlation effects taken into account beyond random-phase approximation scheme. We find at optimal doping the isotope coefficient ${\ensuremath{\alpha}}_{\mathrm{res}}\ensuremath{\approx}0.4$ which can be further tested experimentally.