  We present a numerical study of the isotope effect on the angle resolved
photoemission spectra (ARPES) in the undoped cuprates. By the
systematic-error-free Diagrammatic Monte Carlo method, the Lehman spectral
function of a single hole in the tt't''-J model in the regime of intermediate
and strong couplings to optical phonons is calculated for normal and isotope
substituted systems. We found that the isotope effect is strongly
energy-momentum dependent, and is anomalously enhanced in the intermediate
coupling regime while it approaches to that of the localized hole model in the
strong coupling regime. We predict the strengths of effect as well as the fine
details of the ARPES lineshape change. Implications to the doped case are also
discussed.
