  We show that the unusual doping dependence of the isotope effects on
transition temperature and zero temperature in - plane penetration depth
naturally follows from the doping driven 3D-2D crossover, the 2D quantum
superconductor to insulator transition (QSI) in the underdoped limit and the
change of the relative doping concentration upon isotope substitution. Close to
the QSI transition both, the isotope coefficient of transition temperature and
penetration depth approach the coefficient of the relative dopant
concentration, and its divergence sets the scale. These predictions are fully
consistent with the experimental data and imply that close to the underdoped
limit the unusual isotope effect on transition temperature and penetration
depth uncovers critical phenomena associated with the quantum superconductor to
insulator transition in two dimensions.
