Isotope effect on superconductivity in Josephson coupled stripes in underdoped cuprates

Inelastic neutron scattering data for YBaCuO as well as for LaSrCuO indicate incommensurate neutron scattering peaks with an incommensuration delta(x) away from the (pi,pi) point. T-c(x) can be replotted as a linear function of the incommensuration for these materials. This linear relation implies that the constant that relates these two quantities, where one is the incommensuration (momentum) and the other is T-c(x) (energy), has the dimension of velocity, which we denote by v(*): k(B)T(c)(x)=hv(*)delta(x). We argue that this experimentally determined relation can be obtained in a simple model of Josephson coupled stripes. Within this framework, we address the role of the O-16 -> O-18 isotope effect on T-c(x). We assume that the incommensuration is set by the doping of the sample and is not sensitive to the oxygen isotope given the fixed doping. We find therefore that the only parameter that can change with the O isotope substitution in the relation T-c(x)similar to delta(x) is the velocity v(*). We predict an oxygen isotope effect on v(*) and expect it to be similar or equal to 5%.