The continuity and momentum equations for ionospheric O+ were solved for typical polar cap conditions. Density profiles were obtained both with and without allowance for accidentally resonant charge exchange (ARCE) between O+ and H. It was found that ARCE acts to reduce the maximum (for limiting) O+ escape flux by less than 30% for typical atmospheric conditions (T∞>1000 K) and by only a factor of about 3.5 for atmospheres with low exospheric temperatures (T∞=750). With allowance for ARCE the limiting O+ escape flux is of the order of 5¿108 to 109 cm-2 s-1, depending on the atmospheric conditions, which easily accounts for the existing measurements. This indicates that, contrary to previous predictions, there is no 0+ charge exchange barrier, and consequently, it is necessary to have an acceleration mechanism at low altitudes in order to have an appreciable O+ escape flux. Instead, an O+ depletion at high altitudes due to some acceleration mechanism is sufficent to cause large O+ fluxes to escape from the ionsophere to the magnetosphere.