The energy dependence of the capture cross section and the temperature dependence of the capture rate constants for inverse power attractive potentials Vproportional to-R-n is considered in the regime where the quantum character of the relative motion of colliding partners is important. For practically interesting cases n = 4 and n = 6, a simple formula for the cross section is suggested which interpolates between the classical and the quantum Bethe limits. We have shown that the classical approximation for the capture cross section performs well far below the simple estimations of the onset the quantum regime. This seemingly "classical" feature of the cross section and the rate constant is due to the large quantum effects of the waves in transmission through and reflection above the centrifugal potential barriers. (C) 2003 American Institute of Physics.