A new choice for the order of the semiclassical noninteger Bessel uniform approximation is proposed and used to calculate transition probabilities for collinear atom-oscillator collisions. Calculations have been performed for two collision systems: a Morse oscillator interacting via an exponential potential and a harmonic oscillator interacting via a Lennard-Jones potential. Results are reported for both classically allowed and classically forbidden transitions. The new noninteger Bessel approximation remains accurate in situations where earlier uniform approximations break down. © 1986 American Chemical Society.