Charge transfer in positronium-proton collisions: Comparison of classical and quantum-mechanical theories

Charge transfer in positronium-proton collisions is calculated using the quantum-mechanical convergent close-coupling method and classical trajectory Monte-Carlo method. Previous calculations revealed that at low incident energy the cross section in both theories scales as $n_{\rm Ps}^2/E_{\rm Ps}$, where $n_{\rm Ps}$ and $E_{\rm Ps}$ are the principal quantum number and the center-of-mass energy of the incident positronium atom, respectively. However, the quantum cross section is systematically lower than classical one in absolute magnitude. To investigate the origin of this quantum suppression effect, we compare the charge transfer probabilities as functions of the impact parameter. We show that the quantum suppression in the cross section is mainly due to the low-impact parameter behavior of the probabilities governed by the quantum uncertainty principle.