Comparison of classical and quantum models of anti-hydrogen formation through charge exchange

We compare classical and quantum predictions of the cross section for anti-hydrogen formation by charge exchange between Rydberg positronium and antiprotons as a function of the positronium energy. We show that these two highly different approaches furnish the same scaling law with the principal quantum number of positronium n Ps and numerical values in agreement within some tens of percent for ${n}_{mathrm{Ps}}geqslant 3$ and down to very low collision energy of tens of μeV. We discuss these results in the context of a recently claimed hypothesis of quantum suppression of the reaction driven by supposedly different scaling law of classical and quantum predictions. Finally we underline how the basic agreement between classical and quantum results enforces the reliability of the classical calculations that, presently, are the only ones able to obtain the cross section for positronium initially in high Rydberg states and in the presence of external electric and magnetic fields