Ionization of H by protons colliding at near threshold in adiabatic treatment

Ionization in H(1s)+${\mathrm{H}}^{+}$ collisions is studied near the threshold and at relative collision energies in the range 5–25 keV. Based on the analytic continuation of the adiabatic potential-energy curves in the complex plane of the internuclear distance, the transition probabilities are calculated in the WKB approximation by evaluating the phase integral around the branch points connecting the potential curves. Two different ionization mechanisms are identified: one is the propagation on a ridge of the centrifugal core of the electronic potential when the nuclei approach each other, and the other is associated with the saddle point of the two-center Coulomb potential. The two mechanisms give about equal contributions to the total ionization cross section in the relative energy range 5.0–25.0 keV. Near threshold the second mechanism dominates. The analytical threshold energy-dependence behavior differs from the Wannier law.