Near Threshold Positron Impact Ionization of Hydrogen

The hyperspherical hidden crossing method is used to calculate the ionization cross section for e$^{+}$-H near threshold. The Wannier ridge for positron impact ionization corresponds to a co-linear arrangement with the electron between the positron and proton and $r_- /r_+ =.4643$. The adiabatic Hamiltonian for total angular momentum zero is expanded about the saddle point and the analytic adiabatic energies are used to obtain the threshold law for breakup: $\sigma (E)\propto E^{2.64}\exp [-0.49\sqrt E ].^{ }$Our results are consistent with the previous values of the Wannier exponent$^{1}$ and the second order correction terms to the threshold law$^{2,3}$. Using our numerical results for the transition probability in the interaction region, we calculated the absolute $S-$wave ionization cross section. $^{1}$H. Klar, J. Phys. B \textbf{14}, 4165 (1981). $^{2}$W. Ihra et al., Phys. Rev. Lett. \textbf{78}, 4027 (1997). $^{3}$J. Sternberg et al., Bull. Am. Phys. Soc. \textbf{49}, 52 (2004).