Near-Threshold Cross Sections for Electron and Positron Impact Ionization of Atomic Hydrogen

Abstract

Using classical arguments Wannier [Phys. Rev. 90, 817 (1953)] proposed an electron-impact ionization cross section for neutral atoms to behave as E 1.127 , where E is the excess energy above threshold. Using similar arguments Klar [J. Phys. B 14, 4165 (1981)] obtained E 2.65 to be the corresponding threshold law for positron impact. Recently, Babij et al. [Phys. Rev. Lett. 120, 113401 (2018)] measured near-threshold positron-impact breakup behavior to be similar to that expected for electrons. Using the convergent closecoupling method for the atomic hydrogen target, we examine cross sections at near-threshold energies for electron and positron impact. Contrary to the experiment, the calculated cross sections are found to behave differently for the two projectiles and consistently with the aforementioned threshold laws, despite the entirely quantum nature of these problems. For electron impact, the threshold behavior holds while the total electron spin asymmetry remains constant, whereas for positron scattering the threshold law holds for breakup while the positronium-formation component of the ionization cross section remains constant.

A Precis of Threshold Laws for Positron vs. Electron Impact Ionization of Atoms

“…We conclude by noting that a recent numerical calculation of the positron-atom impact cross section at very low energies by Bray et al [8] gives results that are consistent with Klar's prediction. On the other hand, an experiment on positron-argon ionization [9], with an energy resolution not fine enough to test the modulation of the CD theory, found linear dependence, which is consistent with the CD theory [1,2] in the first approximation.…”

Spin asymmetry in electron-impact ionization

“…There are no simple answers to these questions. We already considered the former in the context of the near threshold behavior of the cross section for the e-H system [14]. In the CCC equations for s i = 1/2 quasi one-electron targets (H-and Li-like) the matrix elements for the two total electron spins S = 0 and S = 1 are a sum and a difference of the direct and exchange terms, respectively.…”

“…In part this is due to the fact that there are relatively few measurements of the ionization-cross-section spin asymmetries. However, those that do exist, such as for e-H(1 2 S) [9,10], e-He(2 3 S) [11], and e-alkali [12] have been instrumental in establishing the utility of the convergent close-coupling (CCC) theory [13], and were helpful in the analysis of the cross-section threshold behavior [14].…”

Radiation from matter-antimatter annihilation in the quark nugget model of dark matter

“…The cross section of this process is on the order of σ col ∼ πa 2 B , with the threshold energy 13.6 eV, see, e.g., Refs. [27][28][29]. In this subsection, we estimate the probability of hydrogen ionization when it moves through the positron cloud of an anti-quark nugget.…”

“…Let σ col (p) be ionization cross section in hydrogen-positron collisions which was found in Refs. [27][28][29]. This cross section (in the hydrogen rest frame) should be averaged over the momenta of incident positrons,…”