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arXiv:0807.2042 · Physical Review A

Resonant phenomena in antihydrogen-hydrogen scattering

Alexei Yu. Voronin, Piotr Froelich

Published Feb 19, 2008• 10 citations
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Abstract

We present a treatment of cold hydrogen-antihydrogen collisions based on the asymptotic properties of atom-antiatom interactions. We derive general formulas for the elastic and inelastic cross sections and for the scattering lengths and analyze their sensitivity to the parameters characterizing the inelasticity of the collision process. Given the inelasticity, we obtain bounds for the complex scattering length. We investigate the influence of strong nuclear forces and the isotope effects in $\text{H}\overline{\text{H}}$ and $\text{D}\overline{\text{H}}$ collisions and demonstrate enhancement of these effects due to the presence of the near-threshold narrow $\text{H}\overline{\text{H}}$ $(\text{D}\overline{\text{H}})$ states. The values of the elastic and inelastic cross sections with simultaneous account of rearrangement and strong forces are presented. General expressions for the (complex) energies of the near-threshold $\text{H}\overline{\text{H}}$ states are obtained.

DOI
10.1103/physreva.77.022505

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We calculate cross sections for elastic scattering and annihilation in antihydrogen-helium collisions at low energies. The calculations are based on the Born-Oppenheimer approximation, and incorporate the effects of the strong interaction through a scattering length approach. We find that the strong nuclear force not only causes significant annihilation, but also cannot be neglected in the elastic channel. In the zero energy limit we obtain the scattering length $a=\ensuremath{-}7.69\ensuremath{-}3.80i\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ for ground state antihydrogen-helium collisions. Annihilation is found to dominate over elastic scattering up to a temperature about 3K3\phantom{\rule{0.3em}{0ex}}\mathrm{K}3K. Loosely bound metastable antihydrogen-helium states are also investigated, and it is found that a number of relatively long-lived states with up to three units of angular momentum exist.
The stability of antimatter in contact with matter has been investigated. The interaction between hydrogen and antihydrogen is considered as the prototype reaction. We have focused interest on the rates for proton-antiproton and/or electron-positron annihilation during hydrogen-antihydrogen collisions at low energies. In particular, we have concentrated on the calculation of the rates for the rearrangement reaction leading to formation of protonium and positronium, ending inevitably in particle-antiparticle annihilation. The cross section for the rearrangement collision has been calculated in a fully quantum-mechanical treatment. Additionally, we have calculated cross sections for direct annihilation during the collision process, which was found to be comparable to the rearrangement cross section. The elastic cross section and its low-energy limit, given by the scattering length, have been calculated, allowing, by comparison to the inelastic processes, a prediction for the efficiency of cooling antihydrogen via collisions with ultracold hydrogen atoms.
We investigate two methods to include the strong nuclear force in hydrogen–antihydrogen scattering calculations. First, we construct a model optical potential with parameters determined by the measured shift and width of the protonium ground state. Although this potential is a very crude model for the strong nuclear force, its parameters may be adjusted to reproduce both bound states and low-energy annihilation cross sections to within the experimental accuracy. It is then shown that this potential may be reduced to a short-distance boundary condition in terms of the proton–antiproton strong-interaction scattering length. Elastic and annihilation cross sections for ground-state hydrogen–antihydrogen scattering are calculated for s- and p-waves, and collision energies up to 1 atomic unit. The two methods are found to agree to within about 1%. The main source of discrepancy is that the scattering-length approach does not account for vacuum polarization, relativistic, and finite-size corrections. We verify that the range of the strong interaction potential does not affect the hydrogen–antihydrogen s-wave scattering properties, and that the strong interaction has negligible influence on p-wave scattering. PACS Nos.: 36.10.-k, 34.90.+q
We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic ``hydrogen'' masses less than 1 u or a ``helium'' mass of 1.951.951.95 u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of 3He^{3}\mathrm{He}3He and 4He^{4}\mathrm{He}4He with H2{\mathrm{H}}_{2}H2​, HD, HT, and DT should be feasible in the near future.
In view of current interest in the trapping of antihydrogen ( ) atoms at very low temperatures, we have carried out a calculation of s-wave hydrogen–antihydrogen scattering at very low energies, using the Kohn variational method, taking into account rearrangement scattering into the three channels that contain positronium in its ground state and lie closest to threshold. We find that our values for the elastic cross section are in good agreement with the values obtained by Jonsell et al (Jonsell et al 2001 Phys. Rev. A 64 052712) using a distorted wave approximation. However, our values for the total rearrangement cross section are much larger than their values. In particular, the largest such cross section is for the N = 23 s-state of protonium and positronium in its ground state, a channel that was estimated to make a negligible contribution by Jonsell et al . As a consequence of our much larger values for the total rearrangement cross section, we predict that cooling of by cold H would be considerably less efficient than was found to be the case by Jonsell et al .
We present a nonadiabatic treatment of the hydrogen-antihydrogen system. The technique used to describe $\mathrm{H}\text{\ensuremath{-}}\overline{\mathrm{H}}$ collisions is based on the coupled-rearrangement-channel method. Within this approach the total, nonadiabatic wave function of the system is divided into two parts: an inner and an outer one. To describe the inner part a set of square-integrable four-body functions is used. These functions are obtained by a diagonalization of the total Hamiltonian projected on a chosen L2{L}^{2}L2 subspace; they explicitly contain components of various arrangement channels expressed in terms of corresponding Jacobi coordinates. The outer part of the total wave function reflects its asymptotic character. Our procedure leads to a system of nonlocal integrodifferential equations that are solved iteratively and simultaneously determine the outer part of the solution and the coefficients in the four-body expansion of the inner part. To solve these equations the compact fine difference method was applied. Using this formalism we perform a one-channel calculation of the elastic scattering to obtain the SSS matrix, the nonadiabatic scattering length, and the cross section for the low-energy elastic scattering in the $\mathrm{H}\text{\ensuremath{-}}\overline{\mathrm{H}}$ channel.