E A G Armour

Quadrupole corrections to matrix elements of transitions in resonant reactions of muonic molecule formation

The calculated resonant formation rates of the muonic molecules ddµ and dtµ are presented. The approach developed earlier for calculating the transition matrix elements in the dipole approximation has been extended to include the quadrupole terms in the multipole expansion of the interaction operator. The calculated dependence of the dtµ formation rates on the energies of the incident tµ muonic atoms shows that the effect of including the quadrupole correction is to reduce the magnitude of the peak rates by about 20–30% at the different temperatures, compared to those calculated in the dipole approximation. The dependence on temperature for the ddµ formation rates is obtained with the differences between the presented and previous calculations being less than 5%.

Calculation of cross sections for very low-energy hydrogen–antihydrogen scattering using the Kohn variational method

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.

An upper bound on the internuclear distance below which a proton and an antiproton are unable to bind an electron and a positron

Initially in a collision between antihydrogen and hydrogen the electron is bound to the proton and the positron to the antiproton. Clearly, if the proton and the antiproton coincide, they cannot bind the light particles. In this letter, an upper bound value of is obtained for the critical value of the internuclear distance below which the electron and the positron cease to be bound to the nuclei as they can attain a lower energy by separating from the nuclei and forming positronium.

The theoretical treatment of low-energy e+-H2 scattering using the Kohn variational method

The authors present calculations of e+-H2 scattering below the positronium formation threshold at 8.63 eV for the Sigma g+, Sigma u+, Pi u and Pi g symmetries using the generalized Kohn method. Mixing of the two lowest partial waves is allowed for in the Sigma g+, Sigma u+ and Pi u symmetries, using a two channel K-matrix. Comparisons with Kohn calculations of the lowest partial waves of these symmetries show that mixing of partial waves has a relatively small effect on the contributions to the total scattering cross section at the energies considered. The Pi g calculation includes only the lowest partial wave. As well as separable short-range correlation functions, the trial functions used in these calculations include Hylleraas-type functions containing the positron-electron distance as a linear factor and functions appropriate for taking into account long-range polarization of the hydrogen molecule.

Inclusion of the strong interaction in low-energy hydrogen-antihydrogen scattering using a complex potential

The aim of experimentalists currently working on the preparation of antihydrogen is to trap it at very low temperatures so that its properties can be studied. Any process that can lead to loss of antihydrogen is thus of great concern to them. In view of this, we have carried out a calculation of the antiproton annihilation cross section in very low-energy hydrogen–antihydrogen scattering using a complex potential to represent the strong interaction that brings about the annihilation. The potential takes into account the isotopic spin state of the proton and the antiproton and the possibility that they may be in either a singlet or a triplet spin state. The results for the annihilation cross section and the percentage change in the elastic cross section due to the inclusion of the strong interaction are similar to those obtained in a recent calculation (Jonsell et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 1195), using an effective range expansion. They are smaller by a factor of 2 and 3, respectively, than those obtained in an earlier calculation (Voronin and Carbonell 2001 Nucl. Phys. A 689 529c), using a coupled channel method and a complex strong interaction potential.

HYDROGEN-ANTIHYDROGEN INTERACTIONS

Abstract A small number of antihydrogen (AH) atoms have recently been prepared at CERN and at Fermilab. However, these atoms were travelling at speeds close to that of light. It is intended to carry out experiments on AH by trapping it at very low temperature (

The importance of an accurate target wavefunction in variational calculations for (e+–H2) scattering

Using the complex Kohn method, we have calculated variational values of phase shifts and the annihilation parameter, Zeff, for the elastic scattering of positrons by molecular hydrogen. Our results are sensitive to small changes in the accuracy of the wavefunction representing the target hydrogen molecule. We have developed a systematic approach to demonstrate that, at low positron energies, there are particular forms of the Kohn trial wavefunction for which the results of variational calculations are not reliable, even when the target wavefunction accounts for as much as 96.8% of the correlation energy of H2. We find that reliable results can be recovered if our calculations are extended to admit more sophisticated target wavefunctions accounting for 99.7% of the correlation energy. Remaining discrepancies between theory and experiment are briefly discussed.

An improved theoretical value for Zeff for low-energy positron-hydrogen-molecule scattering

The value of Zeff, the effective number of electrons per molecule available to the positron for annihilation, is calculated for low-energy positron-hydrogen-molecule scattering using a scattering wavefunction containing terms in which the positron-electron distance is included linearly as a factor. The results at very low energy are much closer to the experimental value than any that have been obtained previously.

Asymptotic form of three-body (dtµ)+ and (ddµ)+ wave functions

In order to investigate a discrepancy between existing literature values for the normalization constant in the asymptotic form of three-body wave functions for (dtµ)+, we report the results of a new calculation of the normalization constants for this system as well as the related system (ddµ)+. These were obtained by fitting to accurate variational wave functions with special care being taken to describe the long-range behavior.

Differential scattering and rotational excitation in low-energy positron-hydrogen-molecule collisions

Differential cross sections are calculated for positron-hydrogen-molecule scattering below the positronium formation threshold usingK-matrix elements obtained by the Kohn variational method. The internuclear separation of the hydrogen molecule is fixed at its equilibrium value, 1.4a0. The trial function used in the Kohn calculation is very flexible. It contains separable and Hylleraas-type basis functions and also basis functions to take into account longrange polarization. The cross sections for rotational excitation are also calculated, using the adiabatic-rotation approximation. Preliminary results are presented in this paper; full details will be published elsewhere.