Polarization in the production of the antihydrogen ion
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
Polarization in the production of the antihydrogen ion? Casey A. Yazejian and Jack C. Stratona Department of Physics, Portland State University, Portland, OR 97207-0751, USA Received 31 October 2019 / Received in final form 1 May 2020 Published online 23 July 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. We provide estimates of both the cross section and rate coefficient for the radiative attachment + + of a second positron to create the H ion, H (1s) + e+ → H 1s2 1 S e + ~ω, for which the polarization of the initial state H (1s) is taken into account. We show how to analytically integrate the resulting six-dimensional, three-body integrals for wave functions composed of explicitly correlated exponentials, a result that may be extended to Hylleraas wave functions. We extend Bhatia’s polarization results for the equivalent matter problem down to the low temperatures required for the Gravitational Behaviour of Antihydrogen at Rest (GBAR) experiment at CERN. The two-electron polarization cross-term is of intrinsic interest because it has every appearance of being singular at the origin, but non-singular when integrated numerically. We show that conventional approaches lead to a final integral with two singular terms that may be made to cancel in lowest order. However, higher-order terms in such approaches defy analytical integration. We use an integro-differential transform based on Gaussian transforms to bypass this blockage to yield a fully analytic result. Even in this method, one avoids the singular form only by integrating out the radial integrals before solving the second Gaussian integral.
1 Introduction For more than a decade, production of antihydrogen (H) atoms at the Antiproton Decelerator (AD) facility at CERN [1] has provided the foundation for a variety of experiments (e.g., [2–4]). The ALPHA and ATRAP collaborations now trap small numbers of these anti-atoms in specialized magnetic minimum neutral atom traps [5–7], and confinement times of many minutes are now possible at ALPHA [8]. This has led to spectroscopic [9] measurements for H, an experimental limit on its charge [10], and even a rough limit on the gravitational interaction of the anti-atom [11]. The GBAR collaboration [12–14] has built on the latter idea to measure the gravitational attraction of matter versus antimatter using neutral H atoms, but these are difficult to cool sufficiently. They plan to form the antihydro+ gen ion H as an intermediate step because its net charge allows for sympathetic cooling with a mixture of positively charged ions of ordinary matter like Be+ . After cooling, the extra positron would then be stripped off for studies of the gravitational interaction of the anti-atom [12–14]. Prior papers [15,16] have calculated the cross section and ?
Contribution to the Topical Issue “Low-Energy Positron and Positronium Physics and Electron-Molecule Collisions and Swarms (POSMOL 2019)”, edited by M
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