Producing the positive antihydrogen ion via radiative attachment

• Published in: Journal of physics. B, Atomic, molecular, and optical physics Vol. 49; no. 7; pp. 74002 - 74011
• Main Authors: Keating, C M, Pak, K Y, Straton, Jack C
• Format: Journal Article
• Language: English
• Published: IOP Publishing 14.04.2016
• Subjects: Antihydrogen; antihydrogen ion; Attachment; Estimates; Integrals; Mathematical analysis; Mathematical models; photodetachment; Positrons; radiative attachment; Wave functions
• ISSN: 0953-4075; 1361-6455
• DOI: 10.1088/0953-4075/49/7/074002

We provide an estimate of the cross section for the radiative attachment of a second positron into the state of the ion that uses a 200-term two-positron wave function composed of explicitly correlated exponentials. This is done by analytically integrating the six-dimensional, three body photoionization integrals that enter into this result (and those utilizing, the alternative, Hylleraas wave functions) and applying the principle of detailed balance. Finally, we obtain the rate coefficient for attaching a second positron to antihydrogen as a function of temperature via a numerical integral that is a Maxwell-Boltzmann distribution of the product of positron velocity and cross section. Our motivation in studying the production of lies in its potential use as an intermediate stage in the cooling of antihydrogen to ultra-cold (sub-mK) temperatures for spectroscopic studies and probing the gravitational interaction of the anti-atom. Estimates of the reaction rates are given for positron temperatures Te in the range from 50 K to 5 K.