Analytical Results for the Three-Body Radiative Attachment Rate Coefficient, with Application to the Positive Antihydrogen Ion H¯+

To overcome the numerical difficulties inherent in the Maxwell–Boltzmann integral of the velocity-weighted cross section that gives the radiative attachment rate coefficient α R A for producing the negative hydrogen ion H - or its antimatter equivalent, the positive antihydrogen ion H ¯ + , we found the analytic form for this integral. This procedure is useful for temperatures below 700 K, the region for which the production of H ¯ + has 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. Our results, utilizing a 50-term explicitly correlated exponential wave function, confirm our prior numerical results.