We provide an estimate of the cross section for the radiative attachment of a second positron into the
state of the
ion using Ohmura and Ohmura’s (1960 Phys. Rev. 118 154) effective range theory and the principle of detailed balance. The
ion can potentially be created using interactions of positrons with trapped antihydrogen, and our analysis includes a discussion in which estimates of production rates are given. Motivations to produce
include its potential use as an intermediary to cool antihydrogen to ultra-cold (sub-mK) temperatures for a variety of studies, including spectroscopy and probing the gravitational interaction of the anti-atom.