Production of antimatter molecular ions

Recent years have seen marked progress in the production of, and experimentation with, atomic antimatter in the form of antihydrogen, $\overline{{\rm H}}$. Now we investigate the feasibility of producing the anti-molecular hydrogen anion, $\overline{{\rm H}}_2^-$ (analogue of ${\rm H}_2^+$, consisting of two antiprotons and a positron), in the laboratory. Recently Myers [1,2] argued that spectroscopic investigations of the anti-anion can offer very sensitive tests of the CPT theorem, which is one of the primary motivations for undertaking experiments with antimatter systems. Taking into account the present day ALPHA $\overline{{\rm H}}$ trap [3], utilizing reaction rates calculated here, from the literature, and via detailed balance, key processes are identified that could lead to the anion production. The feasibility of these reactions are discussed in the context of present day and near future experimental capabilities. [1] E. G. Myers Phys. Rev. A {\bf 98}, 010101(R) (2018). [2] E. G. Myers Hyperfine Interact. {\bf 239}, 43 (2018). [3] C. Amole et al. Nuc. Inst. Meth. In Phys. Research A {\bf 735}, 319 (2014).