Formation of the Positronium Antihydride Molecules (\(\bar{\textrm{H}}\textrm{Ps}\)) in Low Energy, 5-Body Collisions of Antihydrogen Ion \(\bar{\textrm{H}}^+\) with Positronium Atoms Ps

In this paper we present the first pilot calculation of the elastic and inelastic cross sections for the 5-body scattering of antihydrogen ions with positronium atoms. These cross sections have not been calculated before and are not known experimentally. In particular, we focus on the collisional rearrangement reactions \(\bar{{ \mathrm H}}^+ + \textrm{Ps} \rightarrow {\bar{\textrm{H}}}\textrm{Ps} +{\mathrm{e^+}}\) ${\overline{\mathrm{H}}}^{+}+\text{Ps}\to \overline{\text{H}}\text{Ps}+{\mathrm{e}}^{+}$ which deplete the \(\bar{\textrm{H}}^+\) ${\overline{\text{H}}}^{+}$ ions and result in stable atomcules \(\bar{\textrm{H}}\textrm{Ps}\) $\overline{\text{H}}\text{Ps}$ . To better understand the mechanism of this rearrangement, we study the 3-dimensional, angle resolved positron densities of the 3- and 4-body fragments in the initial and final states of the rearrangement collision.