Bound state properties, positron annihilation and hyperfine structure of the four-body positronium hydrides

Bound state properties of the ground (bound) ¹S(L = 0)-state(s) in the four-body positronium hydrides ¹HPs, ²HPs (DPs), ³HPs (TPs) and MuPs are determined and investigated. By using numerical data from our computations of these four-body systems we have determined a number of different annihilation rates for each of these positronium hydrides and evaluated the hyperfine structure splitting. The properties of the ground (bound) states in the four-body exitonic Mh⁺ e⁻₂ e⁺ complexes, where M ≥ 1 and M ≤ 1, have also been evaluated numerically. The neutral four-body systems Mh⁺ e⁻₂ e⁺ with M 1 are similar to the HPs hydrides. In particular, each of these states has only one bound state. We also discuss applications of the exponential and semi-exponential variational expansions for accurate, bound state computations of the four-body positronium hydrides.