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

Bound-state properties of the ground (bound) S-1(L = 0)-state(s) in the four-body positronium hydrides (1)HPs, (2)HPs (DPs), (3)HPs (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 (M)h(+)e(2)(-)e(+) complexes, where M >= 1 and M <= 1, have also been evaluated numerically. The neutral four-body systems (M)h(+)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. [GRAPHICS] .