  The present theoretical work addresses the study of the formation of a
positive Antihydrogen ion in a single charge exchange reaction where a
positronium ( ground or excited state) interacts with a ground state
anti-hydrogen atom, being embedded in a dense Debye plasma. The calculations
are carried out in the frame work of a Coulomb Distorted Eikonal Approximation.
The result shows that Ps(3S) is the most interesting state to enhance the anti
H^+ production at the energy close to the reaction threshold. Regarding the
Debye screening, it may be inferred that in lower energy regime, the screening
effect enhances the TCS for the 1S and 2S states while reduces the same for the
2P and 3S states of Ps.
