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Recent productions of large numbers of cold antiprotons as well as theformation of antihydrogens at CERN and Fermilab have raised basic questionsabout possible coexistence of matter and antimatter in nature. In the presentwork, previous mathematical considerations are revisited which support thepossible coexistence of Antihydrogen with Hydrogen, Deuterium and Tritiumatoms. In particular, the main objective of the present work is to presentcomputational treatments which confirm the possible formation of these quasimolecules in laboratory. These treatments are based on a nonadiabatic pictureof the system in which generalized basis functions are adjusted within theframework of Rayleigh-Ritz' variational method. Thus, it is ruled out in thepresent work the Born-Oppenheimer adiabatic picture of the system, whichdemands the existence of bound states composed of fixed quasi heavy atoms(containing at least two baryons, e.g. protonium (Pn), with mean lifetime1.0x10^^-6 s) and quasi light atoms (composed of two leptons, e.g. positronium(Ps), with mean lifetime 125x10^^-12 s for para-Ps and 142.05x10^^-9 s forortho-Ps). Our calculations of the binding energies and internal structure ofAntihydrogen-Hydrogen, Antihydrogen-Deuterium and Antihydrogen-Tritium showthat these quasi molecules are bound and could be formed in nature. On theother hand, having in mind the adiabatic picture of the systems, our resultssuggest the possible formation of these molecules as resonant states inAntihydrogen-Atom interaction. Nevertheless, several arguments are accumulatedin the conclusion as consequences of the proposed bound states.

Possible Coexistence of Antihydrogen with Hydrogen, Deuterium and Tritium Atoms