Stability conditions for hydrogen-antihydrogen-like quasimolecules

We present a detailed study of the stability conditions of hydrogen-antihydrogen–like quasimolecules using both variational and finite-size scaling calculations. The stability diagram of the nuclear charge Z as a function of the internuclear distance R shows bound and unbound regions separated by a first-order critical line. Calculations of the leptonic annihilation rate show a peculiar behavior for nuclear charges Z 2, which was not observed for the hydrogen-antihydrogen quasimolecule; it goes through a maximum before it decays exponentially for large interhadronic distances. This might have a practical impact on the study of stability of matterantimatter systems.