An upper bound on the internuclear distance below which a proton and an antiproton are unable to bind an electron and a positron

Abstract

Initially in a collision between antihydrogen and hydrogen the electron is bound to the proton and the positron to the antiproton. Clearly, if the proton and the antiproton coincide, they cannot bind the light particles. In this letter, an upper bound value of is obtained for the critical value of the internuclear distance below which the electron and the positron cease to be bound to the nuclei as they can attain a lower energy by separating from the nuclei and forming positronium.