Rydberg states of the hydrogen-antihydrogen quasimolecule

Abstract

A description of the excited lepton states of the hydrogen-antihydrogen quasimolecule is presented. Potential energy curves and the leptonic part of the wave functions corresponding to a variety of such states are calculated within the Born-Oppenheimer approximation employing the Ritz variational principle. Nonadiabatic corrections to the leptonic potentials are also obtained. Basis functions are constructed as products of explicitly correlated Gaussians and spherical harmonics which describe correctly the motion of leptons with arbitrary orbital angular momentum projection onto the molecular (internuclear) axis. The hadronic part of the wave function for each leptonic level of the hydrogen-antihydrogen system is calculated by solving the Schr\odinger equation with the obtained leptonic potentials. Corresponding solutions are generated utilizing precise B-spline representations. Employing leptonic and hadronic parts of the wave function the electron-positron and proton-antiproton annihilation rates are computed for a number of quasimolecular states. The decay rates of the hydrogen-antihydrogen system into separate positronium and protonium atoms are also estimated for the quasimolecular levels under consideration.