Decay channels and decay rates for the hydrogen-antihydrogen quasimolecule

Calculations of leptonic and hadronic annihilation rates in the hydrogen-antihydrogen molecule are presented. Both the leptonic potential and leptonic wave function are evaluated within the Born-Oppenheimer approximation employing the Ritz variational principle. Nonadiabatic corrections to the leptonic potential are also obtained. Explicitly correlated Gaussians are employed as basis functions, which describe accurately the hydrogen-antihydrogen interaction. Given the leptonic potential the hadronic part of the wave function for each molecular level of the hydrogen-antihydrogen quasimolecule is calculated by solving the corresponding Schrödinger equation by means of precise B-spline representations. The decay rates of the quasimolecule into separate positronium and protonium systems are estimated for a number of molecular levels. Utilizing the leptonic and hadronic wave functions the leptonic- and hadronic-annihilation rates for different molecular levels are computed.