Variational calculations for the hydrogen-antihydrogen system with a mass-scaled Born-Oppenheimer potential

TL;DR

This paper employs a variational approach with a mass-scaled Born-Oppenheimer potential to analyze proton-antiproton dynamics in hydrogen-antihydrogen, revealing bound, continuum, and potential resonance states.

Contribution

It introduces a modified nuclear interaction via mass-scaling of the Born-Oppenheimer potential, improving the treatment of the system's adiabatic correction and threshold behavior.

Findings

Calculated vibrational energy levels for L=0 and 1

Determined nuclear wave functions and scattering length

Identified possible resonance states in the system

Abstract

The problem of proton-antiproton motion in the ${\rm H}$--${\rm \bar{H}}$ system is investigated by means of the variational method. We introduce a modified nuclear interaction through mass-scaling of the Born-Oppenheimer potential. This improved treatment of the interaction includes the nondivergent part of the otherwise divergent adiabatic correction and shows the correct threshold behavior. Using this potential we calculate the vibrational energy levels with angular momentum 0 and 1 and the corresponding nuclear wave functions, as well as the S-wave scattering length. We obtain a full set of all bound states together with a large number of discretized continuum states that might be utilized in variational four-body calculations. The results of our calculations gives an indication of resonance states in the hydrogen-antihydrogen system.