  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.
