Three-body resonance states just below the antiproton and hydrogen dissociation threshold

We analyze two shallow resonance states below the antiproton hydrogen dissociation threshold with a non-adiabatic three-body calculation. Rearrangement correlation between initial channel and protonium formation channel is explicitly included in the total wavefunction. The lower resonance state is in good agreement with the resonance position and width calculated with the R-matrix theory. The higher resonance state which is newly found is closer to the threshold and much narrower than the former resonance. A polarization effect of the hydrogen atom is found to be indispensable to support the resonance state. The accuracy of the present calculation is evaluated by the extended virial theorem. The resonance states calculated in the present work gives shallower relative energy below the dissociation threshold than the Born-Oppenheimer calculation, suggesting that the electron motion which is ignored in latter calculation would give positive energy because the electron is unbound inside the distance