Abstract
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.
Highlights
An antiproton (p) scattering off a hydrogen atom has attracted attentions as a fundamental case of the matter-antimatter reaction [1,2,3,4,5] supported by the antiproton beam experiments [6,7,8]
Theoretical studies of the four-body compound HH based on the Born-Oppenheimer (BO) approximation [20,21,22] are pioneering works for this question; the BO approximation involves a fundamental difficulty near the critical distance
The BO potential vanishes inside the critical distance; namely, the electron motion is ignored when the distance between the two nuclei is smaller than the critical distance
Summary
An antiproton (p) scattering off a hydrogen atom has attracted attentions as a fundamental case of the matter-antimatter reaction [1,2,3,4,5] supported by the antiproton beam experiments [6,7,8]. The cold sources of the antiproton and antihydrogen atom can open a vast new scientific field stimulated by interactions between matter and antimatter. A non-adiabatic calculation of HH was performed with complex/real scaling method that includes the explicit description of Pn + Ps states [33]. We perform the non-adiabatic three-body calculation for S-wave resonance states of pH located just below the p+H threshold by ∼ 1 meV. Since the dominant interaction between the antiproton and hydrogen atom is characterized by the induced dipole moment caused by the electric field of the antiproton that is in proportion to r−4 where r is the relative distance between the antiproton and hydrogen atom, the three-body system may have bound (resonance) states below the p + H dissociation threshold.
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