Resonant Phenomena in Antihydrogen-Hydrogen Scattering

We present a treatment of cold hydrogen-antihydrogen collisions based on the asymptotic properties of atom-antiatom interactions. We derive general formulas for the elastic and inelastic cross sections and for the scattering lengths and analyze their sensitivity to the parameters characterizing the inelasticity of the collision process. Given the inelasticity, we obtain bounds for the complex scattering length. We investigate the influence of strong nuclear forces and the isotope effects in $\bar{\rm H}{\rm H}$ and $\bar{\rm H}{\rm D}$ collisions and demonstrate enhancement of these effects due to the presence of the near-threshold narrow ${\rm H}\bar{\rm H}$ ($\bar{\rm H}{\rm D}$) states. The values of the elastic and inelastic cross-sections with simultaneous account of rearrangement and strong forces are presented. General expressions for the (complex) energies of the near-threshold $\rm{H}\bar{\rm H}$ states are obtained.