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Ab initio description of $\bar{p}+\rm{^3H}$ and $\bar{p}+\rm{^3He}$ systems in optical models

In the context of the ongoing PUMA experiment (CERN), which investigates antiproton annihilation on atomic nuclei, we study the energy shifts and widths of Rydberg states in the $\bar{p}+\rm{^3H}$ and $\bar{p}+\rm{^3He}$ systems by performing ab initio calculations. The scattering lengths and scattering volumes are first determined by solving the Faddeev-Yakubovsky equations in configuration space. The level shifts and widths of the corresponding $\bar{p} \, \rm{^3H}$ and $\bar{p} \, \rm{^3He}$ hydrogen-like states are then obtained using the Trueman formula. A pronounced model dependence associated with the nucleon-antinucleon interaction is observed for certain states. Finally, annihilation densities are computed from the four-body wavefunctions. Comparison with the nuclear density distributions indicates that the nucleon-antinucleon annihilation is predominantly peripheral.