In the context of the ongoing PUMA experiment (CERN), which investigates antiproton annihilation on atomic nuclei, we study the energy shifts and widths of hydrogenic states in the $\overline{p}+{}^3\mathrm{H}$ and $\overline{p}+{}^3\mathrm{He}$ 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 $\overline{p}{}^3\mathrm{H}$ and $\overline{p}{}^3\mathrm{He}$ 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 wave functions. Comparison with the nuclear density distributions indicates that the antiproton-nucleus annihilation is predominantly peripheral.

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• Coulomb energies & analogue states
• Energy levels
• Few-body systems
• Inelastic scattering reactions
• Nucleon-nucleon interactions
• A ≤ 5
• Ab initio calculations
• Optical, coupled-channel & distorted wave models