Calculations of antiproton–nucleus quasi-bound states using the Paris $\overline{N}N$ potential

An optical potential constructed using the $\overline{p}N$ scattering amplitudes derived from the 2009 version of the Paris $\overline{N}N$ potential is applied in calculations of $\overline{p}$ quasi-bound states in selected nuclei across the periodic table. A proper self-consistent procedure for treating energy dependence of the amplitudes in a nucleus appears crucial for evaluating $\overline{p}$ binding energies and widths. Particular attention is paid to the role of P-wave amplitudes. While the P-wave potential nearly does not affect calculated $\overline{p}$ binding energies, it reduces considerably the corresponding widths. The Paris S-wave potential supplemented by a phenomenological P-wave term yields in dynamical calculations $\overline{p}$ binding energies $B_{\overline{p}}\approx 200$ MeV and widths ${\Gamma }_{\overline{p}}\sim 200\text{–}230$ MeV, which is very close to the values obtained within the RMF model consistent with $\overline{p}$-atom data.