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

TL;DR

This paper calculates antiproton-nucleus quasi-bound states using the Paris potential, emphasizing the importance of energy dependence and P-wave contributions, resulting in binding energies around 200 MeV and widths of 200-230 MeV.

Contribution

It introduces a self-consistent method for calculating antiproton binding energies and widths using the Paris potential, highlighting the role of P-wave amplitudes in these calculations.

Findings

P-wave amplitudes reduce the widths of bound states.

Calculated binding energies are approximately 200 MeV.

Widths of the states are around 200-230 MeV.

Abstract

An optical potential constructed using the ${\bar p}N$ scattering amplitudes derived from the 2009 version of the Paris ${\bar N}N$ potential is applied in calculations of ${\bar p}$ 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 ${\bar p}$ 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 ${\bar p}$ binding energies, it reduces considerably the corresponding widths. The Paris $S$-wave potential supplemented by a phenomenological $P$-wave term yields in dynamical calculations ${\bar p}$ binding energies $B_{\bar p}\approx 200$ MeV and widths $\Gamma_{\bar p}\sim~200 - 230$ MeV, which is very close to the values obtained within the RMF model consistent with ${\bar p}$-atom data.