Light antiproton-nucleus systems at low energies with the ab initio NCSM/RGM method

Abstract

The availability of low-energy antiproton beams at the CERN Antiproton Decelerator has renewed interest in using antimatter as a probe of nuclear structure and in forming exotic antiprotonic few-body systems. In this work, we extend the ab initio No-Core Shell Model combined with the Resonating Group Method (NCSM/RGM), which was successfully applied to light-nucleus structure and reactions, to antiproton-nucleus dynamics at low energies. The NCSM/RGM formalism is adapted to antiproton projectiles by removing the requirement of antisymmetrization under exchange of target and projectile constituents, while retaining a fully microscopic description of the nuclear target and the relative motion. We focus on the lightest systems, ${\bar p}+d$, ${\bar p}+{}^3 \mathrm{H}$, and ${\bar p}+{}^3\mathrm{He}$, for which benchmarking against exact solutions of the Schr\"odinger equation enables stringent validation and helps disentangle methodological uncertainties -- e.g., those associated with the choice of configurations included in the NCSM/RGM expansion -- so that the dominant residual uncertainty can be attributed to the $N\bar{N}$ interaction. We compute phase shifts, scattering lengths, cross sections, antiprotonic-atom level shifts and widths, nuclear quasi-bound energies, and annihilation densities. We find that the hard short-range components of the meson-exchange-based $N\bar{N}$ interaction lead to slow convergence of the NCSM/RGM kernels expanded in a harmonic-oscillator basis, requiring exceptionally large model spaces and posing significant numerical challenges. We discuss practical strategies to mitigate these limitations and assess the impact of missing closed-channel configurations, which is a significant source of uncertainties in very light systems.