The excited state of the $\alpha$-particle: a benchmark study
Abstract
A benchmark study is performed for the excited state of He. When the Coulomb interaction is switched off, the He nucleus exhibits a bound excited state in the vicinity of H threshold. As the Coulomb interaction is gradually introduced, the excited state crosses the threshold and eventually becomes a resonant state. Using three numerical methods, we track the evolution of this excited state and determine the resonance energy and width. Comparisons of the theoretical predictions reveal a significant discrepancy with commonly used -matrix values based on the analysis of the experimental data. We explain the origin for this discrepancy. Additionally, the two-level energy spectrum of He in the absence of the Coulomb force exhibits characteristics linked to Efimov physics, suggesting a reduced sensitivity to interaction details.
Keywords
Cite
@article{arxiv.2508.08181,
title = {The excited state of the $\alpha$-particle: a benchmark study},
author = {Pierre-Yves Duerinck and Arnoldas Deltuva and Jérémy Dohet-Eraly and Mario Gattobigio and Alejandro Kievsky and Rimantas Lazauskas and Darius Likandrovas and Michele Viviani},
journal= {arXiv preprint arXiv:2508.08181},
year = {2025}
}