The Fate of Excited State of \(^4\text {He}\)

Abstract

We investigate the properties of the excited state of \(^4\textrm{He}\), \(^4\textrm{He}^*\), within the framework of Efimov physics and its connection to the unitary point of the nuclear interaction. We explore two different approaches to track the trajectory of \(^4\textrm{He}^*\) as it crosses the \(^3\textrm{H}\)+p threshold and potentially becomes a resonant state. The first approach involves an analytical continuation of the energy with respect to the Coulomb coupling, while the second approach introduces an artificial four-body force that it is gradually released. By utilizing Padé approximants and extrapolation techniques, we estimate the energy and width of the resonance. Our results suggest a central energy value of \(E_R=0.060(3)\) MeV and a width of \(\Gamma /2=0.036(6)\) MeV using the Coulomb analysis, and \(E_R=0.068(1)\) MeV and \(\Gamma /2=0.007(5)\) MeV with the four-body force analysis. Interestingly, these results are consistent with calculations based on ab-initio nuclear interactions but differ from the accepted values of the \(0^+\) resonance energy and width. This highlights the challenges in accurately determining the properties of resonant states in light nuclei and calls for further investigations and refinements in theoretical approaches.