$^6$He structure from semiclassical 3D models based on $\textit{ab initio}$ spatial correlations

Abstract

We construct semiclassical 3D models based on $\textit{ab initio}$ no-core shell model calculated two-body spatial correlations, which represent the preferred spatial configuration of nucleons for the ground state of $^6$He. We demonstrate that the presence of the two valence neutrons distorts and flattens the $α$ core in $^6$He, marking a clear departure from the tetrahedral configuration of free $^4$He, and that the two valence neutrons and the center of mass of the $α$ cluster ($α$-CM) are roughly located at the three distinct vertices of an equilateral triangle. We compute the geometric parameters that commonly characterize $^6$He structure, 1) $θ_{nn}$, the opening angle of the two valence neutrons with respect to $α$-CM, and 2) $r_{nn}$, the root-mean-square separation between the two valence neutrons. Refining the model with uncertainty estimation, we obtain $θ_{nn}= 58.5^{+5.4}_{-6.2}$ degrees and $r_{nn}= 4.12^{+0.37}_{-0.43}$ fm, agreeing with those calculated via a phenomenologically modified continuum-discretized coupled-channels method, while an interferometry experiment obtained a marginally higher $r_{nn}$.