Updated three-body model of ${}^6$He $\beta$ decay into the $\alpha$ + $d$ continuum

Abstract

The $\beta$-decay process of the ${}^6$He halo nucleus into the $\alpha +d$ continuum is studied in an updated three-body model. The ${}^6$He nucleus is described as an $\alpha +n+n$ system in hyperspherical coordinates on a Lagrange-mesh. The shape and absolute values of the transition probability per time and energy units of new experiments are reproduced with a modified $\alpha +d$ potential. The obtained total transition probabilities are $2.48\times 10^{-6}$ s${}^{-1}$ for the full energy region and $2.40\times 10^{-6}$ s${}^{-1}$ for the cut-off $E>150$ keV. The strong cancellation between the internal and halo parts of the $\beta$ decay matrix element is a challenge for future {\it ab initio} calculations.

Comments: 4 pages, 3 figures