Updated three-body model of $^6$He $β$ decay into the $α$ + $d$ continuum

Abstract

The $β$-decay process of the $^6$He halo nucleus into the $α+d$ continuum is studied in an updated three-body model. The $^6$He nucleus is described as an $α+n+n$ 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 $α+d$ 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 $β$ decay matrix element is a challenge for future {\it ab initio} calculations.

4 pages, 3 figures