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

TL;DR

This paper presents an updated three-body model for the beta decay of the halo nucleus $^6$He into the $ ext{alpha} + d$ continuum, accurately reproducing experimental transition probabilities and highlighting challenges for future ab initio calculations.

Contribution

The study introduces a refined three-body model using hyperspherical coordinates and a modified potential to match experimental decay probabilities.

Findings

Total transition probability: 2.48 x 10^{-6} s^{-1}

Reproduces shape and absolute values of experimental data

Identifies strong internal and halo matrix element cancellation

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.