Updated three-body model of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>He</mml:mi><mml:mprescripts/><mml:none/><mml:mn>6</mml:mn></mml:mmultiscripts><mml:mspace width="4.pt"/><mml:mi>β</mml:mi></mml:math> decay into the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>+</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math> continuum
Abstract
The $\ensuremath{\beta}$-decay process of the $^{6}\mathrm{He}$ halo nucleus into the $\ensuremath{\alpha}+d$ continuum is studied in an updated three-body model. The $^{6}\mathrm{He}$ nucleus is described as an $\ensuremath{\alpha}+n+n$ 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 $\ensuremath{\alpha}+d$ potential. The obtained total transition probabilities are $(2.48\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for the full energy region and $(2.40\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for the cut-off $E>150$ keV. The strong cancellation between the internal and halo parts of the $\ensuremath{\beta}$ decay matrix element is a challenge for future ab initio calculations.