Analysis of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">He</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>β decay into the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>α</mml:mi><mml:mo>+</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math>continuum within a three-body model
Annotatsiya
The \ensuremath{\beta}-decay process of the $^{6}\mathrm{He}$ halo nucleus into the $\ensuremath{\alpha}+d$ continuum is studied in a 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 convergence of the Gamow-Teller matrix element requires the knowledge of wave functions up to about 30 fm and of hypermomentum components up to $K=24$. The shape and absolute values of the transition probability per time and energy units of a recent experiment can be reproduced very well with an appropriate $\ensuremath{\alpha}+d$ potential. A total transition probability of $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ s${}^{\ensuremath{-}1}$ is obtained in agreement with that experiment. Halo effects are shown to be very important because of a strong cancellation between the internal and halo components of the matrix element, as observed in previous studies. The forbidden bound state in the $\ensuremath{\alpha}+d$ potential is found essential to reproduce the order of magnitude of the data. Comments are made on R-matrix fits.