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

Abstract

The beta-decay process of the ${}^6$He halo nucleus into the alpha+d continuum is studied in a three-body model. The ${}^6$He nucleus is described as an 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 alpha+d potential. A total transition probability of 1.6E-6 s${}^{-1}$ 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 alpha+d potential is found essential to reproduce the order of magnitude of the data. Comments are made on R-matrix fits.

18 pages, 9 figures. Accepted for publication in Phys.Rev.C

References in corpus (3)

• Quantum Monte Carlo calculations of excited states in A = 6--8 nuclei
• Microscopic multicluster description of the neutron-rich helium isotopes
• Microscopic description of the beta delayed deuteron emission from \bbox{^6}He

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