Gamma-delayed deuteron emission of the halo state

M1 transitions from the state at 3.563 MeV to the ground state and to the α+d continuum are studied in a three-body model. The bound states are described as an α+n+p system in hyperspherical coordinates on a Lagrange mesh. The ground-state magnetic moment and the gamma width of the resonance are well reproduced. The halo-like structure of the resonance is confirmed and is probed by the M1 transition probability to the α+d continuum. The spectrum is sensitive to the description of the α+d phase shifts. The corresponding gamma width is around 1.0 meV, with optimal potentials. Charge symmetry is analyzed through a comparison with the β-delayed deuteron spectrum of 6He. In 6He, a nearly perfect cancellation effect between short-range and halo contributions was found. A similar analysis for the decay is performed; it shows that charge-symmetry breaking at large distances, due to the different binding energies and to different charges, reduces this effect. The present branching ratio Γγ(0+→α+d)/Γγ(0+→1+)≈1.3×10−4 should be observable with current experimental facilities.