Gamma-delayed deuteron emission of the 6Li (0+;T=1) halo state

Abstract

M1 transitions from the $^6$Li($0^+;T=1$) state at 3.563 MeV to the $^6$Li($1^+$) 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 $^6$Li(0$^+$) resonance are well reproduced. The halo-like structure of the $^6$Li$(0^+)$ 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 $^6$He. In $^6$He, a nearly perfect cancellation effect between short-range and halo contributions was found. A similar analysis for the $^6$Li($0^+;T=1$) $γ$ 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 $Γ_γ(0^+\to α+d)/Γ_γ(0^+\to1^+)\approx 1.3\times 10^{-4}$ should be observable with current experimental facilities.

20 pages, 5 figures. Accepted for publication in Nucl. Phys. A., 2007