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 $\hat{I}\pm +d$ continuum are studied in a three-body model. The bound states are described as an $\hat{I}\pm +n+p$ 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 $\hat{I}\pm +d$ continuum. The spectrum is sensitive to the description of the $\hat{I}\pm +d$ phase shifts. The corresponding gamma width is around 1.0 meV, with optimal potentials. Charge symmetry is analyzed through a comparison with the ${\hat{I}}^2$-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($0^{+};T=1$) ${\hat{I}}^3$ 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 $\hat{I}{“}_{\hat{I}}^3(0^{+}\to \hat{I}\pm +d)/\hat{I}{“}_{\hat{I}}^3(0^{+}\to 1^{+})\approx 1.3\times 10^{-4}$ should be observable with current experimental facilities.

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