Weak transitions in A=6 and 7 nuclei

The ⁶He β decay and ⁷Be electron capture processes are studied using variational Monte Carlo wave functions, derived from a realistic Hamiltonian consisting of the Argonne v₁₈ two-nucleon and Urbana-IX three-nucleon interactions. The model for the nuclear weak axial current includes one- and two-body operators with the strength of the leading two-body term—associated with Δ-isobar excitation of the nucleon—adjusted to reproduce the Gamow-Teller matrix element in tritium β decay. The measured half-life of ⁶He is underpredicted by theory by ≃8%, while that of ⁷Be for decay into the ground and first excited states of ⁷Li is overpredicted by ≃9%. However, the experimentally known branching ratio for these latter processes is in good agreement with the calculated value. Two-body axial current contributions lead to a ≃1.7% (4.4%) increase in the value of the Gamow-Teller matrix element of ⁶He (⁷Be), obtained with one-body currents only, and slightly worsen (appreciably improve) the agreement between the calculated and measured half-life. Corrections due to retardation effects associated with the finite lepton momentum transfers involved in the decays, as well as contributions of suppressed transitions induced by the weak vector charge and axial current operators, have also been calculated and found to be negligible.