First-Forbidden beta decay: Medium enhancement of the axial charge at A=16

Calculations are presented for four relatively strong first-forbidden $\beta$ decays in the region A=11-16 in order to study the very large mesonic-exchange-current enhancement of the rank-zero components. The $\mu^-$ capture on $^{16}$O is considered on the same footing. The wave functions utilized include up to 4$\hbar\omega$ excitations. Two-body exchange-current matrix elements are calculated as well as one-body impulse approximation matrix elements. The resultant enhancement factor that multiplies the impulse-approximation axial-charge matrix element is thereby determined by comparison to experiment to be $\epsilon_{exp}$ = 1.61 $\pm$ 0.03 from three $\beta^-$ decays and $\mu^-$ capture on $^{16}$O, which is in excellent agreement with meson-exchange calculations in the soft-pion approximation.