The axial charge in the weak nucleon axial vector current has been precisely determined by measuring the alignment correlation terms in the $\beta$-ray angular distributions of the purely spin aligned mirror pair nuclei ${}^{12}\mathrm{B}{(I}^{\pi }{=1\mathrm{}}^{+}{,T}_{1/2}=20.2\mathrm{}\hspace{0.5em}\mathrm{ms})$ and ${}^{12}\mathrm{N}{(I}^{\pi }{=1\mathrm{}}^{+}{,T}_{1/2}=11.0\mathrm{}\hspace{0.5em}\mathrm{ms}).\mathrm{}$ The axial charge was determined to be $y=4.96\mathrm{}\pm 0.09$ $(\mathrm{stat}.\mathrm{})\pm 0.05$ $(\mathrm{syst}.\mathrm{})$ at a 90% confidence level. The previously obtained data in the year 1996 was reanalyzed to be added to the present result. The combined result is $y=4.90\mathrm{}\pm 0.10$ at a 90% confidence level. The axial charge is enhanced as much as $(72\mathrm{}\pm 4)\%$ from the impulse approximation model calculated value $y_{\mathrm{IA}}=\mathrm{2.85.}\mathrm{}$ Calculations using the impulse approximation with the soft-$\pi$ contribution $y_{\mathrm{th}}=4.15\mathrm{}$ explain the data quite well but not completely. If we introduce the in-medium mass renormalization the unexplained part of the experimental result corresponds to an in nuclear-medium nucleon mass reduction of $(16\mathrm{}\pm 4)\%$ at a 90% confidence level relative to the free nucleon mass, at the place where the decaying nucleon resides.

• Received 2 July 2001

DOI:https://doi.org/10.1103/PhysRevC.65.015209