In-Medium Mass Renormalization of Nucleons Detected in the Axial Charges of theβDecays of Spin AlignedB12andN12

The axial charge of the weak nucleon axial vector current extracted from the anisotropic β-ray angular distributions of spin aligned ${}^{12}\mathrm{B}$ and ${}^{12}\mathrm{N}$ was accounted for mainly in terms of the impulse value $y_{\mathrm{IA}}$ and the soft pion exchange effect term $y_{\mathrm{exch}}$. The experimental value, $y=4.66\mathrm{}\pm 0.06\left(\mathrm{stat}\right)\pm 0.13\left(\mathrm{syst}\right)$, was enhanced by 63% from the impulse value $y_{\mathrm{IA}}=2.85\mathrm{}$ which includes the core polarization effect. The experimental excess of 0.54 over the theoretical value $y_{\mathrm{IA}}{+y}_{\mathrm{exch}}=4.12\mathrm{}$ is accounted for by the in-medium mass reduction from the free nucleon value, if there is such an effect, of about $(12\pm 4)\%$ for the nucleons decaying in the $A=12\mathrm{}$ triad.