The $G$-parity-violating, second-class current- (SCC) induced tensor term in the weak-nucleon axial-vector current was determined from $\beta$-decay correlation measurements of the mass $A$ = 20 mirror pair. The alignment correlation terms in the $\beta$-decay angular distribution from the purely spin aligned mirror pair, ${}^{20}$F and ${}^{20}$Na, were measured in the present study. Combining the present results with existing results of $\beta$ and delayed $\gamma$-ray angular correlation measurements for the $A$ = 20 mirror pair, the SCC-induced tensor term was extracted to be $d_{\mathit{II}}/Ac$ = 0.18 $\pm$ 0.48. In the extraction, the weak-magnetism term, $b/Ac$ = 8.58 $\pm$ 0.28, evaluated from the $M$1 analog $\gamma$-ray decay strength, was used in a framework of the conserved vector current hypothesis. This is the first unambiguous extraction of the $(b-d_{\mathit{II}})/Ac$ term free from the contribution of the second-forbidden form factor, $j_2$, in the axial-vector current, which was a limiting factor for accurate determination of nonexistence of the SSC in the $\beta$ decay of the $A$ = 20 system.

• Received 1 July 2011

DOI:https://doi.org/10.1103/PhysRevC.84.055501