In-medium nucleon mass renormalization detected inβdecays of spin aligned12Band12N

Abstract

The axial charge in the weak nucleon axial vector current has been precisely determined by measuring the alignment correlation terms in the $\ensuremath{\beta}$-ray angular distributions of the purely spin aligned mirror pair nuclei ${}^{12}\mathrm{B}{(I}^{\ensuremath{\pi}}{=1}^{+}{,T}_{1/2}=20.2 \mathrm{ms})$ and ${}^{12}\mathrm{N}{(I}^{\ensuremath{\pi}}{=1}^{+}{,T}_{1/2}=11.0 \mathrm{ms}).$ The axial charge was determined to be $y=4.96\ifmmode\pm\else\textpm\fi{}0.09$ $(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}0.05$ $(\mathrm{syst}.)$ 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 $y=4.90\ifmmode\pm\else\textpm\fi{}0.10$ at a 90% confidence level. The axial charge is enhanced as much as $(72\ifmmode\pm\else\textpm\fi{}4)%$ from the impulse approximation model calculated value ${y}_{\mathrm{IA}}=2.85.$ Calculations using the impulse approximation with the soft-$\ensuremath{\pi}$ contribution ${y}_{\mathrm{th}}=4.15$ 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 $(16\ifmmode\pm\else\textpm\fi{}4)%$ at a 90% confidence level relative to the free nucleon mass, at the place where the decaying nucleon resides.