Analog-antianalog isospin mixing in ${}^{47}$K ${\beta }^{-}$ decay

Abstract

We have measured the isospin mixing of the I${}^{\pi }$= 1/2${}^{+}$ E${}_x$=2.599 MeV state in nearly-doubly-magic ${}^{47}$Ca with the isobaric analog 1/2${}^{+}$ state of ${}^{47}$K. Using the TRIUMF atom trap for $\beta$ decay, we have measured a nonzero asymmetry of the progeny ${}^{47}$Ca with respect to the initial ${}^{47}$K spin polarization, which together with the $\beta$ asymmetry implies a nonzero ratio of Fermi to Gamow-Teller matrix elements $y$= 0.098$\pm$0.037 for the $1/2^{+}\to 1/2^{+}$ transition. Interpreting $y$ as mixing between this state and the isobaric analog state implies a Coulomb matrix element magnitude 101 $\pm$ 37 keV. This relatively large matrix element supports a model from the literature of analog-antianalog isospin mixing, which predicts large matrix elements in cases involving excess neutrons over protons occupying more than one major shell. The result supports pursuing a search for time-reversal odd, parity-even, isovector interactions using a correlation in ${}^{47}$K $\beta$ decay.

arXiv comment7 (two-column) pages, 7 figures. Reprint of version accepted by Physical Review C Letters May 3, 2024 (proof corrections included, except we retain non-Letter features: section headers; \frac in inline equations; untruncated reference authors)

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