We have measured the isospin mixing of the $I^{\pi }=1/2^{+}, E_x=2.599$ MeV state in nearly doubly magic ${}^{47}\mathrm{Ca}$ with the isobaric analog $1/2^{+}$ state of ${}^{47}\mathrm{K}$. Using the TRIUMF atom trap for $\beta$ decay, we have measured a nonzero asymmetry of the progeny ${}^{47}\mathrm{Ca}$ with respect to the initial ${}^{47}\mathrm{K}$ 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 ${}^{47}\mathrm{K}\beta$ decay.

• Received 4 March 2024
• Accepted 3 May 2024

DOI:https://doi.org/10.1103/PhysRevC.109.L052501