Isospin mixing inMg24

We have used the $\beta -\gamma$ circular polarization correlation technique to measure the isospin-forbidden Fermi matrix element for the ${\beta }^{+}$ decay of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$ to the $4^{+}$ $T=1\mathrm{}$ state in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ at $E_x=8.439\mathrm{}$ MeV. The ${}_{}{}^{24}{}_{}{}^{}\mathrm{Al}$ activity was produced by bombarding a natural Mg target with 18 MeV protons. The $\beta -\gamma$ circular polarization correlation was measured using a novel apparatus which featured good energy resolution in both the $\gamma$ and $\beta$ arms. The circular polarization sensitive $\gamma$-ray detector utilized a transmission-mode Compton polarimeter and a 12.7 cm × 15.2 cm NaI detector. The $\beta$ detector was a telescope with a 700 μm surface barrier detector and a 5.1 cm × 12.7 cm plastic scintillator. The $\beta -\gamma$ circular polarization asymmetry $\tilde{A}$ [defined by $W(\theta , \tau )=1+\frac{\tau v}{c\tilde{A}}cos\theta$ where $\tau$ is the photon helicity] was found to be $\tilde{A}=-0.145\mathrm{}\pm 0.030$. After applying a correction for feeding of the 8.439 MeV state from the analog state this value of $\tilde{A}$ corresponds to a charge dependent matrix element between the 9.5 MeV $4^{+}$ $T=1\mathrm{} \mathrm{and} 8.4$ MeV $T=0\mathrm{}$ levels of $|〈4^{+}; 0|H_{\mathrm{CD}}|4^{+}; 1〉|=106\mathrm{}\pm 40$ keV which is the largest matrix element of $H_{\mathrm{CD}}$ ever observed in $\beta$ decay. For comparison the charge dependent matrix element between the 9.5 MeV state and the 4.1 MeV $4^{+}$ state, previously measured in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Na}$ decays is only 5.4±2.2 keV. Our exceptionally large value occurs because the 9.5 MeV $T=1\mathrm{} \mathrm{and} 8.4$ MeV