Precise measurements of half-lives and branching ratios for the $ \beta$ mirror transitions in the decay of Mg and Si.

Half-lives and branching ratios for the two mirror $ \beta$ decays of Mg and Si have been measured at the University of Jyväskylä with the IGISOL facility. The results obtained, $ T_{1/2}=11.303(3)$ s and $ T_{1/2}= 4.112(2)$ s for the half-lives of Mg and Si , respectively, are 7 and 8 times more precise than the averages of previous measurements. The values obtained for the super-allowed branching ratios of Mg and Si are $ B.R.=92.18(8)\%$ and $ B.R.=99.74(2)\%$ , respectively. The result for Mg is three times more precise than the average of the previous measurements, while for Si the precision has not been improved, the average of the previous measurements being already very precise. Isospin-symmetry-breaking corrections have been calculated for the two nuclei to determine the corrected $ {F}t$ value. [ABSTRACT FROM AUTHOR]