Precision measurements of nuclear β-decays can be used to test the validity of the Standard Model through the evaluation of the Vud element of the Cabbibo-Kobayashi-Masakawa quark mixing matrix and the Fierz interference term b. This dissertation consists of precision half-life measurements for three superallowed mixed mirror β-decays: 13N, 25Al, and 29P. 13N is the second most sensitive decay to Standard Model violating currents. The 25Al and 29P half-lives are the least precisely known of the light mirror transitions (i.e A<40), and both are evaluating from conflicting measurements all of which are over 30 years old. These measurements were conducted at the University of Notre Dame Nuclear Science Laboratory using the TwinSol β-counting station. To help with the identification of possible radioactive contaminants I have also developed and commissioned a new particle identification gas cell detector ACBAR.
The measured 13N half-life value of t½ = 597.13(17) s is the most precise measurement to date by a factor of 2. An evaluation of the 13N literature values results in a tworld = 597.37(15) s, improving the precision of this value by a factor of 1.5. An updated Standard Model prediction for the Fermi to Gamow-Teller mixing ratio ρ and its associated correlation parameters have been calculated using the new 13N world half-life in preparation for a future measurement of the mixing ratio, which will then allow the Fierz interference term b to be constrained.
Our half-life measurement of 25Al resulting in t½ = 7.1657(24) s is in good agreement with the most recent measurement, while being 3 times more precise. Using our new measurement, an evaluation of the 25Al world half-life has been performed, leading to an average half-life of tworld = 7.1665(26) s, which is 5 times more precise than its predecessor. To aid in future measurements of correlation parameters, a new Fermi to Gamow-Teller mixing ratio ρ and correlation parameters for this mixed transition have been calculated assuming Standard Model validity using the new world half-life. A measurement of ρ is stilled needed in order to extract Vud from the 25Al decay.
Finally, the resulting 29P half-life value of t½ = 4.1055(44) s is the most precise 29P half-life measurement to date. Utilizing this measurement and re-evaluating the world data leads to a new world average of tworld = 4.1031(58) s, which is 2.3 times more precise than the previous world value. The new evaluation of the element yields Vud=0.949(44) for 29P shifts closer into agreement with the superallowed pure Fermi β-decay value. The uncertainty in this value of Vud, however, is still dominated by the uncertainty in the Fermi to Gamow-Teller mixing ratio ρ for 29P.