Precision Half-Life Measurements of 13N, 25Al, and 29P for Testing the Standard Model

<p>Precision measurements of nuclear β-decays can be used to test the validity of the Standard Model through the evaluation of the V_ud 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 <i>TwinSol</i> 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.</p><p> The measured 13N half-life value of t_1/2 = 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 t_world = 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.</p><p> Our half-life measurement of ²⁵Al resulting in t_1/2 = 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 t_world = 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 V_ud from the ²⁵Al decay.</p><p> Finally, the resulting ²⁹P half-life value of t_1/2 = 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 t_world = 4.1031(58) s, which is 2.3 times more precise than the previous world value. The new evaluation of the element yields V_ud=0.949(44) for ²⁹P shifts closer into agreement with the superallowed pure Fermi β-decay value. The uncertainty in this value of V_ud, however, is still dominated by the uncertainty in the Fermi to Gamow-Teller mixing ratio ρ for ²⁹P.</p>