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

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 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 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.

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.

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.