The Branching Ratio for Superallowed β⁺ Decay of ²²Mg

High precision measurements of the ft-values for superallowed Fermi β decay transitions between 0⁺ T=1 isobaric analogue states provide a stringent test for weak interactions described by the Standard Model. These superallowed ft-values provide a direct measurement for the weak vector coupling constant G_v which, in addition to G_F calculated from muon decay, provide the V_ud component of the CKM matrix. The top row of the CKM matrix offers the most precise test of its unitarity with V_ud contributing most of its statistics. The branching ratio for ²²Mg currently has one of the highest uncertainties of all the experimental values that contribute to the calculation of G_v. The experiment to achieve a precise branching ratio for ²²Mg was done with GRIFFIN at TRIUMF in 2016 with the hopes of a achieving a 0.15% uncertainty improving on the 21-year-old value by Hardy and Towner that gives an uncertainty of 0.23%. The newly precise branching ratio will have implications on isospin symmetry breaking present in nuclei upon comparison between the Hartree-Fock and Wood-Saxon models used to provide the isospin symmetry breaking correction to the ft-values. In this work Geant4 simulations were done to investigate the positron annihilation gamma ray summing that are peculiar to the decay of ²²Mg. An accurate correction to this summing is crucial to achieve the high precision required for the superallowed branching ratio.