Time-reversal breaking in isospin-hindered $^{45}$K decay

Isospin-hindered Fermi transitions in $\beta$ decay enhance sensitivity to many sources of time-reversal violation (TRV) [Barroso and Blin-Stoyle [Phys Lett 45B 178 (1973)]. The key concept is that the TRV matrix element is compared to the Coulomb interaction's isospin-breaking matrix element, rather than to the entire decay. We are considering two isospin-hindered Fermi/Gamow-Teller decays, $^{45}$K and $^{47}$K, for which measurements of the TRV correlation $D \vec{I} \cdot \vec{v_\beta} \times \vec{v_\nu}$ are possible using TRIUMF's Neutral Atom Trap for $\beta$ decay (TRINAT). Sensitivity could be enhanced by an order of magnitude compared to the Fermi/G-T mirror decay of $^{37}$K. We would first measure the needed isospin breaking using the asymmetry of emission of the nuclear progeny with respect to the initial spin, which vanishes for pure G-T decay [J.R.A. Pitcairn et al. Phys Rev C 79 015501 (2009)] and is linear in the isospin breaking matrix element. We will also update use of GAGG scintillators for radiative beta decay TRV experiments.