Experimental Validation of the Largest Calculated Isospin-Symmetry-Breaking Effect in a Superallowed Fermi Decay

A precision measurement of the $\gamma$ yields following the $\beta$ decay of ${}^{32}\mathrm{Cl}$ has determined its isobaric-analogue branch to be $({22.47}_{-0.18}^{+0.21})\%$. Since it is an almost pure-Fermi decay, we can also determine the amount of isospin-symmetry breaking in this superallowed transition. We find a very large value, ${\delta }_C=5.3(9)\%$, in agreement with a shell-model calculation. This result sets a benchmark for isospin-symmetry-breaking calculations and lends support for similarly calculated, yet smaller, corrections that are currently applied to $0^{+}\to 0^{+}$ transitions for tests of the standard model.

Figure 1

Top: Percent differences in the absolute efficiency from Ref. 10 (solid line) and our adopted uncertainties (shaded region). This adopted efficiency curve and its Cyltran-calculated extrapolation (dashed line) are compared to a Penelope simulation (dotted line). Bottom: $\gamma$-energy spectrum of the $11.2\times {10}^6$ $\beta$-coincident events observed in this work. Aside from the isolated ${}^{30}\mathrm{S}$ contaminant peak at 677 keV, labeled peaks are associated with the decay of ${}^{32}\mathrm{Cl}$ (the symbols * and ** indicate their single- and double-escape peaks). Boxed values indicate transitions from the 7002-keV isobaric-analogue state.

Figure 2

Our determination of the isospin-breaking correction for ${}^{32}\mathrm{Cl}$ (filled circle), and calculations for ${}^{32}\mathrm{Cl}$ as well as other superallowed transitions (open points), with the ${\delta }_{C1}$ and ${\delta }_{C2}$ components shown separately. The measurement and prediction for ${}^{32}\mathrm{Cl}$, particularly the ${\delta }_{C1}$ component, is significantly larger than in any of the $0^{+}\to 0^{+}$ transitions.