High-precision branching ratio measurement and spin assignment implications for ${}^{62}\mathrm{Ga}$ superallowed $\beta$ decay

A high-precision branching ratio measurement for the superallowed Fermi ${\beta }^{+}$ emitter ${}^{62}\mathrm{Ga}$ was performed with the Gamma-Ray Infrastructure for Fundamental Investigations of Nuclei (GRIFFIN) spectrometer at the Isotope Separator and Accelerator (ISAC) radioactive ion beam facility at TRIUMF. The high efficiency of the GRIFFIN spectrometer allowed 63 $\gamma$-ray transitions, with intensities down to $\approx 1$ part per million (ppm) per ${}^{62}\mathrm{Ga}{\beta }^{+}$ decay, to be placed in the level scheme of the daughter nucleus ${}^{62}\mathrm{Zn}$, establishing the superallowed $\beta$ branching ratio for ${}^{62}\mathrm{Ga}$ decay to be $99.{8577}_{-0.0029}^{+0.0023}\%$, a factor of 4 more precise than the previous world average. For several cascades, $\gamma \text{−}\gamma$ angular correlation measurements were performed to assign spins and/or determine the mixing ratios of transitions. In particular, the spin of the 2.342 MeV excited state in the daughter nucleus ${}^{62}\mathrm{Zn}$ was definitively assigned as $J=0$. This assignment resolves a discrepancy between previous measurements and has important implications for the isospin symmetry breaking correction, ${\delta }_{C1}$, in ${}^{62}\mathrm{Ga}$ superallowed Fermi $\beta$ decay.

Figure 1

(a) Absolute $\gamma$-ray photopeak efficiency of the GRIFFIN spectrometer operated in “single crystal” mode obtained using ${}^{56}\mathrm{Co}, {}^{60}\mathrm{Co}, {}^{133}\mathrm{Ba},$ and ${}^{152}\mathrm{Eu}$ calibration sources as well as a radioactive ion beam of ${}^{66}\mathrm{Ga}$. The black line is the fit to the data points using methods described in Ref. [42] and the turquoise-hatched band represent the uncertainty in the absolute efficiency. (b) Relative uncertainty in the absolute efficiency calibration.

Figure 2

Summed $\beta$ activity measured with SCEPTAR over the 8560 cycles used in the analysis on a linear (a) and logarithmic (b) scale. The first 2.5 s of the cycle involved background counting with no beam. From 2.5 s to 32.5 s the beam was turned on, as indicated by the vertical green lines. In the last 4 seconds the beam was turned off and the implanted radioactive beam decays. The tape was moved over a period of 1.5 s between each cycle (not shown). Panel (a) highlights the fit to the entire $\beta$ activity curve, while panel (b) illustrates the very small contributions of the contaminants to the total $\beta$ activity. Panel (c) shows the residuals to the fit, with a line indicating 0.

Figure 3

Gamma-ray spectra of (a) $\gamma$-singles without a $\beta$ coincidence, (b) $\beta \text{−}\gamma$ coincident events during the beam-on time, and (c) $\beta \text{−}\gamma$ coincident events during the last 2.5 s of the cycle, after the ${}^{62}\mathrm{Ga}$ activity had decayed to a negligible level.

Figure 4

The spectrum of $\gamma$-rays in coincidence with a $\beta$ particle detected in SCEPTAR during the beam-on portion of the cycle. Single- and double-escape peaks are labeled as S.E. and D.E., respectively, and the full energy is indicated.

Figure 5

Spectra of background subtracted $\beta$-tagged $\gamma$-rays in coincidence with (a) the 954-keV $\gamma$-ray, (b) the 851-keV $\gamma$-ray, and (c) the 1388-keV $\gamma$-ray. Single- and double-escape peaks are labeled as S.E. and D.E., respectively, and the full energy is indicated.

Figure 6

Level scheme of ${}^{62}\mathrm{Zn}$ populated in the ${\beta }^{+}$ decay of ${}^{62}\mathrm{Ga}$. The widths of the arrows indicate the relative intensities of the transitions. Transitions with intensities that are consistent with zero at the $1.5\sigma$ level are shown as tentative with dashed arrows. Additionally, given that the only observed transition from the proposed 5584-keV level was directly to the ground state, this level is also labeled as tentative (dashed).

Figure 7

Experimental data for the $\gamma \text{−}\gamma$ angular correlation between the 1388- and 954-keV $\gamma$ rays. The red line is not a fit to the data, but the result of a Geant4 [52] simulation of the expected $\gamma \text{−}\gamma$ angular correlation for a $0_1^{+}\to 2_1^{+}\to 0_{\text{gs}}^{+}$ cascade.

Figure 8

${\chi }^2/\nu$ versus $arctan$ of the mixing ratio, $\delta$, for the 1388-keV $\gamma$ ray in the 1388–954-keV $\gamma \text{−}\gamma$ cascade under different spin assumptions for the 2342-keV state in ${}^{62}\mathrm{Zn}$. For this cascade the ${\chi }^2/\nu$ minimum allows a definitive spin assignment of $J=0$ for the 2342-keV state.

Figure 9

The measured $\gamma \text{−}\gamma$ angular correlation between the 2227- and 954-keV $\gamma$ rays is shown by the data points with error bars. The red line is not a fit to the data, but the result of a Geant4 [52] simulation of the expected $\gamma \text{−}\gamma$ angular correlation for a $1^{(+)}\to 2_1^{+}\to 0_{\text{gs}}^{+}$ cascade.

Figure 10

${\chi }^2/\nu$ versus $arctan$ of the mixing ratio, $\delta$, for the 2227-keV $\gamma$ ray in the 2227–954-keV $\gamma \text{−}\gamma$ cascade under different spin assumptions for the 3181-keV state in ${}^{62}\mathrm{Zn}$. For this cascade the ${\chi }^2/\nu$ does not allow a definitive spin assignment for the 3181-keV state, but combined with $\beta$ feeding information an assignment of $J^{\pi }=1^{(+)}$ (green, solid curve) with a mixing ratio of $\delta =-0.01\left(8\right)$ is adopted (see text for details).

Figure 11

The measured $\gamma \text{−}\gamma$ angular correlation between the 2093- and 954-keV $\gamma$ rays is shown by the data points with error bars. The red line is not a fit to the data, but the result of a Geant4 [52] simulation of the expected $\gamma \text{−}\gamma$ angular correlation for the $0_2^{+}\to 2_1^{+}\to 0_{\text{gs}}^{+}$ cascade.

Figure 12

${\chi }^2/\nu$ versus $arctan$ of the mixing ratio, $\delta$, for the 2093-keV $\gamma$ ray in the 2093–954-keV $\gamma \text{−}\gamma$ cascade under different spin assumptions for the 3046-keV state in ${}^{62}\mathrm{Zn}$. For this cascade the ${\chi }^2/\nu$ does not allow a definitive spin assignment for the 3046-keV state, but is consistent with the tentative $J^{\pi }=0^{+}$ assignment.

Figure 13

A comparison between the current experimental results and the theoretical calculations of Refs. [16, 17, 18] for the isospin mixing components with low-lying $0^{+}$ states in the daughter nucleus ${}^{62}\mathrm{Zn}$ during ${}^{62}\mathrm{Ga}\beta$ decay. For the excited $0^{+}$ states the thicknesses of the levels are proportional to the ${\delta }_{C1}^n$ values, while for the ground state the thickness is proportional to the total ${\delta }_{C1}$. The dashed lines in the experimental level scheme represent excited $0^{+}$ states from Ref. [34] that were not observed in the current work and for which only upper limits could be set on the ${\delta }_{C1}^n$ values.