$2_1^{+}$ to $3_1^{+}$ $\gamma$ width in ${}^{22}\mathrm{Na}$ and second class currents

Background: A previous measurement of the $\beta \text{−}\gamma$ directional coefficient in ${}^{22}\mathrm{Na}\beta$ decay was used to extract recoil-order form factors. The data indicate the requirement of a significant induced-tensor matrix element for the decay. This conclusion largely relies on a standard-model-allowed weak magnetism form factor which was determined using an unpublished value of the analog $2_1^{+}\to 3_1^{+}$ $\gamma$ branch in ${}^{22}\mathrm{Na}$, with the further assumption that the transition is dominated by its isovector $M1$ component.

Purpose: Our aim is to determine the $2_1^{+}\to 3_1^{+}$ width in ${}^{22}\mathrm{Na}$ in order to obtain an independent measurement of the weak magnetism form factor for the $\beta$ decay.

Methods: A ${}^{21}\mathrm{Ne}(p,\gamma )$ resonance reaction on an implanted target was used to produce the first $2^{+}$ state in ${}^{22}\mathrm{Na}$ at $E_x=1952$ keV. Deexcitation $\gamma$ rays were registered with two 100% relative efficiency high purity germanium detectors.

Results: We obtain for the first time an unambiguous determination of the $2_1^{+}\to 3_1^{+}$ branch in ${}^{22}\mathrm{Na}$ to be $0.45\left(8\right)\%$.

Conclusions: Using the conserved vector current (CVC) hypothesis, our branch determines the weak magnetism form factor for ${}^{22}\mathrm{Na}\beta$ decay to be $|b/A{c}_1|=8.9\left(1.2\right)$. Together with the $\beta \text{−}\gamma$ angular correlation coefficient, we obtain a large induced-tensor form factor for the decay that continues to disagree with theoretical predictions. Two plausible explanations are suggested.

Figure 1

Decay scheme of ${}^{22}\mathrm{Na}$ shown with the transitions of interest. Energies are in keV.

Figure 2

Detector geometry used for this measurement. The target-to-detector distances for HPGe1 and HPGe2 are 4.5 and 8.4 cm respectively. HPGe2 is oriented at ${119}^{\circ }$ to the beam axis. The model shown in this picture was used for the simulations mentioned in the text.

Figure 3

Singles ${}^{21}\mathrm{Ne}(p,\gamma )$ spectra from HPGe1 for both resonances. The relevant ${}^{22}\mathrm{Na}\gamma$ rays produced from the resonances are marked with asterisks. A few contaminant lines are present and are discussed in the text.

Figure 4

Comparison of simulated efficiencies with the experimentally determined values for both detectors. ${10}^6$ primary showers were used in the simulations at each $\gamma$-ray energy.

Figure 5

HPGe1 spectrum highlighting the three $\gamma$ rays of interest (amongst others) from the 908-keV resonance and their fits.

Figure 6

Fit to the 1952 keV peak from HPGe1 for the 1113 keV resonance. In the fit we kept the centroid of the 1951 keV peak from ${}^{22}\mathrm{Ne}(p,\gamma )$ and the width of the 1956 keV peak fixed based on the values listed in Table 3. The broad 1967 keV line is an escape peak of a 2988 keV $\gamma$ ray from ${}^{22}\mathrm{Ne}(p,p^{\prime })$.

Figure 7

Top panel: Singles NaI spectrum. Bottom panel: Coincidence spectrum for HPGe1 generated by gating on the 5848 keV peak in the NaI detector as shown. The relevant peaks from ${}^{21}\mathrm{Ne}(p,\gamma )$ are labeled.

Figure 8

Monte Carlo simulations for 4 million $1952\to 583\to 0$ keV cascades. Top panel: Histogram for an unshielded Ge detector at ${\theta }_{\gamma }=0^{\circ }$ where the efficiencies show $\sim 5$% summing corrections. Bottom panel: Simulated result obtained with Pb shielding incorporated as shown in Fig. 2.