Q-value of the superallowed β decay of ⁶²Ga

Abstract

Masses of the radioactive isotopes ⁶²Ga, ⁶²Zn and ⁶²Cu have been measured at the JYFLTRAP facility with a relative precision of better than $1.8\times {10}^{\mathrm{-8}}$. A $Q_{\mathrm{EC}}$ value of ($9181.07\pm 0.54$) keV for the superallowed decay of ⁶²Ga is obtained from the measured cyclotron frequency ratios of ⁶²Ga⁶²Zn, ⁶²Ga⁶²Ni and ⁶²Zn⁶²Ni ions. The resulting $\mathcal{F}t$-value supports the validity of the conserved vector current hypothesis (CVC). The mass excess values measured were ($-51986.5\pm 1.0$) keV for ⁶²Ga, ($-61167.9\pm 0.9$) keV for ⁶²Zn and ($-62787.2\pm 0.9$) keV for ⁶²Cu.

Introduction

According to the conserved vector current hypothesis (CVC), the matrix elements of the superallowed Fermi transitions between the $0^{+}$ isobaric analog states (IAS) should all be equal, independent of nuclear structure apart from small terms for radiative and isospin-symmetry breaking corrections. Provided this is true, the experimental values of the comparative half-life (ft) corrected for isospin mixing and radiative corrections $\mathcal{F}t$, allow for an accurate determination of the weak vector coupling constant $G_{\mathrm{V}}$. This value combined with the muon decay constant $G_{\mu }$ allows the extraction of $V_{\mathrm{ud}}$, the weak coupling matrix element between up and down quarks in the Cabibbo–Kobayashi–Maskawa (CKM) quark mixing matrix. Combining this value with other data on the matrix elements of the first row of the CKM matrix, $V_{\mathrm{us}}$ and $V_{\mathrm{ub}}$, it becomes possible to test the unitarity of the CKM matrix and the validity of the electroweak standard model. Depending on which value for $V_{\mathrm{us}}$ is taken from the recent literature, the current world data as reviewed by Hardy and Towner implies a slight failure for the unitarity test by a maximum of 2.4 standard deviations [1]. More recently, a new measurement of the $Q_{\mathrm{EC}}$-value of the superallowed β decay of ⁴⁶V is indicating a need for the re-evaluation of the $Q_{\mathrm{EC}}$-values of all the nine best-known cases employed in the unitarity analysis [2]. Therefore, it is now becoming of utmost importance to improve the $Q_{\mathrm{EC}}$-value data for these cases as well as to provide accurate data on new cases, as represented by ⁶²Ga studied in this Letter.

Following the notations of Hardy and Towner [1], the true $\mathcal{F}t$-value for the $0^{+}\to 0^{+}$ ($T=1$) decays is obtained using the equation

$$\mathcal{F}t\equiv ft(1+{\delta }_{{\mathrm{R}}^{\prime }})(1+{\delta }_{\mathrm{NS}}-{\delta }_{\mathrm{C}})=\frac{K}{2G_{\mathrm{V}}^2(1+{\Delta }_{\mathrm{R}}^{\mathrm{V}})}=\mathrm{constant},$$

where f is the β decay phase-space factor, t is the partial half-life, K is a constant, ${\delta }_{{\mathrm{R}}^{\prime }}$, ${\delta }_{\mathrm{NS}}$ and ${\Delta }_{\mathrm{R}}^{\mathrm{V}}$ are radiative corrections and ${\delta }_{\mathrm{C}}$ accounts for the isospin-symmetry breaking correction, see Refs. [1], [3] for a detailed discussion on these correction terms. A critical survey of 20 superallowed $0^{+}\to 0^{+}$ nuclear β decays [1] shows that the corrected $\mathcal{F}t$-values are constant to three parts in 10⁴. In the case of the nine best known $0^{+}\to 0^{+}$ transitions, the experimental ft-values are known to better than 0.15%. In most of the cases [1], the correction terms (${\delta }_{\mathrm{NS}}-{\delta }_{\mathrm{C}}$), ${\delta }_{{\mathrm{R}}^{\prime }}$ and ${\Delta }_{\mathrm{R}}^{\mathrm{V}}$, obtained from theory, are the limiting factors for improving the accuracy of the determination of the value of the vector coupling constant $G_{\mathrm{V}}$. Using Eq. (1) together with the radiative corrections as determined by the theory and assuming the validity of the conserved vector current, the isospin correction ${\delta }_{\mathrm{C}}$ can be experimentally determined providing thus important means to improve the theoretical model calculations. Currently, the dominant source of uncertainty in ${\delta }_{\mathrm{C}}$ arises from the disagreement between the results from different theoretical calculations.

To extend the well-known cases, it is important to measure new cases where nuclear structure dependent corrections are large or particularly challenging for model calculations. Typically, these are nuclei with $T_z=-1$ as well as heavy $T_z=0$ nuclei with $Z>30$. Recently, three such cases—²²Mg [4], [5], [6], ³⁴Ar [7] and ⁷⁴Rb [8], [9], [10]—have been studied with high precision for their $Q_{\mathrm{EC}}$-value but with only a modest accuracy for the half-life or the superallowed decay branch resulting in more moderate accuracies for their $\mathcal{F}t$-values ranging between 0.24 and 0.40% [1].

The next heaviest nucleus in the series of $T_z=0$, $T=1$, $I^{\pi }=0^{+}$ superallowed β emitters beyond ⁵⁴Co is ⁶²Ga, which is a particularly interesting $T_z=0$ nucleus because its β decay half-life has already been determined with high precision in several experiments yielding an average value of ($116.175\pm 0.038$) ms [11], [12], [13]. The current value and precision of the experimental branching ratio is (${99.85}_{\mathrm{-0.15}}^{\mathrm{+0.05}}$)%. However, possible additional unobserved Gamow–Teller transitions could increase the branching ratio to the excited $1^{+}$ states in ⁶²Zn, calling for more precise measurements of these transitions [14]. Prior to the present work, the $Q_{\mathrm{EC}}$-value of ⁶²Ga has been determined in only one experiment where a β end-point measurement resulted in a value of ($9171\pm 26$) keV [15].

In this Letter we present the first precise measurement of the $Q_{\mathrm{EC}}$-value and the mass of ⁶²Ga employing a double Penning trap setup connected to the on-line isotope separator IGISOL at the University of Jyväskylä [16]. In the same experiment, the masses of ⁶²Zn and ⁶²Cu were determined using ⁶²Ni as the reference ion whose mass excess is given with 0.6 keV uncertainty in the most recent atomic mass evaluation tables [17].