Penning trap mass measurements utilizing highly charged ions as a path to benchmark isospin-symmetry breaking corrections in ${}^{74}\mathrm{Rb}$

Penning trap mass measurements of neutron-deficient Rb isotopes have been performed at TRIUMF's Ion Trap for Atomic and Nuclear Science (TITAN) facility by utilizing highly charged ions (HCIs). As imperative for a new approach with significant gain in measurement precision, experimental procedures, and systematic uncertainties are discussed in detail. Among the investigated nuclides, the superallowed nuclear $\beta$ emitter ${}^{74}\mathrm{Rb}$ will especially benefit from the advantage offered by HCI because the limited attainable precision owing to its short half-life $(T_{1/2}=65$ ms) represents a challenge for conventional Penning trap mass spectrometry. Motivated by an updated $Q_{\mathrm{EC}}$ value for ${}^{74}\mathrm{Rb}$ of 10 416.8(3.9) keV and its large isospin-symmetry breaking corrections, we present a new test to benchmark the consistency between theoretical models of isospin-symmetry breaking corrections in superallowed decays, the conserved vector current hypothesis, and experimental data.

Figure 1

Layout of the TITAN transport beamline from the RFQ cooler and buncher to the EBIT and to the measurement Penning trap (MPET). Only critical beamline and diagnostics components such as microchannel plates (MCPs) or the pulsed drift tube after the RFQ (PLT) are displayed while omitting other einzel lenses and steerers. Elements displayed in red are controlled by fast HV switches. Devices with blue double arrows are retractable.

Figure 2

Schematic of the EBIT with an insert of the radial space charge potential on the left and the axial injection, charge breeding, and extraction potentials underneath.

Figure 3

Measured number of ions of ${}^{85}\mathrm{Rb}$ in various charge states for different charge-breeding times in the EBIT with a 2.5-keV and a 10-mA electron beam. The number of counts for each breeding time is the sum of 200 extractions from the EBIT.

Figure 4

TOF ion-cyclotron resonances for Rb isotopes in charge state $q=8+$. In (a), the rf field to couple magnetron and reduced cyclotron motion was continuously applied for $T_{\mathrm{rf}}=997$ ms. The quality of the resonance for longer storage times was reduced by background counts of HCIs which underwent charge exchange. In (b), a Ramsey excitation scheme with 6-85-6 ms was utilized. The (red) lines represent the fit to the theoretical line shapes [57, 59].

Figure 5

A TOF histogram of detected ions after they were released from the MPET. In addition to ${}^{76}\mathrm{Rb}{}^{8+}$, a peak expected to correspond to ${\mathrm{H}}_2^{+}$ was observed, which was attributable to charge exchange in the MPET between the stored HCIs and the residual gas. Vertical solid lines represent expected mean TOF for different charge states, while dashed lines indicate the TOF range of ion counts considered in the main analysis.

Figure 6

A histogram of ${\chi }^2$ from fits of the theoretical line shape to experimental resonances is compared to the expectation of the statistical ${\chi }^2$ distribution. Each fit was based on 41 data points in a resonance and 4 free parameters $({\nu }_c$, the initial magnetron radius ${\rho }_{-}$, the TOF offset, and the damping parameter), hence 37 degrees of freedom. For the resonance data, the sum-statistics method was used for the determination of the uncertainty of the TOF measurements. The experimental data consist of a measurement set of ${}^{87}\mathrm{Rb}{}^{9+}$ versus ${}^{85}\mathrm{Rb}{}^{9+}$ which was performed prior to the online measurement.

Figure 7

Dependency of the frequency ratio $R={\nu }_c^{\mathrm{ref}}/{\nu }_c^{\mathrm{meas}}$ of ${}^{76}\mathrm{Rb}{}^{8+}$ to ${}^{85}\mathrm{Rb}{}^{9+}$ on the lower limit of the selected TOF range (a). The data are from the measurement runs with the conventional excitation of $T_{\mathrm{rf}}=97$ ms. Note that the uncertainties are not independent but highly correlated because cuts with smaller lower TOF levels include the data of higher ones. With increasing lower limit one starts to cut into the ion distribution for ions on resonance. As a consequence, the averaged TOF for ions with an rf field of ${\nu }_{\mathrm{rf}}={\nu }_c$ becomes larger, as indicated by the arrow in (b).

Figure 8

Dependency of the frequency ratio $R={\nu }_c^{\mathrm{ref}}/{\nu }_c^{\mathrm{meas}}$ of ${}^{76}\mathrm{Rb}{}^{8+}$ to ${}^{85}\mathrm{Rb}{}^{9+}$ on the lower limit of the selected TOF range with data from the measurement runs with the Ramsey excitation (a). The discrepancy for increased lower TOF limits is resolved by a count-class analysis in $R$. Panel (b) shows an example of such an analysis for a TOF range of 13–$50\mu \text{s}$. See text for details.

Figure 9

Measurements to check the accuracy of the measurement setup with ${}^{85}\mathrm{Rb}{}^{9+}$ as the reference ion. The dashed red lines represent the upper limit on remaining systematic uncertainties which was assigned to the frequency ratios of the online measurement. See text for details.

Figure 10

Improvements in the $\mathcal{F}t$ value of ${}^{74}\mathrm{Rb}$ owing to laser spectroscopy [23], a recent BR measurement [86], and this work. Panel (a) shows the partial contributions to the uncertainty of the $\mathcal{F}t$ value of ${}^{74}\mathrm{Rb}$. In (b) it is compared to the data of the most recent survey of superallowed $\beta$ decays [7]. The gray band corresponds to the weighted average of all 13 cases. Isospin-symmetry breaking corrections, ${\delta }_C$, in (a) and (b) are based on shell-model calculations with Saxon-Woods radial wave functions [7].

Figure 11

Test of the isospin-symmetry correction term ${\delta }_C$ for the heavier superallowed $\beta$ decays. The legend of (b) also applies to (a) and (c). The inset in (b) shows the error contributions to these six theoretical $ft$ values for ${\delta }_C$ from the shell model with Hartree-Fock radial wave functions. Of the three error contributions, statistical uncertainties enter only in the $\overline{\mathcal{F}t}$ value. Panel (c) is identical to (a) except that in the former ${}^{26m}\mathrm{Al}$ is not considered for the $\overline{\mathcal{F}t}$ value. The horizontal dashed line illustrates that the differences are small when omitting ${}^{26m}\mathrm{Al}$. See text for details.