Recoil ions from the $\beta$ decay of ${}^{134}\mathrm{Sb}$ confined in a Paul trap

The low-energy recoiling ions from the $\beta$ decay of ${}^{134}\mathrm{Sb}$ were studied by using the Beta-decay Paul Trap. Using this apparatus, singly charged ions were suspended in vacuum at the center of a detector array used to detect emitted $\beta$ particles, $\gamma$ rays, and recoil ions in coincidence. The recoil ions emerge from the trap with negligible scattering, allowing $\beta$-decay properties and the charge-state distribution of the daughter ions to be determined from the $\beta$-ion coincidences. First-forbidden $\beta$-decay theory predicts a $\beta \text{−}\nu$ correlation coefficient of nearly unity for the $0^{-}$ to $0^{+}$ transition from the ground state of ${}^{134}\mathrm{Sb}$ to the ground state of ${}^{134}\mathrm{Te}$. Although this transition was expected to have a nearly 100% branching ratio, an additional 17.2(52)% of the $\beta$-decay strength must populate high-lying excited states to obtain an angular correlation consistent with unity. The extracted charge-state distribution of the recoiling ions was compared with existing $\beta$-decay results and the average charge state was found to be consistent with the results from lighter nuclei.

Figure 1

The levels of ${}^{134}\mathrm{Te}$ populated by the decay of ${}^{134}\mathrm{Sb}$ with their published $\beta$ intensities and energies in keV [15].

Figure 2

A cross-sectional view of the BPT and the detector array used in this work, not to scale. The beam axis points out of the page, and the detectors are identified according to their positioning relative to this axis. In the left and bottom positions are the two $\mathrm{\Delta }E\text{−}E$ plastic-scintillator detectors used for $\beta$-particle detection, and in the right and top positions are two MCP detectors and two HPGe detectors used for recoil-ion and $\gamma$-ray detection, respectively.

Figure 3

Time-of-flight spectrum for $\beta$-ion coincidences for (a) the ${}^{134}\mathrm{Sb}$-optimized measurement cycle, (b) the ${}^{134m}\mathrm{Sb}$-optimized measurement cycle scaled to have the same ${}^{134m}\mathrm{Sb}$ decay contribution as in the ${}^{134}\mathrm{Sb}$-optimized measurements (as described in the text), and (c) the ${}^{134}\mathrm{Sb}$ spectrum obtained by subtracting the ${}^{134m}\mathrm{Sb}$ contribution. The data collected with the $\mathrm{\Delta }E$-MCP detector pairs separated by ${180}^{\circ }$ (left $\mathrm{\Delta }E$ with right MCP and bottom $\mathrm{\Delta }E$ with top MCP) are shown in blue while the data for detector pairs separated by ${90}^{\circ }$ (left $\mathrm{\Delta }E$ with top MCP and bottom $\mathrm{\Delta }E$ with right MCP) are shown in red.

Figure 4

(a) The rf-phase dependence of $\beta$-ion coincidences from the decay of ${}^{134}\mathrm{Sb}$. The best fit (red) from simulations consists of the sum of $2^{+}$ (green), $3^{+}$ (cyan), and $4^{+}$ (magenta) contributions. (b) The resulting TOF spectra from the charge-state distribution determined from the rf phase, confined to 2000 to 2800 ns to illustrate the low TOF behavior of the charge states.

Figure 5

The rising edge of the ${}^{134}\mathrm{Sb}$ decay TOF compared with three simulated cloud sizes, labeled by the FWHM of the Gaussian distribution used. The 1 mm (red) simulation is scaled to match counts between 2400–2600 ns, and the 2.5 mm (green) and 4 mm (cyan) are shown with the same number of $\beta$-ion coincidences as the 1 mm simulation.

Figure 6

The measured ${}^{134}\mathrm{Sb}$ TOF spectrum compared with simulations using the decay scheme in Ref. [16] with different $a_{\beta \nu }$ values. The value which matches $R_{180/90}=9.33$ from the data is $a_{\beta \nu }=0.47$ and the resulting TOF distribution is shown in red. The TOF spectra for $a_{\beta \nu }=0$ (cyan) and $a_{\beta \nu }=1$ (green) are also shown and result in $R_{180/90}$ values that are inconsistent with the data.

Figure 7

The TOF spectrum for $\beta$-ion coincidences compared with simulations (red) which include the decay scheme from the Nuclear Data Sheets [16] with $a_{\beta \nu }=1$ (cyan) and a single fictitious allowed Gamow–Teller transition with $a_{\beta \nu }=-1/3$ to a 5 MeV excited state (green) which decays directly to the ground state by a single $\gamma$ ray.

Figure 8

The $\beta$-energy spectrum for $\beta$-ion coincidences compared with simulations which include the decay scheme from the Nuclear Data Sheets [16] with $a_{\beta \nu }=1$ (red) combined with a single fictitious allowed Gamow–Teller transition with $a_{\beta \nu }=-1/3$ to a 5 MeV (blue) excited state which decays directly to the ground state by a single $\gamma$ ray, scaled to match counts above 200 keV.