Direct $Q$-Value Determination of the ${\beta }^{-}$ Decay of ${}^{187}\mathrm{Re}$

The cyclotron frequency ratio of ${{}^{187}\mathrm{Os}}^{29+}$ to ${{}^{187}\mathrm{Re}}^{29+}$ ions was measured with the Penning-trap mass spectrometer PENTATRAP. The achieved result of $R=1.000000013882(5)$ is to date the most precise such measurement performed on ions. Furthermore, the total binding-energy difference of the 29 missing electrons in Re and Os was calculated by relativistic multiconfiguration methods, yielding the value of $\mathrm{\Delta }E=53.5(10)\mathrm{eV}$. Finally, using the achieved results, the mass difference between neutral ${}^{187}\mathrm{Re}$ and ${}^{187}\mathrm{Os}$, i.e., the $Q$ value of the ${\beta }^{-}$ decay of ${}^{187}\mathrm{Re}$, is determined to be 2470.9(13) eV.

Figure 1

(a) Schematic of the PENTATRAP setup (not to scale). The ions are produced in an external ion source (electron beam ion trap, or EBIT) with a kinetic energy of $6.5\mathrm{keV}/q$, get $m/q$ separated with a magnetic bender, slowed down with two pulsed drift tubes to a few $\mathrm{eV}/q$ energy, and finally captured in the Penning traps hosted in a superconducting magnet. (b) Ion positions inside the traps, which are sequentially repeated during the measurement. The electric potential $\mathrm{\Phi }$ along the trap axis is depicted on the left side. For details, see text.

Figure 2

Top: the cyclotron frequencies of ${{}^{187}\mathrm{Os}}^{29+}$ and ${{}^{187}\mathrm{Re}}^{29+}$ ions in trap 2 (in red, left ordinate) and trap 3 (in blue, right ordinate) acquired over the entire measurement campaign, giving, in total, about 1100 ${\nu }_c$ data points. Middle four plots: enlargement of data block 4 plotted at the top. The interval is divided into five sub-blocks and the simultaneous fit of the third-order polynomials is applied to each sub-block for both traps (solid curves). Alternatively, a fifth-order polynomial was found to be the most reasonable model for the entire data block using the corrected Akaike information criterion as a model quality estimator (dashed purple curves). A common drift of $-2.4\mathrm{mHz}/\mathrm{h}$ is subtracted for the sake of clarity of the scattered data points. Bottom: the corresponding cyclotron frequency ratios $R_{\mathrm{sb}}$ determined for each sub-block for both traps. The black line and the gray shaded band are the weighted mean of the $R_{\mathrm{sb}}$ values for both traps and its statistical uncertainty, respectively.

Figure 3

The cyclotron frequency ratios $R_{\mathrm{sb}}$ determined over the entire measurement campaign for trap 2 (left) and trap 3 (right). The ratios are calculated by fitting polynomials of the third order to the sub-blocks of data, as shown in Fig. 2, middle. The weighted mean value and its statistical uncertainty for each trap are represented by the black line and the gray shaded band, respectively.

Figure 4

The blue filled circles are endpoint energy values $E_0$ obtained from the analysis of the ${\beta }^{-}$ decay of ${}^{187}\mathrm{Re}$ in Alessandrello [9], Galeazzi [10], and Arnaboldi [2]. The green empty circle is the evaluated $Q$ value from AME [11]. The red filled square is the $\mathrm{\Delta }M$ (in energy units) determined in this work.