Direct determination of the atomic mass difference of ${}^{187}\mathrm{Re}$ and ${}^{187}\mathrm{Os}$ for neutrino physics and cosmochronology

For the first time a direct determination of the atomic mass difference of ${}^{187}\mathrm{Re}$ and ${}^{187}\mathrm{Os}$ has been performed with the Penning-trap mass spectrometer SHIPTRAP applying the novel phase-imaging ion-cyclotron-resonance technique. The obtained value of $2492\left({30}_{\mathrm{stat}}\right)\left({15}_{\mathrm{sys}}\right)$ eV is in excellent agreement with the $Q$ values determined indirectly with microcalorimetry and thus resolves a long-standing discrepancy with older proportional counter measurements. This is essential for the determination of the neutrino mass from the ${\beta }^{-}$ decay of ${}^{187}\mathrm{Re}$ as planned in future microcalorimetric measurements. In addition, an accurate mass difference of ${}^{187}\mathrm{Re}$ and ${}^{187}\mathrm{Os}$ is also important for the assessment of ${}^{187}\mathrm{Re}$ for cosmochronology.

Figure 1

$Q$ values of the ${\beta }^{-}$ decay of ${}^{187}\mathrm{Re}$ obtained in Brodzinski-1965 [13], Huster-1967 [14], Ashktorab-1993 [15], Cosulich-1992 [16], Alessandrello-1999 [17], Galeazzi-2000 [18], Arnaboldi-2003 [1], and this work. The uncertainty of our value comprises the statistical and systematical uncertainties.

Figure 2

Schematic of the SHIPTRAP setup used for the determination of the $Q$ value of the ${\beta }^{-}$ decay of ${}^{187}\mathrm{Re}$. Note that while the ions perform cyclotron and magnetron revolutions in the same sense, their cyclotron phase image is inverted during the cyclotron-to-magnetron conversion [19].

Figure 3

$XY$ distributions of ${}^{187}{\mathrm{Os}}^{+}$ ions on the position-sensitive MCP detector. There are the central spot and the phase spots corresponding to the ions in the center of trap, ions after applying (a) pattern 1 of the excitation-pulse scheme for accumulating the magnetron-motion phase and (b) pattern 2 for accumulating the cyclotron-motion phase [19]. For details see text.

Figure 4

$Q$ values of the ${\beta }^{-}$ decay of ${}^{187}\mathrm{Re}$ calculated from the cyclotron-frequency ratios $R_{4\mathrm{h}}$. The middle black line and grey shaded band are the average $Q$ value and its uncertainty of the work reported here. The upper red line and red shaded band are the average $Q$ value and its uncertainty, respectively, obtained with proportional counters. The lower blue line represents the average $Q$ value obtained with cryogenic microcalorimeters. The thickness of the line exceeds the uncertainty of this $Q$ value.