Penning-Trap Mass Measurement of Helium-4

Light-ion trap (LIONTRAP), a high-precision Penning-trap mass spectrometer, was used to determine the atomic mass of ${}^4\mathrm{He}$. Here, we report a 12 parts-per-trillion measurement of the mass of a ${}^4{\mathrm{He}}^{2+}$ ion, $m({}^4{\mathrm{He}}^{2+})=4.001506179651(48)\mathrm{u}$. From this, the atomic mass of the neutral atom can be determined without loss of precision: $m({}^4\mathrm{He})=4.002603254653(48)\mathrm{u}$. This result is slightly more precise than the current CODATA18 literature value but deviates by 6.6 standard deviations.

Figure 1

Cross-sectional sketch of the trap setup. The mEBIS produces ions in situ. ${}^4\mathrm{He}$ atoms (blue) are released upon heating the source and guided into the electron beam (dotted black line) from the FEP, which enables the production of ${}^4\mathrm{He}$ ions. The electron beam also ablates and ionizes atoms from the target’s surface. The trapped ion cloud (orange-shaded spot) is adiabatically transported from the CT to the PT to prepare single ions. The axial detection system in the PT is also depicted. The lower right side of the image illustrates how the ions are stored and shuttled between the PT and one of the STs for the ${\nu }_c$ measurements. In this example, ${}^4{\mathrm{He}}^{2+}$ and ${}^{12}{\mathrm{C}}^{6+}$ are measured at time $t_1$ and $t_2$, respectively.

Figure 2

An axial dip spectrum of ${}^4{\mathrm{He}}^{2+}$. The axial frequency of the ion is extracted from the $\sim 500\mathrm{mHz}$ wide ion signal (green) fit with a line shape model (blue). To this end, the resonator’s parameters must be precisely known. The black and red lines indicate the line shape that results from artificially shifting the resonator frequency by 50 and 25 Hz, respectively. Because of the resulting asymmetry, these fits result in systematically shifted axial frequency values (marked with vertical dotted lines).

Figure 3

Timeline diagram of a measurement cycle. At the beginning of a cycle, ion-I is selected randomly and transported to PT, where all the modes are cooled, and the ${\nu }_z$ (dip) and ${\nu }_{+}$ (double-dip) are measured, followed by a ${\nu }_{+}$ (PnA) measurement. Ion-I is then moved away, ion-II is transported to the PT, and the frequencies are measured in the inverse sequence. The time periods mentioned are only approximate. Every measurement cycle consists of 17 PnA cycles, each performed with a different ${\mathrm{T}}_{\mathrm{evol}}$: $6\times 0.1\mathrm{s}$, 0.5 s, 1 s, 2 s, 5 s, 10 s, $6\times 20\mathrm{s}$. The long $T_{\mathrm{evol}}$ enable the determination of ${\nu }_{+}$ with the highest precision.

Figure 4

Residuals of the 3-parameter surface fit. Individual points in the plot correspond to different PnA settings. The $x$ axis marks the respective cyclotron radii of ${}^4{\mathrm{He}}^{2+}$ $r(\mathrm{He})$ and ${}^{12}{\mathrm{C}}^{6+}$ $r(\mathrm{C})$ and the number of cyclotron frequency ratios used to obtain each value ($N$). Each point is the mean of the corresponding $N$ measurements, and the error bar is the standard error of the mean. The $y$ axis shows the residuals of the surface fit for different excitation settings. The region between the dotted lines indicates the $1\sigma$ confidence interval of the frequency ratio extracted from the fit ($R_{\mathrm{stat}}^{\mathrm{CF}}$).

Figure 5

High-precision ${}^4\mathrm{He}$ mass values from different experiments. On the top, ${}^4\mathrm{He}$ mass measurements over the years [18, 26, 27, 28, 29, 30] are plotted as blue points. The red points indicate the mass of ${}^4\mathrm{He}$ reevaluated based on the recent proton [19] or deuteron [11] mass values (where these were used as reference ions). The red shaded area indicates the AME2020 value, and the grey shaded region indicates the CODATA18 value. On the bottom, an enlarged view into the result of this work is shown. The CODATA18 and AME2020 values coincide with the latest UW result (see text).