Atomic Masses of Tritium and Helium-3

By measuring the cyclotron frequency ratios of ${}^3{\mathrm{He}}^{+}$ to ${\mathrm{HD}}^{+}$ and ${\mathrm{T}}^{+}$ to ${\mathrm{HD}}^{+}$, and using ${\mathrm{HD}}^{+}$ as a mass reference, we obtain new atomic masses for ${}^3\mathrm{He}$ and T. Our results are $M[{}^3\mathrm{He}]=3.01602932243(19)\mathrm{u}$ and $M[\mathrm{T}]=3.01604928178(19)\mathrm{u}$, where the uncertainty includes an uncertainty of 0.12 nu in the mass reference. Allowing for cancellation of common systematic errors, we find the $Q$ value for tritium $\beta$ decay to be $(M[\mathrm{T}]-M[{}^3\mathrm{He}])c^2=18592.01(7)\mathrm{eV}$. This allows an improved test of systematics in measurements of tritium $\beta$ decay that set limits on neutrino mass.

Figure 1

Example of a single run of cyclotron frequency data for the ratio ${\mathrm{HD}}^{+}/{\mathrm{T}}^{+}$. The curves are a simultaneous least-squares fit using a fourth-order polynomial, as determined using an $F$ test [22].

Figure 2

Cyclotron frequency ratios from the individual runs. The $y$ axis shows the difference, in parts in ${10}^{12}$, between the results of the individual runs for ${\mathrm{HD}}^{+}/{}^3{\mathrm{He}}^{+}$ (squares) and ${\mathrm{HD}}^{+}/{\mathrm{T}}^{+}$ (triangles), and their respective (uncorrected) weighted means, as given in the second column of Table 1.