Rotational Energy as Mass in ${{\mathrm{H}}_3}^{+}$ and Lower Limits on the Atomic Masses of D and ${}^3\mathrm{He}$

We have made precise measurements of the cyclotron frequency ratios ${{\mathrm{H}}_3}^{+}/{\mathrm{HD}}^{+}$ and ${{\mathrm{H}}_3}^{+}/{{}^3\mathrm{He}}^{+}$ and observe that different ${{\mathrm{H}}_3}^{+}$ ions result in different cyclotron frequency ratios. We interpret these differences as due to the molecular rotational energy of ${{\mathrm{H}}_3}^{+}$ changing its inertial mass. We also confirm that certain high $J$, $K$ rotational levels of ${{\mathrm{H}}_3}^{+}$ have mean lifetimes exceeding several weeks. From measurements with the lightest ${{\mathrm{H}}_3}^{+}$ ion we obtain lower limits on the atomic masses of deuterium and helium-3 with respect to the proton.

Figure 1

Ion mass differences measured with the three ${{\mathrm{H}}_3}^{+}$ ions. Data for $M[{{\mathrm{H}}_3}^{+}]-M[{\mathrm{HD}}^{+}]$ are indicated by round points, and for $M[{{\mathrm{H}}_3}^{+}]-M[{{}^3\mathrm{He}}^{+}]$ by triangles.

Figure 2

Rotational levels of the ground vibrational level of ${{\mathrm{H}}_3}^{+}$ with $J=K$ (lower) or $K+1$ (upper), for $J\le 19$. Levels that are absolutely stable against electric dipole decay are shown with heavier lines.