Precision mass measurements with molecular ions: resolving rotational and vibrational energy

Precision measurements of the cyclotron frequency ratios H$_{3}^{+}$/HD$^{+}$ and H$_{3}^{+}$/$^{3}$He$^{+}$ have shown differences in the masses of H$_{3}^{+}$ ions due to rotational energy. From this, we have confirmed that some high J,K states of H$_{3}^{+}$ have mean lifetimes exceeding several weeks. Using the lightest H$_{3}^{+}$ ion, we have obtained lower limits on the atomic masses of the deuteron and helium-3 with respect to the proton. To obtain further information on the relative masses of the proton and deuteron, we are now measuring the cyclotron frequency ratio H$_{2}^{+}$/D$^{+}$. From our measurements we can observe the vibrational decay of H$_{2}^{+}$ and identify its vibrational state.