Precise multiphoton spectroscopy of the $\ce{H2}$, $\ce{HD}$, and $\ce{D2}$ molecules and a new determination of the ionization potential of $\ce{HD}$, , Ph.D. dissertation. (Yale University ). Thesis


In recent years, advances in theoretical treatments have made molecular hydrogen attractive for studies of fundamental physics in molecules. The relativistic and radiative corrections to the ground-state binding energy have been calculated, but few measurements have been able to test these predictions. With frequency-tripled pulse-amplified light from a continuous-wave single-frequency dye laser, it is possible to make precise measurements of two-photon transitions in the deep ultraviolet. Several two-photon transitions from the ground state to the $EF$ state of the stable isotopes of molecular hydrogen were measured with accuracies around $0.015~\text{cm}^{-1}$. Saturated absorption spectra of $\ce{I2}$ were acquired simultaneously to allow the accuracy to be improved to $0.003~\text{cm}^{-1}$ in the future by measuring the absolute frequencies of visible transitions in $\ce{I2}$. A second experiment used laser double resonance to measure the energies of transitions in $\ce{HD}$ from the $EF$ state to singlet Rydberg $p$ states ranging from $n=40$ to 80. A quantum defect analysis of these transitions was used to extrapolate to the series limit. Combining the series limit with the measured $EF$ state energy gives a value of $124\,568.479(19)~\text{cm}^{-1}$ for the ionization potential, in good agreement with ab initio calculations. The measurements of transitions to the $EF$ state in  allows a previous measurement of the ionization potential of $\ce{D2}$ to be improved by a factor of four to $\pm 0.027~\text{cm}^{-1}$. The ionization potentials of $\ce{H2}$, $\ce{D2}$, and $\ce{HD}$ have now been measured with accuracies of $0.014–0.027~\text{cm}^{-1}$. These accuracies are better than those of the ab initio calculations. The agreement between the measurements and the ab initio values confirms the calculated relativistic and radiative corrections.

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