IMPROVEMENT OF THE DISSOCIATION ENERGY OF THE HYDROGEN MOLECULE (PART TWO)

The dissociation energy $D_0$ of ortho H$_2$ is a benchmark quantity in quantum chemistry, with recent QED calculations now approaching accuracies achievable in simple atoms. In the light of recent discrepancies between experiment and theory [1], a combined effort (see also part one) has been undertaken to provide an improved experimental value for $D_0$. We report the transition frequency from the $GK~^1\Sigma_g^+~(v=1, N=1)$ state to the 56p~$(N=1, S=0,F=0-2)$ Rydberg state belonging to the series converging on the $X^+~^2\Sigma_g^+~(v^+=0,N^+=1)$ ground state of ortho H$_2^+$. A resonant three-photon excitation scheme was employed, using pulsed VUV and VIS laser sources to reach the intermediate GK state and a continuous-wave near-infrared (NIR) laser source for the transition to the Rydberg state. To reach the desired accuracy, the procedure involved [2]: (i) minimizing the Doppler width through the use of a doubly skimmed, supersonic molecular beam produced by a cryogenic pulsed valve, (ii) minimizing stray electric and magnetic fields, (iii) cancelling the first-order Doppler shift using two counterpropagating laser beams, (iv) calibrating the NIR-laser frequency using a frequency comb referenced to an atomic clock. The ionization energy of the intermediate $GK$ state was obtained by adding the binding energy of the Rydberg state determined previously by millimeter-wave spectroscopy and multichannel quantum-defect theory [3]. In combination with the $GK~^1\Sigma_g^+~(v=1,N=1) \leftarrow X~^1\Sigma_g^+~(v=0,N=1)$ transition frequency presented in part one, an order-of magnitude improvement for $D_0$ at the $10^{-9}$ level of accuracy has been achieved, while remaining consistent with the previously most precise determination [4]. \footnotesize{[1] M. Puchalski et al., Phys. Rev. A 95, 052506 (2017)}\quad\quad\quad\quad\quad \footnotesize{[2] M. Beyer et al., Phys. Rev. A 97, 012501 (2018)} \footnotesize{[3] D. Sprecher et al., J. Chem. Phys. 140, 104303:1-18 (2014)}\quad\quad \footnotesize{[4] J. Liu et al., J. Chem. Phys. 130 (17), 174306 (2009)