Benchmarking Theory with an Improved Measurement of the Ionization and Dissociation Energies of ${\mathrm{H}}_2$

The dissociation energy of ${\mathrm{H}}_2$ represents a benchmark quantity to test the accuracy of first-principles calculations. We present a new measurement of the energy interval between the $EF$ ${{}^1\mathrm{\Sigma }}_g^{+}(v=0,N=1)$ state and the $54p{1}_1$ Rydberg state of ${\mathrm{H}}_2$. When combined with previously determined intervals, this new measurement leads to an improved value of the dissociation energy $D_0^{N=1}$ of ortho-${\mathrm{H}}_2$ that has, for the first time, reached a level of uncertainty that is 3 times smaller than the contribution of about 1 MHz resulting from the finite size of the proton. The new result of $35999.582834(11){\mathrm{cm}}^{-1}$ is in remarkable agreement with the theoretical result of $35999.582820(26){\mathrm{cm}}^{-1}$ obtained in calculations including high-order relativistic and quantum-electrodynamics corrections, as reported in the following Letter [M. Puchalski, J. Komasa, P. Czachorowski, and K. Pachucki, Phys. Rev. Lett. 122, 103003 (2019)]. This agreement resolves a recent discrepancy between experiment and theory that had hindered a possible use of the dissociation energy of ${\mathrm{H}}_2$ in the context of the current controversy on the charge radius of the proton.

Figure 1

(a) Schematic diagram of the experimental setup. (b) Potential energy functions of the relevant electronic states of ${\mathrm{H}}_2$ and ${\mathrm{H}}_2^{+}$ and excitation scheme used to determine the ionization and dissociation energies of ${\mathrm{H}}_2$ (see text for details).

Figure 2

Upper panels: Spectra (black dots with error bars) of the $54p{1}_1\leftarrow EF(0,1)$ (a) and $77p{1}_1\leftarrow EF(0,1)$ (b) transitions and corresponding fits based on a Voigt line-shape model (blue traces), taking into account the hfs of the Rydberg states (orange stick spectra). Lower panels: Corresponding relative weights (blue) and weighted residuals.

Figure 3

Frequency of the $54\mathrm{p}{1}_1\leftarrow EF(0,1)$ transition of ${\mathrm{H}}_2$ measured on five different days (indicated by different colors and symbols) and after regular realignment of the laser beam and its reflection (indicated by changes from full to open symbols). The valve temperature was 80 K. The top and bottom panels present the frequencies of the two Doppler components and the central panel displays their average value. The symbols and error bars represent the line positions obtained by fitting the center positions and their corresponding statistical uncertainties (one standard deviation), respectively. The dashed blue lines and the blue area give the standard deviations of the full data set and of the mean, respectively.