Dissociation Energy of the Hydrogen Molecule at ${10}^{-9}$ Accuracy

The ionization energy of ortho-${\mathrm{H}}_2$ has been determined to be $E_{\mathrm{I}}^{\mathrm{o}}({\mathrm{H}}_2)/(hc)=124357.238062(25){\mathrm{cm}}^{-1}$ from measurements of the $GK(1,1)-X(0,1)$ interval by Doppler-free, two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the $GK(1,1)$ state by continuous-wave, near-infrared laser spectroscopy. $E_{\mathrm{I}}^{\mathrm{o}}({\mathrm{H}}_2)$ was used to derive the dissociation energy of ${\mathrm{H}}_2$, $D_0^{N=1}({\mathrm{H}}_2)$, at $35999.582894(25){\mathrm{cm}}^{-1}$ with a precision that is more than one order of magnitude better than all previous results. The new result challenges calculations of this quantity and represents a benchmark value for future relativistic and QED calculations of molecular energies.

Figure 1

Potential energy diagram of electronic states in molecular hydrogen relevant to this Letter.

Figure 2

Schematic layout of the $GK\text{−}X$ experimental setup, where the pulsed pump laser for the oscillator and amplifier is not shown.

Figure 3

(a) Recording of a $GK(1,1)\leftarrow X(0,1)$ transition in ${\mathrm{H}}_2$ (black circles). The red line is a fitted Gaussian curve with the residuals shown below. (b) Assessment of the residual first-order Doppler effect. Each color indicates an individual alignment configuration, where the largest deliberate misalignment is about 0.3 mrad. The blue and magenta points are shifted by 0.02 and $-0.02$ in velocity axis for clarity. The colored lines show a linear global fit for all alignments, resulting in the Doppler-free value indicated with the open circle. (c) Transition frequency measurements in different days. Each point indicates an average value for one day with its standard deviation. The dash line shows the mean value. The magenta line and the cyan area give the standard deviation of the data and of the mean, respectively, where the former is taken as a conservative statistical uncertainty.

Figure 4

(a) Typical spectrum of the $56p{1}_1\leftarrow GK(1,1)$ transition of ${\mathrm{H}}_2$ and its analysis based on a Lorentzian line shape model and the hyperfine structure of the $56p{1}_1$ Rydberg state given as red ($F=1$), blue ($F=0$), and green ($F=2$) sticks. The weighted residuals are depicted below the spectrum. (b) Doppler-free frequencies with standard deviations of individual measurements. The magenta line and the cyan area give the standard deviation of the full data set and of the mean, respectively. The symbols label measurements carried out on different days.

Figure 5

Comparison between experimental and theoretical values of $D_0^{N=1}$ for ortho-${\mathrm{H}}_2$.