Benchmarking theory with an improved measurement of the ionization and dissociation energies of H\(_2\)

The dissociation energy of 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 \(^1\Sigma_g^+(v=0,N=1)\) state and the 54p1\(_1\) Rydberg state of 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-H\(_2\) that has, for the first time, reached a level of uncertainty that is three times smaller than the contribution of about 1 MHz resulting from the finite size of the proton. The new result of 35999.582834(11) cm\(^{-1}\) is in remarkable agreement with the theoretical result of 35999.582820(26) cm\(^{-1}\) obtained in calculations including high-order relativistic and quantum electrodynamics corrections, as reported in the companion article (M. Puchalski, J. Komasa, P. Czachorowski and K. Pachucki, submitted). This agreement resolves a recent discrepancy between experiment and theory that had hindered a possible use of the dissociation energy of H\(_2\) in the context of the current controversy on the charge radius of the proton.