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The dissociation energy of H$_2$ represents a benchmark quantity to test theaccuracy of first-principles calculations. We present a new measurement of theenergy 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 ofuncertainty that is three times smaller than the contribution of about 1 MHzresulting from the finite size of the proton. The new result of35999.582834(11) cm$^{-1}$ is in remarkable agreement with the theoreticalresult of 35999.582820(26) cm$^{-1}$ obtained in calculations includinghigh-order relativistic and quantum electrodynamics corrections, as reported inthe companion article (M. Puchalski, J. Komasa, P. Czachorowski and K.Pachucki, submitted). This agreement resolves a recent discrepancy betweenexperiment and theory that had hindered a possible use of the dissociationenergy of H$_2$ in the context of the current controversy on the charge radiusof the proton.

Benchmarking theory with an improved measurement of the ionization and dissociation energies of H$_2$