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

## TL;DR

This paper presents a highly precise measurement of the H$_2$ dissociation energy, aligning experimental results with advanced theoretical calculations, thereby resolving previous discrepancies and contributing to fundamental physics debates.

## Contribution

The study provides the most accurate experimental measurement of H$_2$ dissociation energy to date, reducing uncertainty and confirming theoretical predictions including relativistic and quantum electrodynamics effects.

## Key findings

- Measured dissociation energy with three times smaller uncertainty.
- Achieved agreement between experiment and high-level theory.
- Resolved a discrepancy impacting proton charge radius debates.

## Abstract

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.