The alpha and helion particle charge radius difference from spectroscopy of quantum-degenerate helium

Accurate spectroscopic measurements of calculable systems provide a powerful method for testing the Standard Model and extracting fundamental constants. Recently, spectroscopic measurements of finite nuclear size effects in normal and muonic hydrogen resulted in unexpectedly large adjustments of the proton charge radius and the Rydberg constant. We measured the $2^3\mathrm{S}\to 2^1\mathrm{S}$ transition frequency in a Fermi gas of ${}^3$He with an order of magnitude higher accuracy than before. Together with a previous measurement in a ${}^4$He Bose-Einstein condensate, a squared charge radius difference $r_h^2-r_{\alpha }^2=1.0757(15)\mathrm{f}{\mathrm{m}}^2$ is determined between the helion and alpha particle. This measurement provides a benchmark with unprecedented accuracy for nuclear structure calculations. A deviation of 3.6$\sigma$ is found with a determination (arXiv:2305.11679) based on spectroscopy of muonic helium ions.