  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
$2^3\mathrm{S}\rightarrow2^1\mathrm{S}$ 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 $r^2_h - r^2_{\alpha} = 1.0757(15)\ \mathrm{fm^2}$ 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.
