Nuclear matter radii from molecular rotations using ultra-high-resolution spectroscopy

The rotational constant parametrizes the relative spacing between a molecule's rotational energy levels. It depends on the molecule's classical moments of inertia, which, in all studies, are expressed by treating the constituent nuclei as point masses separated by the bond length. We point out that treating the finite nuclear size leads to a correction to the rotational constant at the hertz level, which is resolvable with recently developed ultra-high-resolution molecular spectrometers. Nuclear-model-independent measurements of nuclear matter radii can thus be envisioned in the future using such apparatuses, advancing beyond the existing hadronic scattering experiments and further developing the intersection of nuclear and molecular physics. At the present time, it appears that the computational ability of quantum chemistry might be the limiting factor to the technical readiness of the approach. To test the premises of the proposed method, we call for benchmark experiments using <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msup><a:mrow><a:mi>HD</a:mi></a:mrow><a:mo>+</a:mo></a:msup></a:math> that are feasible with state-of-the-art experiment and theory.