Nuclear Predictions for $H$ Spectroscopy without Nuclear Errors

TL;DR

This paper demonstrates that nuclear finite-size effects in hydrogen can be characterized by only two parameters, enabling nuclear-error-free predictions of atomic energy shifts and enhancing the potential for precision tests of fundamental physics.

Contribution

The authors develop a method using effective field theory to eliminate nuclear-model uncertainties in hydrogen energy predictions, reducing nuclear error to below 1 kHz.

Findings

Nuclear effects depend on only two parameters, independent of nuclear models.

Predictions for nuclear-size effects are accurate below 1 kHz.

Atomic measurements can now test fundamental physics with minimal nuclear theory error.

Abstract

Nuclear-structure effects often provide an irreducible theory error that prevents using precision atomic measurements to test fundamental theory. We apply newly developed effective field theory tools to Hydrogen atoms, and use them to show that (to the accuracy of present measurements) all nuclear finite-size effects (e.g. the charge radius, Friar moments, nuclear polarizabilities, recoil corrections, Zemach moments {\it etc.}) only enter into atomic energies through exactly two parameters, independent of any nuclear-modelling uncertainties. Since precise measurements are available for more than two atomic levels in Hydrogen, this observation allows the use of precision atomic measurements to eliminate the theory error associated with nuclear matrix elements. We apply this reasoning to the seven atomic measurements whose experimental accuracy is smaller than 10 kHz to provide predictions for nuclear-size effects whose theoretical accuracy is not subject to nuclear-modelling uncertainties and so are much smaller than 1 kHz. Furthermore, the accuracy of these predictions can improve as atomic measurements improve, allowing precision fundamental tests to become possible well below the 'irreducible' error floor of nuclear theory.