Precision Rydberg State Spectroscopy with Slow Electrons and Proton Radius Puzzle

TL;DR

This paper proposes enhanced Rydberg state spectroscopy of hydrogen to improve measurements of the Rydberg constant, potentially helping resolve the proton radius puzzle by leveraging slow electrons in high-n circular Rydberg states.

Contribution

It introduces a novel approach to measure Rydberg states with slow electrons, aiming to refine the Rydberg constant and address the proton radius discrepancy.

Findings

Estimated improved quality factors for Rydberg transitions

Identified instrumentation advancements facilitating experiments

Proposed specific Rydberg states around n=18 for precise measurements

Abstract

The so-called proton radius puzzle (the current discrepancy of proton radii determined from spectroscopic measurements in ordinary versus muonic hydrogen) could be addressed via an accurate measurement of the Rydberg constant, because the proton radius and the Rydberg constant values are linked through high-precision optical spectroscopy. We argue that, with manageable additional experimental effort, it might be possible to improve circular Rydberg state spectroscopy, potentially leading to an important contribution to the clarification of the puzzle. Our proposal involves circular and near-circular Rydberg states of hydrogen with principal quantum number around $n=18$, whose classical velocity on a Bohr orbit is slower than that of the fastest macroscopic man-made object, the Parker Solar Probe. We obtain improved estimates for the quality factor of pertinent transitions, and illustrate a few recent improvements in instrumentation which facilitate pertinent experiments.