Measurement of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mrow><mml:mi mathvariant="normal">S</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mn>8</mml:mn><mml:msub><mml:mrow><mml:mi mathvariant="normal">D</mml:mi></mml:mrow><mml:mrow><mml:mn>5</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> Transition in Hydrogen
A. D. Brandt, S. F. Cooper, C. Rasor, Z. Burkley, A. Matveev, D. C. Yost
Abstract
We present a measurement of the hydrogen $2{\mathrm{S}}_{1/2}\ensuremath{-}8{\mathrm{D}}_{5/2}$ transition performed with a cryogenic atomic beam. The measured resonance frequency is $\ensuremath{\nu}=770649561570.9(2.0)\text{ }\text{ }\mathrm{kHz}$, which corresponds to a relative uncertainty of $2.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$. Combining our result with the most recent measurement of the $1\text{S}\ensuremath{-}2\text{S}$ transition, we find a proton radius of ${r}_{p}=0.8584(51)\text{ }\text{ }\mathrm{fm}$ and a Rydberg constant of ${R}_{\ensuremath{\infty}}=10973731.568332(52)\text{ }\text{ }{\mathrm{m}}^{\ensuremath{-}1}$. This result has a combined $3.1\ensuremath{\sigma}$ disagreement with the Committee on Data for Science and Technology (CODATA) 2018 recommended value.