A determination of fundamental constants using HD⁺ ion and atomic hydrogen spectroscopy data

Laboratoire PhLAM, CNRS UMR 8523, 59655 Villeneuve d’Ascq, France

^* Corresponding author: FL.Constantin@univ-lille1.fr

Published online: 15 January 2019

Abstract

A determination of fundamental constants using HD⁺ ion spectroscopy data is discussed from comparisons between precision measurements and accurate theoretical predictions by taking into account recent measurements and updated CODATA values of the fundamental constants. The deuteron-proton mass ratio is determined with an uncertainty of 10^-9. The ratio between the HD⁺ reduced mass and the electron mass is determined with an uncertainty of 7.3 × 10^-10. The Rydberg constant, the proton-electron mass ratio and the deuteron-electron mass ratio are consistently determined with 10^-9 , 10^-6 , and 10^-6 level uncertainties from an adjustment of the (v,L)=(0,0)→(0,1) and (v,L)=(0,2)→(8,3) HD⁺ ion transitions and of the (n,l,j,f)=1S_1/2f=1→2S_1/2f=1 atomic hydrogen transition. The result of the adjustment provides a test of the consistency of the two-body and three-body quantum electrodynamics energy level calculations for the atomic hydrogen and the HD⁺ ion.