HIGHLY CHARGED RYDBERG IONS AND THE PROTON RADIUS PUZZLE
Nicholas D. Guise, Samuel M. Brewer, and Joseph N. Tan
A recent large discrepancy in measurements of the proton charge radius , when taken together with precise measurements of various transitions in hydrogen and deuterium, has significant impact upon the determination of the Rydberg constant . This inexplicably large discrepancy ( ≈ 7 sigma) has renewed interest in alternative systems capable of providing a Rydberg constant measurement that is independent of the proton radius. Earlier theoretical work at NIST considered the possibility of testing theory with one-electron ions in high angular momentum states . The energy levels for high-angular momentum states can be calculated much more accurately than for low-angular momentum states, in part because the nuclear size correction is vanishingly small. In the high-L regime, theoretical uncertainties are smaller than the uncertainties of fundamental constants; in particular, the Rydberg constant is the leading source of uncertainty in this regime . Spectroscopy of one-electron ions in Rydberg states could thus enable a Rydberg constant determination that is independent of nuclear size. At sufficiently high precision, such a measurement could help to illuminate the proton radius puzzle .
We report on progress made at NIST towards the goal of forming one-electron ions in Rydberg states that can be probed accurately using optical frequency metrology. Bare nuclei created in an electron beam ion trap (EBIT) were recently extracted and captured in a novel compact Penning trap  designed to facilitate experiments with controlled recombination and laser spectroscopy. To produce one-electron ions in Rydberg states, this experimental apparatus will allow electron transfer from a laser-excited atom to a bare nucleus stored in an ion trap. For nuclear charge in the range 1 < Z < 11, it is possible to find many E1 transitions between Rydberg states in the optical domain accessible to a frequency comb . Other applications include spectroscopic studies of highly-charged ions of interest in atomic physics, astrophysics, and metrology; for example, lifetimes of metastable states have recently been measured by observing fluorescence from highly charged ions isolated in a compact Penning trap.
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