Nicholas D. Guise, Samuel M. Brewer, and Joseph N. Tan



A recent large discrepancy in measurements of the proton charge radius [1], when taken together with precise measurements of various transitions in hydrogen and deuterium, has significant impact upon the determination of the Rydberg constant [2].  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 [3][4].  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 [3].  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 [5].


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 [6] 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 [3].  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.



[1] R. Pohl, et al., “The size of the proton,” Nature, vol. 466, pp. 213-218, July 2010.

[2] P. J. Mohr, B. N. Taylor and D. B. Newell, “CODATA recommended values of the fundamental physical constants,” Rev. Mod. Phys., vol. 80, pp. 633-730, June 2008.

[3] U. D. Jentschura, P. J. Mohr, J. N. Tan and B. J. Wundt, “Fundamental constants and tests of theory in Rydberg states of hydrogenlike ions,” Phys. Rev. Lett., vol. 100, p. 160404, April 2008.

[4] U. D. Jentschura, P. J. Mohr and J. N. Tan, “Fundamental constants and tests of theory in Rydberg states of one-electron ions,” J. Phys. B: At. Mol. Opt. Phys., vol. 43, p. 074002, March 2010.

[5] U. D. Jentschura, “Lamb shift in muonic hydrogen—II. Analysis of the discrepancy of theory and experiment,” Annals Phys., vol. 326, p. 516-533, February 2011.

[6] J. N. Tan, S. M. Brewer and N. D. Guise, “Penning traps with unitary architecture for storage of highly charged ions,” Rev. Sci. Instrum., vol. 83, p. 023103, February 2012.