Laser spectroscopy of the 1S-2Stransition in hydrogen and deuterium: Determination of the 1SLamb shift and the Rydberg constant

Abstract

We have observed the narrow 1S-2S transition in hydrogen and deuterium with high resolution using Doppler-free two-photon absorption of continuous-wave 243-nm light. The transition frequencies were measured by direct comparison with accurately calibrated lines in the spectrum of the "Te2 molecule. We find the 1S-2S interval to be 2466061414.1(8) MHz in hydrogen and 2466732408.5(7) MHz in deuterium. By combining these results with recent measurements of the Rydberg constant we obtain the values 8172.6(7) and 8183.7(6) MHz for the 1S Lamb shifts in hydrogen and deuterium, respectively. These are the most precise measurements of the 1S Lamb shifts in these atoms and they are in excellent agreement with the theoretical values of 8173.03(9) and 8184.08(12) MHz. Alternatively, if the 1S Lamb shift is supposed known from theory, our measurements determine the Rydberg constant as R = 109 737.315 73 (3) cm Recently, the 1S-2S transition in hydrogen was observed using this source and its frequency was measured. ' By using an accurate value of the Rydberg constant it was possible to extract the Lamb shift. This calibration procedure is essentially the same comparison of hydrogen transitions used in the early experiments, but with several intermediate steps linking the two transitions. Our work at Oxford University" has concentrated on the development of frequency doubling as a means of generating cw 243-nm light because it offers the longterm prospect of a direct comparison of the 1S-2S and Balmer-P transitions. In this paper we describe the first experiment on hydrogen 1S-2S using cw 243-nm light generated by frequency doubling. ' ' We have measured the 1S-2S transition frequency f (1S-2S) in both hydrogen and deuterium. As in Ref. 9 our determination of the Lamb shift uses an indirect calibration via the Rydberg constant; however, the use of frequency doubling reduces the number of intermediate steps and by employing two lasers it was possible to calibrate the measurement using accurate heterodyne techniques.These improvements lead to a value of the hydrogen 1S Lamb shift which is a factor of 3 more precise than the previous value, and to the first cw measurement of the 1S Lamb shift in deuterium, improving the precision in this case by a factor of 50. An alternative interpretation of our measurements is pos-40 6169

Theory of light hydrogenlike atoms

“…Hence, the would be infrared divergence in the electron charge radius is cut off by its virtuality ρ = (m 2 − p 2 )/m which is of order of the nonrelativistic binding energy ρ ≈ m(Zα) 2 .…”

“…There are three characteristic scales in the atom. The smallest is determined by the binding energy ∼ m(Zα) 2 , the next is determined by the characteristic electron momenta ∼ mZα, and the last one is of order of the electron mass m.…”

“…where < r > (2) is the first Zemach moment (or the Zemach radius) [166], defined via the weighted convolution of the electric and magnetic densities ρ E(M ) (r) corresponding to the respective form factors (compare with the third Zemach moment in eq. (169))…”

“…where Σ (2) is an "exact" second-order self-energy operator for the electron in the Coulomb field (see Fig. 23), and hence contains the unmanageable exact Dirac-Coulomb Green function.…”

Thirty Years of Hydrogen Spectroscopy in Paris

“…In Paris, the experiment was not easy to achieve, but during one year we benefited from the precious help of Derek Stacey, who had an expertise in the UV domain since he had studied the 1S-2S transition in the Oxford group [27]. A 1S beam was build and we had to develop a new laser source at 205 nm.…”