Crossed-Beam Spectroscopy of Hydrogen: A New Value for the Rydberg Constant

Abstract

Hfi/2) with the measure {exp -n' 1 S^i 2 /2 V[q(r)]dr}d^0/p(-*e/ 2 ,^e xp^The high-temperature limit (classical limit) of the above expression gives dii B~f ) eq (q)=Z-1 e~^ while in the low-temperature limit (j3-**>), from the comparison of Eq. (20) with (10) it is obvious that the Feynman process goes over to Nelson's stochastic process for the ground state, provided r is identified with the physical time of evolution of the process. In other words the Feynman formulation of quantum statistical mechanics, upon lowering of the temperature, produces the switch from the ensemble averages of the classical regime to the time averages of the groundstate process arising in the stochastic quantization. From the general point of view, this makes precise the connection between the zero-temperature limit of quantum statistical mechanics and Nelson's formulation of the quantum theory. With respect to the question originally posed in connection with quantum critical phenomena, the comparison of Eq. (19) with Eq. (3) makes it evident that the framework of stochastic quantization allows us to bypass the current notion of dimensional crossover by introducing the dynamical PACS numbers: 06.In a crossed laser-atomic beam experiment the wavelengths of the 2s-3p transitions are measured in H and D to a precision of one part in 10 9 . Our value for the Rydberg constant is Roc =109 737.315 21(11) cm" 1 . The fine-structure splittings of the Sp states in H and D are 3249.8(8) and 3251.7(7) MHz, respectively; the isotope shifts for the 2s-3p 1 / 2 and 2s-3p 3 / 2 transitions are 124260.7(7) and 124262.6(7) MHz, respectively. Our results largely agree with previous, less precise experiments and with theory.

Hydrogen atom and its energy level shifts in de Sitter universe

“…The wavelengths of the 2S − 3P transitions in hydrogen and deuterium were measured to precision of one part in 10 9 [7]. Corresponding to this accuracy we have ≈ 10 4 n −6 cm −2 .…”

Laser spectroscopy of atomic hydrogen

“…This eliminated the systematic errors due to the inevitable electric fields in discharges. In 1981 a group at Yale University reported on a crossed atomic and laser beam study of Balmer c1 (Amin et al 1981). This experiment was the optical analogue of the Lamb and Retherford experiment (Lamb and Retherford 1947).…”

“…If we use the value of the Rydberg constant measured by the Yale group, namely R , = 10973 731369(73m-' (Amin et al 1981) we can deduce the valuk of the groundstate Lamb shift from the absolute frequency measurements of the lS1,, to 2S,,, energy difference. This gives a value for the lS,,, Lamb shift of 81 82(25) MHz (Barr et al 1986) and 8184.8(5.4) MHz (Hildum et al 1986).…”

“…Phase-shift corrections can be estimated either by calculation or by using the method of virtual mirrors in which the use of different interferometer lengths enables the elimination of the phase shift (Lichten 1985. The weighted mean of the Amin et al (1981) results is R , = 10973 731.544(1 l)m-', a number which has been corrected from their original paper to take account of the redefinition of the metre and a sign change for a diffractioncorrection effect. The Yale group have recently reported a remeasurement of the Rydberg constant by making several improvements to their apparatus .…”

Thirty Years of Hydrogen Spectroscopy in Paris

“…The most recent determinations of the Rydberg constant were previously deduced either from the one-photon 2S-3P and 2P-3S Balmer-α transitions [11][12][13], or from the 1S-2S two-photon transition, both methods in which Ted Hänsch took a pioneer role. The first one has the disadvantage of being limited to about 10 −9 by the natural width of the P level involved.…”