According to Arthur Schawlow, 'The spectrum of the hydrogenatom has proved to be the Rosetta stone of modern physics: once thispattern of lines had been deciphered much else could also beunderstood.' In the early 20th century the spectrum of atomichydrogen was a key factor in the development of quantum mechanics. Asexperimentalists made more detailed measurements, increasingly refinedtheoretical models kept pace with explanations of the proliferatingnumber of features in the hydrogen spectrum. But some measurementsmade in the 1930's hinted at a discrepancy for which even the Diractheory could not account. In 1947 Lamb and Retherford measured theenergy difference between the lowest n = 2 statespredicted to be degenerate by the Dirac theory. This measurementprovided one of the first tests for the now well-established theoryreferred to as quantum electrodynamics (QED), which continues toprovide a benchmark against which increasingly refined versions ofthis theory are tested even today. In this experiment, atomichydrogen is generated in a discharge tube, and students initiallyobserve the Doppler broadened fine structure lines of the Balmer alphatransition at 656 nm. Then, deploying the technique of saturationspectroscopy, students record the Doppler-free spectrum, easilyresolving the fine structure components of this line, and also theLamb shift. In addition to measuring the fine structure splittingsand the Lamb shift, one can use the recorded linewidths to estimatethe lifetimes of the various excited states.

1.1 Lamb Shift We learned with Dirac equation that states of hydrogen atom with the same principal quantum number nand the total angular momentum jremain de-generate despite the corretions from spin-orbit coupling, relativistic correc-tions, and Darwin term. They are, however, split as a. To listen to more of Freeman Dyson’s stories, go to the playlist: Freeman.

Experiment Information

• Hansch, T. W., A. L. Schawlow, and G. W. Series, 'Thespectrum of atomic hydrogen,'Scientific American,March 1979, pp. 94-110.
• Lamb, W. E., and R. C. Retherford, 'Fine structureof the hydrogen atom by a microwave method,'Phys. Rev. 72, 241 (1947).
• Welton, T. A., 'Some observable effectsof the quantum-mechanical fluctuations of the electromagneticfield,'Phys. Rev. 74, 1157 (1948).
• Hansch, T. W., I. S. Shahin, and A. L. Schawlow, 'Opticalresolution of the Lamb shift in atomic hydrogen by laser saturationspectroscopy,'Nature 235, 63 (1972).

Lamb Shift Wiki

When you try to obtain very high resolution to examine small splittings in spectral lines, such as the hydrogen fine structure and the Lamb shift, those details are obscured by the sources of line broadening. In a low pressure gas, the main source of broadening is Doppler broadening from the thermal motion of the atoms or molecules of the gas. This is particularly serious in hydrogen, since it has a low mass and therefore high thermal velocity.

In physics, the Lamb shift, named after Willis Lamb, is a difference in energy between two energy levels 2S1/2 and 2P1/2 (in term symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy. Calculation of the Lamb Shift Kyle Schmitt University of Tennessee One of the first motivating achievements of quantum field theory was the calculation of the Lamb shift by Hans Bethe1 in agreement with experimental data taken by Lamb and Retherford2 in 1947. The Lamb Shift Δν=1058 MHz = 0.035 cm-1 1. Gold physics 330, Spring 2020 Williams Phys.Rev. 54.558 (1938) Dirac Theory 2S1/2,2P1/2 exact same energy.

Lamb Shift Energy

Tunable dye lasers are used to excellent advantage in 'Doppler-free saturation spectroscopy' to minimize the effects of the Doppler broadening. The light from the laser is split into two beams, a saturating beam and a probe beam, arranged so that they cross in a region of a gas cell containing hydrogen gas. When the laser is tuned to the frequency of an electron transition, the saturating beam is intense enough to deplete the lower level of the transition. The saturating beam is 'chopped', or modulated, so that the saturation of the transiton is turned on and off. The probe beam is then absorbed, or not, depending on whether the saturating beam is on. The probe beam strikes a sensitive detector, locked to the modulation frequency, which can then detect a signal at that frequency corresponding to the turning on and off of the absorption of the probe beam.

Lamb Shift Pdf

The tremendous advantage of this technique for eliminating the effects of Doppler broadening comes from directing the saturation beam and probe beam through the gas in opposite directions. The only hydrogen atoms which are in resonance with both of the beams are those which have no component of velocity in the direction of the beams, and therefore absorb at the frequency associated with the rest frame of the atom. Other atoms in their rest frames see the incoming radiation shifted up for the saturation beam and down for probe beam or vice versa, so they are not resonant for both. The spectrum shown was obtained by tuning the dye laser slowly through the frequency range of the transition and measuring the change in intensity of the probe beam at the modulation or 'chopping' frequency.

For hydrogen gas at 300 K, the rms velocity is about 2700 m/s. This speed corresponds to a Doppler shift of about 4 GHz, or a line broadening of twice that. This would effectively obscure the Lamb shift, since it is only 1.057 GHz.

Lamb Shift Pdf

Microwave measurement of the Lamb shift.

Significance of the Lamb shift