Lamb shift

In physics, the Lamb shift, named after Willis Lamb (1913-2008), is a small difference in energy between two energy levels $^2S\_\{1/2\}$ and $^2P\_\{1/2\}$ of the hydrogen atom in quantum mechanics. According to Dirac and Schrödinger theory, "hydrogen" states with the same $n$ and $j$ quantum numbers but different $l$ quantum numbers ought to be degenerate.

Experimental work

In 1947 Lamb and Robert Retherford carried out an experiment using microwave techniques to stimulate radio-frequency transitions between$^2S\_\{1/2\}$ and $^2P\_\{1/2\}$ levels of hydrogen. By using lower frequencies than for optical transitions the Doppler broadening could be neglected (Doppler broadening is proportional to the frequency). The energy difference Lamb and Retherford found was a riseof about 1000MHz of the $^2S\_\{1/2\}$ level above the $^2P\_\{1/2\}$ level.

This particular difference is a one-loop effect of quantum electrodynamics, and can be interpreted as the influence of virtual photons that have been emitted and re-absorbed by the atom. In quantum electrodynamics (QED) the electromagnetic field is quantizedand, like the harmonic oscillator in quantum mechanics, its lowest state is not zero. Thus, there exist small zero-point oscillationsthat cause the electron to execute rapid oscillatory motions. The electron is "smeared out" and the radius is changedfrom $r$ to $r+delta\; r$.

The Coulomb potential is therefore perturbed by a small amount and the degeneracy of the two energy levels is removed. The new potential can be approximated (using Atomic units) as follows:

:$langle\; E\_mathrm\{pot\}\; angle=-frac\{Ze^2\}\{4piepsilon\_0\}leftlanglefrac\{1\}\{r+delta\; r\}\; ight\; angle.$

The Lamb shift itself is given by

:$Delta\; E\_mathrm\{Lamb\}=alpha^5\; m\_e\; c^2\; frac\{k(n,0)\}\{4n^3\}\; mathrm\{for\}\; ell=0,$

with $k(n,0)$ around 13 varying slightly with $n$, and

:$Delta\; E\_mathrm\{Lamb\}=alpha^5\; m\_e\; c^2\; frac\{1\}\{4n^3\}left\; [k(n,ell)pm\; frac\{1\}\{pi(j+frac\{1\}\{2\})(ell+frac\{1\}\{2\})\}\; ight]\; mathrm\{for\}\; ell\; e\; 0\; mathrm\{and\}\; j=ellpmfrac\{1\}\{2\},$

with $k(n,ell)$ a small number (< 0.05).

Lamb shift in the hydrogen spectrum

In 1947, Hans Bethe was the first to explain the Lamb shift in the hydrogen spectrum, and he thus laid the foundation for the modern development of quantum electrodynamics. The Lamb shift currently provides a measurement of the fine-structure constant α to better than one part in a million, allowing a precision test of quantum electrodynamics.

A different perspective relates Zitterbewegung to the Lamb shift.cite book
author=Henning Genz
title=Nothingness: the science of empty space
publisher= Oxford: Perseus
location=Reading MA
page=p. 245 ff.
year=2002
isbn=0738206105
url=http://books.google.com/books?id=Cn_Q9wbDOM0C&printsec=frontcover&dq=%22empty+space%22&lr=&as_brr=0&sig=udf6V66Xial28_JKFJZHgm92M1M#PPA245,M1]

References

Further reading

*cite book
author=Boris M Smirnov
title=Physics of atoms and ions
year= 2003
page=pp. 39-41
publisher=Springer
location=New York
isbn=038795550X
url=http://books.google.com/books?id=I1O8WYOcUscC&pg=PA166&sig=ZyyQ27aBsPhfb4tL_0sH1qpqva8#PPA39,M1
*cite book
author=Marlan Orvil Scully & Muhammad Suhail Zubairy
title=Quantum optics
year= 1997
page=pp. 13-16
publisher=Cambridge University Press
location=Cambridge UK
isbn=0521435951
url=http://books.google.com/books?id=20ISsQCKKmQC&pg=PA430&sig=d5TzC9UTl7CGU3PIJiCV0c0M6HU#PPA13,M1

External links

* [http://www.peoplesarchive.com/browse/movies/2073/en/off/ Hans Bethe talking about Lamb-shift calculations] on Peoples Archive