Lamb Shift

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. 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 rise
of about 1060MHz 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 Photon s that have been emitted and re-absorbed by the atom. In Quantum Electrodynamics (QED) the electromagnetic field is quantized
and as for the Harmonic Oscillator in Quantum Mechanics its lowest state is not zero. So there exist little Zero-point oscillations
that cause the Electron to execute rapid oscillatory motions. The electron is kind of "smeared out" and the radius is changed
by

r+\delta r

.

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

:

\langle E_\mathrm{pot} 
angle=-rac{Ze^2}{4\pi\epsilon_0}\left\langlerac{1}{r+\delta r}
ight
angle.

The Lamb shift itself is given by

:

\Delta E_\mathrm{Lamb}=\alpha^5 m_e c^2 rac{k(n,0)}{4n^3}\ \mathrm{for}\ \ell=0\,

and

:

\Delta E_\mathrm{Lamb}=\alpha^5 m_e c^2 rac{1}{4n^3}\left[k(n,\ell)\pm rac{1}{\pi(j+rac{1}{2})(\ell+rac{1}{2})}
ight]\ \mathrm{for}\ \ell
e 0\ \mathrm{and}\ j=\ell\pmrac{1}{2},

with

k(n,\ell)

a small number (< 0.05).

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	CATEGORIES ABOUT LAMB SHIFT

	quantum field theory

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Information About

Lamb Shift