\abstract{The Lamb shift, one of the most fundamental interactions in atomic physics, arises from the interaction of H atoms with the electromagnetic fluctuations of the quantum vacuum. The energy shift has been computed in a variety of ways. The energy shift, as Feynman and Power demonstrated, equals the change in the vacuum energy in the volume containing the H atoms due to the change in the index of refraction arising from the presence of the H atoms. By using this result and a group theoretical calculation of the contribution to the Lamb shift from each frequency of the vacuum fluctuations, we can obtain an expression for the size of the region of vacuum energy for each frequency \texorpdfstring{
ω}{ω} around the H atom due to the Lamb shift. The ground state atom is surrounded by a region of positive vacuum energy that extends well beyond the atom for low frequencies. This region can be described as a steady state cloud of virtual quanta. For energies \texorpdfstring{
E=ℏω}{E=hbar omega} eV less than 1 eV, the radius of the positive energy region is approximately 14. 4/E Angstroms. For a vacuum fluctuation of wavelength \texorpdfstring{
λ}{lambda} the radius is \texorpdfstring{
(α/2π)λ}{(alpha/2pi) lambda}. Thus, for long wavelengths, the region has macroscopic dimensions. The energy-time Uncertainty Relation predicts a maximum possible radius that is larger than this by a factor of \texorpdfstring{
1/4α}{1/(4 alpha)}.}
\keyword{Bethe; radiative shift; shift spectral density; spectral volume; vacuum fluctuations; vacuum field; Lamb shift; QED; energy field, renormalization, zero point fluctuations; hydrogen atom}.
Within the framework of thermofield dynamics, the wavefunction of the thermal vacuum is given in terms of the position coordinates, and a thermal coordinate representation is introduced through the thermal unitary transformation. Exploting the representation, we obtain position-coordinate wavefunctions of thermal coherent and squeezed states. In the thermal coordinate representation, these wavefunctions are correspondingly the same forms as vacuum, coherent and squeezed states in the coordinate representation.
The Lamb shift of a Rydberg atom in a cavity is shown to be enhanced with the resonance interaction of a virtual atomic transition and cavity modes. The dependence of the Lamb shift on quantum numbers and atomic number changes drastically. By shifting cavity walls and scanning the atomic beam one can vary the Lamb shift. The value of the Lamb shift in a cavity may exceed a typical magnitude of the fine-structure energy. For a rough resonance tuning the Coulomb multiplet is strongly mixed and a novel classification is necessary.
A principle is proposed for the observation of the stationary interference pattern of two phase-shifted components of the 2p (or 2s) state of the hydrogen atom (Yu. L. Sokolov, Sov. Phys. JETP 36, 243 (1973)); (Proc. 6-th Internat. Conf. on Atomic Phys., Riga, 1978, p. 207). An atomic interferometer, a device analogous in principle to a two-channel optical (such as Michelson's) interferometer, is used to measure the frequency of the (2s/sub 1/2/, F = 0)--(2p/sub 1/2/, F = 0) transition in the hydrogen atom, which is found to equal 909.9014 +- 0.0019 MHz. The corresponding Lamb shift is delta(H, n = 2) = 1057.8594 +- 0.0019 MHz.