Is the H Atom Surrounded by A Cloud of Virtual Quanta Due to the Lamb Shift?

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, Power, and Milonni 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. Using this result and a group theoretical calculation of the contribution to the Lamb shift from each frequency of the vacuum fluctuations, in this paper we obtain an expression for the region of the vacuum energy for each frequency ω around the H atom due to the Lamb shift. This same field plays an essential role in the van der Waals force. We show 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 vacuum fluctuations. For energies E=ℏω less than 1 eV, where ℏ is the reduced Planck constant and ω is frequency, the radius of the positive energy region is shown to be approximately 14.4/E Å. For a vacuum fluctuation of wavelength, λ, the radius is (α/2π)λ, where α is the fine-structure constant. Thus, for long wavelengths, the region has macroscopic dimensions. The energy–time uncertainty relation predicts a maximum possible radius that is larger than the radius based on the radiative shift calculations by a factor of 1/4α.