The Weisskopf-Wigner theory of the natural linewidth of a single isolated atom is extended to a system of iVCM) identical nonoverlapping atoms which are all in the same excited state at time /=0. The positions Xi • • 'Xiv of the atoms are assumed to fill a volume *0 of given shape and size with macroscopically constant density. Emission of radiation from this system takes place only in the form of one narrow, but nonzerowidth, bundle of nearly equal photons, which contains all the emitted radiation. If the density of atoms within V exceeds a certain threshold, the rate of emission of photons has the form of a typical spike. All effects depend sensitively on the shape and size of V and on the density of atoms within V, and cannot be explained in conventional terms of spontaneous or stimulated emission of radiation.
The quantum-mechanical method developed earlier is applied to the four-photon resonant ionization of Cs. Comparisons of the present calculations with the experiments by Held et al. are given, and good agreement with the experiments is obtained. The application of the present theoretical method to the six-photon ionization of hydrogen is indicated .Recently Held et al.^ published experimental results on the four-photon ionization of Cs by light of frequency near that required to produce three-photon excitation of the 6/ state. They found very rapid variation of the transition probability with frequency and with incident intensity. This Letter describes briefly a theoretical calculation which reproduces the experimental results on the two sides of the resonance and at exact resonance. The calculation very near resonance is numerically complicated and is being carried out. The main features are, however, already clear.The method developed earlier^»^ is used straightforwardly. The electron propagator in the presence of the incident radiation field, including forward scattering processes, can be written in the notation of I and II asThe tilde denotes the renormalized quantity; J^^"(--O) is the resonant part of H"^"{-Q), the nonresonant part being incorporated in the shifted energy E". Use of this propagator leads to the four-photon ionization amplitude in the form Cis-^^{t)={e'Noo/2Vr E
The application of the Bohr correspondence principle to quantum electrodynamics is considered, taking into account the existence of the scattering of light by light and of intensity-dependent radiative corrections. When the effect of the latter is allowed for, the discrepancy between completely quantum-mechanical and completely classical calculations of Thomson scattering is removed.
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