An experiment is described which tests the semi-classical radiation theory proposed by E. T. Jaynes and his collaborators.Their work predicted that the n = 2 level of hydrogen will have a lifetime which varies linearly with the 2s state population for small excited state components.By applying a short electrical pulse to a 60 keV atomic hydrogen beam with a 2s population of approximately 9%, the variation of the lifetime could be measured as a function of the 2s occupation after the pulse.A total change of approximately + 4% is predicted while the observed change was -.2%.
An experiment is described which tests the semi-classical radiation theory proposed by E. T. Jaynes and his collaborators.Their work predicted that the n = 2 level of hydrogen will have a lifetime which varies linearly with the 2s state population for small excited state components.By applying a short electrical pulse to a 60 keV atomic hydrogen beam with a 2s population of approximately 9%, the variation of the lifetime could be measured as a function of the 2s occupation after the pulse.A total change of approximately + 4% is predicted while the observed change was -.2%.
In Jaynes's semiclassical radiation theory, the decay of an excited atomic state depends on its initial population. For the radiative decay of the 2P level in atomic hydrogen, produced by pulsed excitation from the 2S level, the theory predicts a decay rate $\ensuremath{\Gamma}=(1\ensuremath{-}f){\ensuremath{\Gamma}}_{0}+\ensuremath{\beta}P$, where $\ensuremath{\beta}=f{\ensuremath{\Gamma}}_{0}$. Here f is the initial 2S population, ${\ensuremath{\Gamma}}_{0}$ is the natural 2P decay rate, and P is the 2P population relative to f. For $f=0.086\ifmmode\pm\else\textpm\fi{}0.016$, and P values in the range 0.15 to 0.64, we have measured $\ensuremath{\beta}=\ensuremath{-}(2.8\ifmmode\pm\else\textpm\fi{}2.8)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. The corresponding value from the semiclassical theory is $\ensuremath{\beta}=+(53.8\ifmmode\pm\else\textpm\fi{}10.0)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$.
The neoclassical or semiclassical theory (NCT) of the radiative decay of an isolated atom predicts that the decay rate of an excited state is proportional to the atoms's population in the state to which the atom is decaying. For weak excitation of a two-level system, this prediction is consistent with observations and with the Weisskopf-Wigner theory of decay, which assumes a quantized electromagnetic field as in quantum electrodynamics (QED). But for weak excitation of a system with three or more levels, there can be gross disagreements between NCT and QED. NCT predicts that the lifetime of an excited state depends on the nuclear spin which determines the number of ground states between which the atom's unity population density is divided. Also NCT predicts no fluorescence to a third level not initially populated, even though the transition is highly allowed. Observations in Pb vapor are inconsistent with NCT and consistent with QED. The oscillator strengths of the 2833-, 3640-, and 4058-A transitions were determined to be 0.167(20), 0.061(04), and 0.146(10), respectively, by measuring the ratios of oscillator strengths and using the lifetime measurements of Happer and Saloman.
A sensitive test for any mixing of the 2S21 and 2P21 state of atomic hydrogen is the measurement of the rate for single-quantum decay of the 2S atom to the ground state. A new upper limit of this decay rate has been determined. A section along a beam of 2S atoms, produced by electron excitation of a ground-state atom beam, was viewed by an iodine-vapor-filled ultraviolet photon counter, which responds to the Lymanalpha radiation of the single-quantum decay process. From the counts observed when an electrostatic quenching field was superposed on the counter's field of view, the necessary experimental parameter (product of 2S atom current and counter efficiency) was determined. With the field removed, a portion of the remaining counts could be ascribed to quenching on collision of the 2S atoms with residual gases in the vacuum chamber, the quenching cross sections for which were measured. The decay rate not ascribable to known quenching effects was 420 ${\mathrm{sec}}^{\ensuremath{-}1}$. Since unknown quenching effects may have been operative, this figure must be considered only as an upper limit for the natural single-quantum decay rate.
A sensitive test for any mixing of the 2S21 and 2P21 state of atomic hydrogen is the measurement of the rate for single-quantum decay of the 2S atom to the ground state. A new upper limit of this decay rate has been determined. A section along a beam of 2S atoms, produced by electron excitation of a ground-state atom beam, was viewed by an iodine-vapor-filled ultraviolet photon counter, which responds to the Lymanalpha radiation of the single-quantum decay process. From the counts observed when an electrostatic quenching field was superposed on the counter's field of view, the necessary experimental parameter (product of 2S atom current and counter efficiency) was determined. With the field removed, a portion of the remaining counts could be ascribed to quenching on collision of the 2S atoms with residual gases in the vacuum chamber, the quenching cross sections for which were measured. The decay rate not ascribable to known quenching effects was 420 ${\mathrm{sec}}^{\ensuremath{-}1}$. Since unknown quenching effects may have been operative, this figure must be considered only as an upper limit for the natural single-quantum decay rate.
In our preceding treatments of the interaction of radiation with matter, we assumed that the electric field is classical. In most cases, this assumption is validated by experiment. There are several instances, however, for which a classical field fails to give experimentally observed results, whereas a quantized field succeeds. This is true, for example, of spontaneous emission, a phenom enon which was described phenomenologically in our earlier work (see Chaps. 2 and 7). Another case involves the 2 and 2p \ states in the hydrogen atom, which are predicted to have the same energy not only by the simple theory of Chap. 1, but also by the more sophisticated Dirac theory. In both cases, a classical electric field was assumed. Experimentally, the two levels differ by approximately the Lamb shift, 1057 MHz. A fully quantized treatment of the field and atom system gives impressive agreement with the experimentally observed shift. Derivation of the fluctuations in intensity of a laser near threshold requires the quantum theory o f radiation. In addition there are other problems for which the concept of a “particle,” the photon, is either necessary or convenient. Despite a popular impression to the contrary, however the explanation of the photoelectric effect is not one of these (see Prob. 2-10).
It has recently been shown by Jaynes and collaborators that semiclassical radiation theory contains a description of spontaneous emission of radiation and of radiative level shifts. The present paper gives a gauge-invariant derivation of the radiant energy production rate, using only Maxwell's equations and the usual definitions of electric current and charge density for a many-particle material system described by Schr\"odinger's equation. A complementary derivation, using the time-dependent Schr\"odinger equation, verifies the instantaneous conservation of energy and probability during the radiation process. The semiclassical rate of spontaneous emission differs from the usual formula (Einstein's A coefficient) because it depends on the occupancy of both initial and final states of the material system. The implications of this with regard to thermal equilibrium and Planck's law are examined. If a new hypothesis is introduced, postulating the decomposition of the equilibrium radiation into incoherent components, each interacting with a specific pair of energy levels of the material system, then Planck's law is shown to hold for the total intensity of radiation. If this hypothesis is not introduced, the equilibrium conditions for different transitions are incompatible, and the semiclassical radiation theory is incapable of describing thermal equilibrium.