The propagation of C̆erenkov radiation through a medium in which the population of two energy levels is inverted has been studied. The population inversion is represented by an imaginary part of the index of refraction of the medium at the resonance frequency. The resonant atoms are embedded in a host medium which has the shape of a slab of finite width $L$ and dielectric constant ${\epsilon }_h$, which is real and varies slowly for frequencies close to the resonance frequency of the embedded atoms. It is assumed that the host medium and the embedded atoms inside the slab behave as an isotropic noncrystalline medium. The slab is covered by a mirror on each of its surfaces and the medium outside the slab and the mirrors has dielectric constant ${\epsilon }_1$ (${\epsilon }_1=1\mathrm{}$ for vacuum). While each individual charged particle can stimulate coherent emission by different resonant atoms, the phase of radiation which is due to different particles is uncorrelated. It is shown, however, that radiation of high intensity in the direction of the C̆erenkov cone can be produced by highcurrent particle beams. Exact expressions, in integral form, are obtained for the electromagnetic field everywhere in space. Using the method of stationary phase approximate expressions are derived for the C̆erenkov fields as well as the radiated energy in the foward and backward direction, far away from the slab.

Theoretical results for the photoionization cross section of the ions of iron are presented. The calculations are performed in the Hartree-Slater central-potential model and are carried out for each occupied subshell from neutral iron to the two-electron system (${\mathrm{Fe}}^{+24\mathrm{}}$). The results show that removal of outer-shell electrons have essentially no effect on inner-shell cross sections other than to shift the threshold. The general systematic of the cross sections for the various subshells as one moves along an isonuclear sequence are discussed.

The photoionization cross section of neutral iron, in thermal equilibrium 2300 K, was measured to be (${5.0}_{-0.7\mathrm{}}^{+0.4\mathrm{}}$) × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ at 1540 Å (8.05 eV). At this temperature more than 98% of the atoms are in the levels of the ground term. The iron vapor was produced in a resistively heated furnace, and the column density was determined by the hook method. The optical depth of the iron vapor was measured with a photoelectric detector. The absolute measurement of the cross section can be used to calibrate existing data which cover a wide range of wavelengths.

The Hanle effect and its variation with density has been used to determine the depolarization cross section for collisions between the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ barium ions and neutral atoms. An extrapolation of the data to zero density gives a value of the average lifetime $\tau =6.22\mathrm{}$ ns for the $6p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ level. A further experiment gives $\tau =7.55\mathrm{}$ ns for the $6p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ level.

Profiles of $L_{\beta }$ emitted from small hydrogen additions in a dense argon plasma ($n_e=1, 2, \mathrm{and} 3\times {10}^{23}$ ${\mathrm{m}}^{-3\mathrm{}}$, $T\approx {10}^4$ K) were measured under controlled optical depth over wavelength separation $\Delta \lambda$ from ${\lambda }_{L\beta }$ of about eight times the half-halfwidth $\Delta {\lambda }_{\frac{1}{2}}$. Reabsorption in the boundary layers of the plasma, usually caused by hydrogen as well as argon atoms, was avoided. The Stark profiles $P\left(\Delta \lambda \right)$ obtained (uncertainty ±4% for $\frac{\left|\Delta \lambda \right|}{\Delta {\lambda }_{\frac{1}{2}}}\le 4$) were found to be for $\frac{\left|\Delta \lambda \right|}{\Delta {\lambda }_{\frac{1}{2}}}>0.6\mathrm{}$ in good agreement with calculations according to the "unified" theories (Vidal et al. and Seidel) and to the modified impact theories (Griem and Bacon). For $\frac{\left|\Delta \lambda \right|}{\Delta {\lambda }_{\frac{1}{2}}}<0.6\mathrm{}$ deviations remain, particularly in the line center, even when time ordering and ion dynamics (Seidel) are taken into account. These residual discrepancies indicate, in accordance with deviations recently found for $L_{\alpha }$, that broadening mechanisms which are not finally identified are efficacious. The experimental $L_{\beta }$ profiles exhibit an asymmetry behavior similar to that calculated by Bacon, yielding that the asymmetry is mainly caused by ion-field inhomogeneities. Using the scale of angular frequencies the change of sign of the asymmetry is found to be at $\frac{\Delta \omega }{\Delta {\omega }_{\frac{1}{2}}}=0.5\mathrm{}$, whereas it is predicted by Bacon at $\frac{\Delta \omega }{\Delta {\omega }_{\frac{1}{2}}}=1.2\mathrm{}$. The measurements indicate red shifts of the centers of the profiles of about ${10}^{-2\mathrm{}}\Delta {\omega }_{\frac{1}{2}}$ (≃ ${10}^{-3\mathrm{}}$ nm for $n_e=2\mathrm{}\times {10}^{23}$ ${\mathrm{m}}^{-3\mathrm{}}$).

We review the merits and shortcomings of the Born-Oppenheimer separation and suggest a nonadiabatic approach to molecular spectra using the generator-coordinate method. The adiabatic approximation and the new scheme are worked out in parallel for diatomic molecules.

Calculations of binding-energy curves and charge distributions have been carried out for low-lying states of ${\mathrm{Si}}_2$ and ${\mathrm{Ge}}_2$ using the local-density-functional formalism. Calculated spectroscopic constants are in good agreement with experiment for the states of ${\mathrm{Si}}_2$ which have been identified, so that predictions for other states should be reliable. The binding-energy curves of the two dimers are remarkably similar, as are the $s-p$ valence orbitals of silicon and germanium atoms. Charge-density differences are similar to those calculated previously for ${\mathrm{C}}_2$ and orbital densities show pronounced differences from results of a recent pseudopotential calculation, even in regions far from the cores.

The total absorption cross sections for 52.4-, 60-, 72.2-, and 84.4-keV photons in Al, Fe, Mo, Ag, W, and Pt have been measured. Also, the photoelectric cross sections at these photon energies have been deduced by subtracting the scattering cross sections from the measured values of total absorption cross sections. The results so obtained have been compared with the corresponding theoretical values as interpolated from the work of (i) Schmickley and Pratt and (ii) Scofield.

The two-photon ionization of the He atom in the $2{}_{}{}^1{}_{}{}^{}S$ state is studied in the electric dipole plus quadrupole approximation. A quadrupole resonance peak in the generalized cross section is obtained at 5043.5 ÅA. It is shown that for incident photons having wavelengths between 5042 and 5045 ÅA, the quadrupole term gives a significant contribution to the total generalized cross section.

Extensive new data on the even parity $J=0\mathrm{}$ and $J=2\mathrm{}$ levels of neutral barium have been obtained using two-photon absorption spectroscopy with a nitrogen-pumped dye laser and space-charge detection. Members of the Rydberg series $6sns{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ ($16<~n<~61$), $6snd{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ ($15<~n<~81$), and $6snd{}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$ ($15<~n<~30$) and perturbing levels of these series belonging to the $5d7d$ configuration have been observed; the corresponding wave numbers have been determined. A detailed description of the experimental method is given, followed by the presentation of the new data and the theoretical analysis of the $J=0\mathrm{}$ spectrum. All $J=0\mathrm{}$ levels in the energy range between 34370 ${\mathrm{cm}}^{-1\mathrm{}}$ and the first limit were interpreted by means of the multichannel quantumdefect theory. In this energy range, the $6sns{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ series is perturbed by two levels at 38924 and 41441 ${\mathrm{cm}}^{-1\mathrm{}}$; these levels are assigned to $5d6d{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and $5d7d{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$, respectively.

The quantum electrodynamics of two atoms in free space, separated by many wavelengths and interacting with one another via the coupling of their dipole moments to the electromagnetic field, is studied using the Heisenberg-operator approach. The problem is formulated in such a way that one of the atoms, which has two levels, plays the role of a detector; the other atom, whose levels are arbitrary but do not involve cascadelike transitions, plays the role of the source. Several aspects of the interaction are considered, including: a review of photodetection theory, the theory of an alternative detection method that uses an excited-state detector, and a study of quantum beats. These dynamical studies of emission and detection provide new insights into the observation of quantum beats in the transition rate of a detector. We show that ground-state beats are not observed by a detector atom making an upward transition, but that ground-state beats are, in principle, observable if the detector atom makes a downward transition.

The induced-emission cross section of the copper laser lines $4p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}-4S{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ (5106 Å) and $4p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}-4S{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$ (5782 Å) have been measured for He and Ne as buffer gases at different pressures by using an amplification-gain technique. The line broadenings are deduced from the experimental data and compared to the values predicted by a pressure-broadening impact theory.

Superfluorescence is treated in the Markovian master-equation approach. We show that we have to consider the complex coupling between any pair of atoms in order to reproduce superfluorescence signals with ringings as exhibited by experiments. We compare numerical results of our model with those obtained by a semiclassical approach of superfluorescence. The quantum treatment is found to be in agreement with the semiclassical approach only if the semiclassical tipping angle is taken equal to the square root of the number of radiating particles.

The resonant radiation due to the coherent excitation of the electric dipole moments of the atoms which are embedded in a host medium with real dielectric constant $\epsilon$ has been studied. These dipole moments are induced by the electric field of a relativistic charge particle moving through the resonant medium. In this context, coherent excitation refers to the correlation of phases of the dipole moments, which are induced by a single relativistic charged particle. The phases of dipole moments which are induced by different charged particles are, of course, uncorrelated. The density $\mathfrak{N}$ of the embedded atoms in the host medium is assumed to be sufficiently small so that $\mathfrak{N}\left|\alpha \right({\omega }_r\left)\right|\ll 1$, where $\alpha \left({\omega }_r\right)$ is the polarizability of the atoms at the resonance frequency ${\omega }_r$. Under this assumption, the electric field acting upon each atom is approximately equal to the electric field of the incident relativistic charged particle. This field is analyzed into its frequency spectrum and the effect of each frequency component on the embedded atoms is determined. Expressions for the fields, far away from the resonant medium, and the radiated energy are derived for transitions between bound states. Two cases are considered. In the first case, it is assumed that $\zeta ={(1-\epsilon {\beta }^2)}^{-\frac{1}{2}}$ is real, where $\beta =\frac{v}{c}, v$, being the velocity of the incident charged particle and $c$ the velocity of light. It is shown that if $\zeta \gg 1$, the radiation is emitted in the direction of motion of the incident charged particle. In the second case, it is assumed that $\zeta$ is imaginary. Since the Čerenkov condition is satisfied, i.e., $\beta \sqrt{\epsilon }>1\mathrm{}$, there is a primary Čerenkov radiation in the host medium which excites coherently the embedded atoms at their resonance frequency. In spite of the fact that both the primary and stimulated radiations are emitted in the direction of the Čerenkov cone, it is shown that it is possible to detect the presence of the latter because of the finite lifetime of the embedded atoms. Therefore, the possibility arises for the manifestation of their coherent excitation by relativistic charged particles.

Two-time correlations in the emissions of photons by a single atom of sodium in the presence of a coherent exciting field near resonance have been investigated. In the experiment sodium atoms in an atomic beam are excited by a perpendicular light beam from a tunable dye laser, and they are prepared by optical pumping to behave as two-level quantum systems. The fluorescent light is collected by a microscope objective in a direction that is approximately orthogonal to both beams and imaged on two photomultipliers. Photoelectric pulse correlations are measured in the presence of exciting fields of various strengths and for various detunings from the atomic resonance, and are found to exhibit significant nonclassical features. The results show clearly that the emitted photons exhibit antibunching, in good quantitative agreement with the predictions of quantum electrodynamics.

Sharp peaks observed recently in a levitation-power experiment are caused by partial-wave resonances. The theoretical results computed from the Mie-Debye theory are compared with experimental observations. The first resonances in each partial wave are extremely narrow and they were not detected in the experiment. We conjecture that the peaks in levitation power do not exist if levitated particles are irregularly shaped.

We present a theoretical study of photodetection with coupling of the photosensitive atoms to a reservoir. We investigate the effects of nonzero detector temperature, where the initial thermal-equilibrium occupation of the atomic levels and the thermalization of the radiation field interfere with the measurement of the photon statistics. We derive formulas exhibiting the temperature dependence of the field dynamics, the relationship between field and atomic moments, and the photocounting probability. We present examples illustrating how the coherence properties of the incoming field are affected by the detection process in the presence of thermal noise.

We determine the dispersion law of the carrier wave of an exciton-photon pulse which propagates as a solitary wave. For short pulses, four branches $\Omega =\Omega$ ($\overrightarrow{\mathrm{K}}$) appear: a branch which goes through the intersection point $\hslash cK=E_o+\frac{{\hslash }^2{K}^2}{2M}$ of the uncoupled modes of the free exciton and the free light field, two polaritonlike branches and an excitonlike branch. The polaritonlike branches have a normal dispersion, whereas the branch which goes through the intersection point of the free modes has an anomalous dispersion for sufficiently short pulse width. This branch contains the solution of McCall and Hahn as a special case. For very short pulses the branch with anomalous dispersion continues into the two polaritonlike branches. For increasing pulse width a forbidden energy gap appears at $\overrightarrow{\mathrm{K}}=0\mathrm{}$. For long pulses, only the two polaritonlike solutions exist.

The analogy of a laser with an autocatalytic chemical reaction is used to write down a macroscopic stochastic master equation of the birth-and-death type for the photon probability function in a semiclassical laser formalism. This equation may be solved exactly in the steady state using a generating function. This leads to a prescription for calculating all the higher-order moments of the photon number as well as providing a unique truncation of the hierarchy of moment equations at any given order. Further, the variance is given by a Poisson distribution, in agreement with the strong-signal Scully-Lamb theory. This master equation is also shown to lead to an exact Fokker-Planck equation by using a modified Kramers-Moyal expansion. A comparison between our results and the (microscopic) Scully-Lamb theory shows that the two approaches give the same results at large photon number.

A model is proposed to explain the reflection and transmission of laser light through transparent materials. This model is valied for laser intensities less than threshold power for diffuse scattering. Our model takes into account multiphoton absorption or cascade effects causing the electrons to jump from the valence band to the conduction band. The problem is solved analytically using Maxwell's equations with a time-dependent electric conductivity and Newton's law for the mobile electrons. Our results are compared with experiments in the intensity range from ${10}^{11}$ to ${10}^{13}$ W/${\mathrm{cm}}^2$. Excellent agreement between the present calculations and the experiment is obtained. We predict that the reflection and transmission coefficients for transparent dielectrics are not very sensitive to the irradiating-laser-light frequency.