The time dependence of free-precession signals from an ensemble of spin-$\frac{3}{2}$ atoms in the presence of a quadrupole perturbation is calculated by examining the time dependence of the density matrix which describes the ensemble. The calculations yield explicit expressions for signals obtained using either a linearly or elliptically polarized off-resonant readout light, applied to a mixture of orientation, alignment, and octupole spin distributions. The results are obtained by expressing the density matrix in terms of spherical basis operators. The theoretical predictions are in good agreement with experimental results which are characterized by "beats" in the decay transients of signals from ${}_{}{}^{201}{}_{}{}^{}\mathrm{Hg}$.

The theory of relaxation of a weakly perturbed spin system is extended to the case of a nonisotropic perturbation. The calculation follows the method of Happer who uses spherical basis operators. Explicit expressions are derived for a spin-$\frac{3}{2}$ system in the presence of dipole and quadrupole perturbations. The results are then applied to the quadrupole relaxation of oriented vapor-phase atoms which occurs while these atoms are adsorbed onto the walls of containers of various shapes. Although the relaxation rates due to the cell wall depend upon the orientation of the wall with respect to the externally applied magnetic field, it is found that the sum of the contributions to the relaxation due to the six faces of a cube-shaped container is independent of the orientation of the container. This prediction is verified experimentally.

The initial-state valence relaxation of the molecular orbitals to the presence of the core hole is found to have a significant effect upon the core-valence-valence Auger decay probabilities and hence upon the Auger line shape. Comparisons are made of experimental and theoretical line shapes of ammonia and ethane. The best theoretical amplitudes were calculated by using self-consistent initial-state molecular orbitals which were projected upon the final states. The use of explicit initial-state orbitals leads to significant improvement over a simpler approach consisting of the use of minimum basis set ground-state orbitals and atomic Auger matrix elements.

The atomic absorption of C i has been studied in the 1100-385-Å spectral region, using the flash-pyrolysis method to produce the absorbing layer and a BRV as a continum source. Thirty-four lines belonging to the $2s^{2}2p^2{}_{}{}^3{}_{}{}^{}P-2s2\mathrm{}{p}^2\mathrm{np}{}_{}{}^3{}_{}{}^{}D_{}^o{}_{}{}^{}$ series converging to the $2s2p^2{}_{}{}^4{}_{}{}^{}P$ ionization limit have been observed and for the first time resolved in fine structure. In addition, energies of $\mathrm{np}{}_{}{}^3{}_{}{}^{}D_{1,2,3}^o{}_{}{}^{}$ are deduced from these observed lines. Three new lines have been observed and identified as simultaneous excitation of the two outer electrons to the final state $2s^{2}3pnd{}_{}{}^3{}_{}{}^{}D_{}^o{}_{}{}^{}$. The relative photoionization cross section of the ground state ${}_{}{}^3{}_{}{}^{}P$, as measured in the same range of wavelengths, is found to be consistent with theoretical predictions.

Spectra of molybdenum in the wavelength region 80-430 Å have been observed using the beam-foil method at 5-25-MeV beam energies. The lifetimes of the upper levels of the resonance transitions in Mo XIV, $4s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-4p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$ (at 423.6 Å and 373.6 Å, respectively) have been measured as $\tau \left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)=118\mathrm{}\pm 8$ ps and $\tau \left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)=79\mathrm{}\pm 6$ ps. These results are compared with theoretical calculations, and the problems encountered in analyzing the decay curves are discussed.

Nonadiabatic transitions in state-selection experiments on beams of metastable hydrogen atoms ($2S_{\frac{1}{2}}$) display oscillations in the population of the $F=1\mathrm{}$, $m=-1\mathrm{}$ state R. D. Hight and R. T. Robiscoe, [Phys. Rev. A 17, 561 (1978)]. In this paper, theoretical calculations using exact and model solenoid fields averaged over a velocity distribution show that the population oscillations arise from the presence of at least two nonadiabatic regions in the solenoid. No oscillations occur theoretically if only a single nonadiabatic region exists, unless the unlikely assumption of a coherent hydrogen-atom beam is invoked.

Exact closed-form expressions for the probability $p\left(n\right)\mathrm{}$ that $n$ photons are spontaneously emitted in a given time by a two-level atom in a coherent exciting field are derived using the theory of atomic motion in a traveling wave.

The long-wavelength, backward mode of the free-electron laser is shown theoretically to be absolutely unstable for sufficient system length and applied magnetic-field strength. Finite-length one-dimensional particle simulations also show the mode to be absolutely unstable when the theoretical criteria are satisfied. The broad parameter regime in which a free-electron laser can produce the desired forward-propagating short-wavelength radiation, yet be stable to the backward mode, is calculated.

Time-dependent fluorescence measurements were made on Ar-${\mathrm{F}}_2$, Kr-${\mathrm{F}}_2$, and Ar-Kr-${\mathrm{F}}_2$ mixtures excited by a short-pulse, low-current electron beam excitation in pressure ranges appropriate for rare-gas-halide lasers. A kinetic model was assembled that correctly analyzes integrated intensities and time dependences of the various emission bands of ArF*, ${\mathrm{Ar}}_2$F*, KrF*, and ${\mathrm{Kr}}_2$F*. We present the structure of the model and several revised rate coefficients obtained from it. The model also fits other published experimental data and agrees well with KrF laser pulse shapes and efficiencies. Cross sections for electron-impact dissociative excitation of ${\mathrm{F}}_2$, which were obtained from analysis of published data, are also presented.

We calculate the effect of self-phase modulation of a pulse propagating in a long-geometry waveguide. Our calculations go beyond the usual theory, which does not take into account the envelope time variation in the nonlinear term of the wave equation. We show that for long waveguides with relatively small group-velocity dispersion but finite nonlinear coefficient $n_2$, the pulse will develop a sizable asymmetric frequency and temporal spectra.

A simple diagrammatic approach to the description of laser-induced macroscopic ordering processes in gases is developed. We derive a set of simple rules which can be used to construct diagrams—each of which represents the macroscopic properties of a gaseous sample after it has been excited by a particular sequence of short, resonant, laser-excitation pulses. The features of the diagrams which signify various forms of laser-induced macroscopic ordering, e.g., photon echoes, grating echoes, stimulated echoes, standing-wave echoes, trilevel echoes, nonthermal velocity distributions, etc., are discussed. Important differences between the actions of traveling-wave and standing-wave excitation pulses are pointed out. The diagrammatic technique presented here for gases can easily be generalized to describe laser-induced macroscopic ordering in solids as well.

In the limit of large field-relaxation rates as compared to the rates of collective and atomic relaxation, we model the stochastic evolution of a bistable system with the aid of the Langevin equations for atomic variables. This semiclassical approach leads to a Fokker-Planck equation for the joint probability distribution of the atomic polarization and inversion. The Monte Carlo integration scheme, consisting in construction of approximate random trajectories, enables us to evaluate numerically the adiabatic values of the output field, intensity, and intensity fluctuations as functions of time. The final model used in numerical work is equivalent to ignoring microscopic fluctuations and considering delta-correlated external fluctuations impressed on the driving field.

We extend the previous theoretical treatment of standing-wave deflection of two-level atoms to include nonresonant excitation, nonorthogonal laser and atomic beams, and excitation duration upper bounded only by atomic relaxation times. Numerically solving equations analogous to those of abruptly initiated multilevel atomic excitation, we find bounds on the maximum deflection fixed by balancing acquired kinetic energy against interaction energy. We find that frequency detuning or nonorthogonal orientation of laser and atomic beams can enhance the deflection and, given sufficiently long interaction time, one can observe deflections at larger discrete angles. We comment on the connection between these Bragg scatterings and multiphoton resonances.

Systems exhibiting dispersive optical bistability are considered as examples of nonequilibrium steady states lacking detailed balance. Methods for describing such states are developed. The Fokker-Planck equation for the steady-state distribution function of the transmitted electromagnetic field is derived. In the limit of small fluctuations the Fokker-Planck equation is reduced to the form of a Hamilton-Jacobi equation for a "nonequilibrium thermodynamic potential." This equation is solved in various approximations. The nonequilibrium thermodynamic potential acts like a free-energy for the first-order-type transition far from thermodynamic equilibrium lacking detailed balance. The potential entirely determines the steady-state distribution, the coexistence curve in the bistable domain, a Lyapunoff function of the deterministic equations of motion, and allows us to cast the deterministic equations of motion into the standard form of nonequilibrium thermodynamics.

We discuss the delay-time statistics of superfluorescent pulses by introducing the concept of a passage time at which the field intensity reaches a specified value. Such passage times can be estimated accurately from the early-stage linear dynamics of the radiating system. The distribution function for the passage times, we show, can be expressed as a functional integral over the random zero point fluctuations of the atomic polarization. The functional integral can be evaluated exactly and reduced to an elementary closed form. Our theory applies both to the sharp and the broadened atomic line. The results we obtain agree with experimental data and numerical calculations already in existence for the unbroadened line. For the broadened line we predict substantial changes of the mean value and the variance of the passage time as the width of the atomic line increases. We also investigate the influence of the shape of the spectral distribution of atomic frequencies and show that the delay statistics depend significantly on the way in which the spectral density decreases in the wings of the atomic line.

This paper augments previous theoretical descriptions of superradiance in an extended optically thick medium by giving expressions which limit the length and density of a high-gain system which can superradiate as a whole, or equivalently, the shortness of its output radiation pulses. Limits arising from experimental conditions such as finite inversion time, finite decay and dephasing times, finite transit time (cooperation length), feedback, diffraction, and Fresnel number not approximately one, are discussed. Modifications to the simple analytical expressions for the output radiation of the superradiant system due to each of these effects are described in detail. Detailed computer results are also given.

A theoretical study of static electromagnetic field generation due to laser radiation force in multiphoton ionization of atomic media is presented. The static fields are spontaneously induced in atomic media and have electric field components in the radial and axial directions of the incident laser beam and an azimuthal magnetic field component. Multiphoton ionization process, which is inevitably apt to occur in the interaction, significantly enhances the spontaneous fields. Numerical calculations of the fields generated in atomic sodium vapor and helium gas have been made, assuming an incident picosecond Nd-doped yttrium aluminum garnet laser pulse. The results show the characteristic natures and magnitude of the spontaneous fields.

It is theoretically and experimentally demonstrated that optical second-harmonic generation (SHG) is possible to be observed in atomic media irradiated with an intense laser pulse. The SHG is induced by a static electric field spontaneously generated in the interaction, and any special condition is not required for the SHG. The experiment to observe the SHG has been made using atomic sodium vapor and a mode-locked Nd-doped yttrium aluminum garnet laser system (pulse duration, 28 psec; output energy ≲50 mJ). The second harmonic (SH) polarization, spatial beam pattern, and dependences of SH signal on the sodium density and on the fundamental intensity have been examined. The experimental results agree well with the theoretical predictions and numerical results.

The optical Hanle effect (light-shift-induced zero-field level crossing) has been investigated theoretically and experimentally. In the case of a $J=0\mathrm{}\to 1\to 0$ three-level system and of a $J=0\mathrm{}\to 1$ two-level system, the resonance line shape has been obtained using a nonlinear-response-function method. Approximate expressions, valid under the conditions for the observation of light shifts, are obtained and compared with exact calculations as well as with the corresponding expression for the magnetic Hanle effect. As concerns the weak laser beam which produces the coherent excitation of atomic substates, we have calculated the linear response in the limiting case of monochromatic and of broad-band excitation. The experimental investigation has been performed for the Ba resonance line using two cw dye lasers at $\lambda =5535\mathrm{}$ Å and an atomic beam. The absorption- and dispersion-shaped level crossing resonances have been observed, for narrow- and broad-band excitation, by varying the power of the strong nonresonant laser beam. We have checked that the line shapes are only dependent upon the reduced variable $\frac{P_L}{\delta }$ ($P_L$; beam power; $\delta$: frequency detuning). Using the theoretical expressions, we have tried to fit the experimental curves. Provided that the Gaussian distribution of the beams is taken into account, we have obtained a good agreement between theory and experiment for the whole set of experimental data.

Frequency-modulated spectra of coherently driven quantum systems are calculated using the density-matrix formulation. The modulated spectra are shown to be related to the two-time correlation functions of the polarization operators of the system. In the limit of modulation frequencies small compared to the width of the spectral features under study, the in-phase signal (quadrature signal) is shown to be related to the derivative of absorption (second derivative of dispersion) in the absence of any modulation. Modulation spectra in strong fields are calculated explicitly for two-level systems; such spectra are shown to yield useful information concerning light shifts and Rabi splittings. The influence of laser temporal fluctuations on such modulation spectra is also discussed.