The Stokes parameters of light emitted following beam-foil excitation have been measured as a function of foil tilt angle from 0° to 70° for the $2s{}_{}{}^1{}_{}{}^{}S-3p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$, $2s{}_{}{}^1{}_{}{}^{}S-4p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$, $2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}-3d{}_{}{}^1{}_{}{}^{}D$, and $2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}-4d{}_{}{}^1{}_{}{}^{}D$ transitions in He i. The precision of the measurements has been established using the $2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}-4s{}_{}{}^1{}_{}{}^{}S$ transition. A new method is described for analyzing beam-tilted-foil data. The results are compared with those forecast by the theory suggested by Band, and good agreement is found for the transitions from ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ terms but somewhat poorer agreement is found for the transitions from ${}_{}{}^1{}_{}{}^{}D$ terms. In particular, the $\frac{M}{I}$ polarization is shown to become negative for a foil tilt angle of around 60° in the case of the ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ terms and 45° for the ${}_{}{}^1{}_{}{}^{}D$ terms, while the total polarization fraction remains nearly constant at all tilt angles observed for the ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ terms but shows a pronounced minimum at about 45° for the ${}_{}{}^1{}_{}{}^{}D$ terms. A simple procedure is also outlined for the accurate determination of the phase of a retarder plate at any required wavelength.

A revised and expanded analysis of XeII is presented. The new analysis is used to predict the photoelectron satellite spectrum of atomic Xe in the limit of high photon energy in the neighborhood of the $5s$ peak. The agreement with the experimental observations of Gelius is good.

Atoms moving through a magnetic field suffer a Stark effect whose magnitude is dependent upon the atom's velocity. This velocity-dependent perturbation has recently been exploited as a Doppler narrowing technique, and in this paper we consider atomic anticrossings induced by it. Experimentally such anticrossings are observed between $n{}_{}{}^3{}_{}{}^{}D-n{}_{}{}^{1,3}{}_{}{}^{}F$ states of He for $n=4-9\mathrm{}$, with $n=8\mathrm{}$ being considered in detail. Theoretical expressions are derived for motional-Stark-effect-induced anticrossing line shapes. Good agreement with the observed line shapes is obtained and the theoretical analysis allows a value of the $n={}_{}{}^3{}_{}{}^{}D-{}_{}{}^{1,3}{}_{}{}^{}F$ interval to be obtained which is in good agreement with previous predictions.

Vacuum ultraviolet continuous emission from selectively excited vibrational levels of the $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state of molecular hydrogen into the dissociation continuum of the electronic ground state has been observed. The intensity distribution in the continuous spectra measured quantitatively proves the theory of Dalgarno, Herzberg, and Stephens. The new radiative dissociation process makes tunable vacuum ultraviolet laser action in molecular hydrogen appear feasible.

A systematic study of radiative lifetimes of low-lying levels in Clxv through ClIx has been made using the beam-foil time-of-flight techniques. These results are used to derive $f$ values for allowed $\Delta n=0\mathrm{}$ transitions of the type $2s^{2}2p^k-2s2\mathrm{}{p}^{k+1\mathrm{}}$ and $2s2p^{k+1\mathrm{}}-2\mathrm{}{p}^{k+2\mathrm{}}$.

The partial photoionization cross sections of sulphur hexafluoride have been measured between 20 and 54 eV using synchrotron radiation. Some of these cross sections are dominated by strong resonance effects. These resonances are shape resonances, resulting from the interaction between the photoelectron and the molecular field and hence always occur at approximately the same photoelectron kinetic energy. Expressed somewhat differently, they are final-state effects and can be thought of as arising from the multiple scattering of the photoelectron. Following Dehmer, the prominent resonance immediately above threshold in S${\mathrm{F}}_6$ is identified as having $g$ symmetry. Hence, only valence orbitals with $u$ symmetry may couple to it. This provides a powerful selection rule, which allows making an assignment of the peaks in the photoelectron spectrum. Even in the absence of resonances, the partial cross sections are qualitatively different for different orbitals. It is argued that measurements and calculations of partial cross sections should, in many cases, yield easier and more unambiguous assignments of peaks in photoelectron spectra than corresponding studies of ionization potentials.

A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\alpha$ above the threshold and for $\alpha \gg {\gamma }_c$; however, now the peak heights (widths) are in the ratio $3x$ ($\frac{2}{3x}$), $x=\frac{[{\gamma }_c+\frac{(T_1^{-1\mathrm{}}+T_2^{-1\mathrm{}})}{3}]}{[2\mathrm{}{\gamma }_c+T_2^{-1\mathrm{}}]}$, where ${\gamma }_c^{-1\mathrm{}}$ is the correlation time for laser phase fluctuations. For ${\gamma }_c\gg \alpha$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.

A general theory of quantum beats induced by pulsed-laser excitation is presented. The theory accounts for laser saturation effects such as stimulated emission from the excited atomic state during passage of the light pulse and light-induced atomic-level displacements. Under certain experimental conditions saturation may result in a modification, sometimes even in a regeneration, of the beat amplitudes.

A general theory of laser-induced quantum beats introduced in paper I is extended to include the effects of sequential laser excitation by several lasers for atomic systems either free or subjected to external static fields. A detailed study is made of the dependence of the quantum beat signal on the polarizations of the exciting laser pulses and detected spontaneous emission. The theory is applied to the echelon excitation of sodium $\mathrm{nD}$ Rydberg states. An analysis of the Zeeman beats produced by excitation in an external magnetic field suggests new ways to measure the fine-structure interaction constant of the Rydberg levels.

We analyze the enhancement of the coherent anti-Stokes Raman-scattering (CARS) susceptibility when the frequencies of the waves involved are tuned into resonance with discrete and continuum one-photon absorptions, and discuss the applications. We first derive the expression for the susceptibility by means of the usual iterative treatment of density-matrix perturbations. We then show that this derivation can be done in a straightforward manner by means of a time-ordered diagrammatic representation, which brings novel physical insight into CARS mechanisms. This representation can also be used to analyze the transient behavior of CARS as the pump fields are turned on and off. In addition, we discuss resonant CARS spectroscopy in the gas phase. The spectrum is composed of the expected enhanced Raman lines and also of double-electronic-resonance lines. All these lines occur as doublets. We derive their relative intensities based on detunings, collisional broadening, Franck-Condon overlap integrals, and rotational transition moments. The line contours are predicted by representing the susceptibility in the complex plane. The problems arising from saturation and the optical Stark effect are also considered; all should be small below pump densities of 100 MW/${\mathrm{cm}}^2$ in gas mixtures near STP. Fluorescence interference is negligible, except at power densities high enough for the Stark effect to be large. Beam absorption is also negligible at STP if the resonant species' concentration is less than 1000 ppm; phase matching is then satisfied. Finally, an experimental resonant CARS spectrum of ${\mathrm{I}}_2$ at 1 mb in air near STP is presented and interpreted; the susceptibility is about 400 times larger than that of ${\mathrm{O}}_2$ off resonance and under the same thermodynamic conditions.

The dynamical evolution of an excited-state population in a macroscopic volume of three-level molecules is considered where the population is driven optically between the initial ground state and the excited states by an externally applied ($c$-number) coherent pump. The intermediate and ground states are taken as nonradiatively coupled whereas the excited-to-intermediate-state transition is coupled to the radiation field which is treated quantum mechanically. It is found that stimulated Raman processes can significantly influence the dynamical evolution of population inversion and macroscopic polarization by producing coherence effects among the populations. We examine the evolution of collective relaxation between the excited and intermediate levels in the time regime of the pump pulse duration. It is shown, using the mean-field approximation, that for uniform pumping and conditions such that the pump Rabi rate ${\omega }_R$, the characteristic collective radiation time ${\tau }_R$, and the pump pulse duration ${\tau }_P$ satisfy the inequalities, ${\omega }_R>\frac{1}{{\tau }_R}>\gamma$ and ${\tau }_P\gtrsim {\tau }_R$ ($\gamma$ is a characteristic internal dephasing rate for the molecules), the system is left in a state with classical transverse polarization when the pump pulse terminates. The system can evolve collectively from such a state only as superradiant (classical) evolution. For superfluorescent evolution which requires a state of preparation of complete inversion (zero transverse polarization), it is shown that the pump pulse must be effectively of area $\pi$ and that ${\tau }_P<{\tau }_R$. Our results show that when the former conditions are satisfied the delay time ${\tau }_D$ for collective free pulse evolution is a function of both ${\tau }_P$ and ${\tau }_R$. It is shown further that the pump pulse shape as well as temporal duration significantly affect the final state of preparation. The results of this work are interpreted in connection with recent reported results of experiments in superfluorescence and superradiance.

We analyze the transient and steady-state properties of a model system consisting of a collection of atoms interacting cooperatively and driven by a classical external field. We obtain numerical solutions for selected atomic expectation values and suggest a steady-state scaling relation.

This paper investigates the effective field acting in an infinite, nonmagnetic, inhomogeneous medium. A self-consistent, integrodifferential equation may be written for the effective field at a point, accounting for scattering at every other site in the medium. One may solve this equation by iteration to write the effective field as a power series of operators acting on the uniform-medium effective field. We rewrite this series so that all local fields are augmented by all orders of the self-field. This means that each order of scattering is represented by a single integral operator. The action of this scattering operator on an arbitrary field may be expressed in terms of integrals over reciprocal space, if the product of the fluctuating function and the field is Fourier transformed. One of the integrals contains a weighting function that discriminates in favor of Fourier wave numbers similar to the uniform medium wave number. This integral gives the Bragg-like contributions to the effective field. The other integral extends over all of reciprocal space and contributes equally to the effective field for all fluctuation wave vectors. This integral determines the background effective field. A general term of the complete multiple-scattering expansion for the effective field is given. If the fluctuation distribution has a single cosine Fourier wave vector, then the effective-field expansion simplifies considerably. The Bragg contributions are examined. Finally, the background effective field that ignores all Bragg-like contributions is given, where all orders of scattering are considered. This field is modulated by the fluctuations in the medium in a straightforward way and it obviously provides a better approximation of the local field than either the incident or uniform-medium fields. This background field is used to find the effective dielectric constant that is correct for media in which the inhomogeneities are uncorrelated over lengths comparable to a wavelength.

This paper considers the nonlinear propagation of an intense laser pulse in plasmas. The equation for the wave envelope is derived accounting for the nonlinearities originating from the electron-mass variation as well as the self-interaction of the laser field. It is shown that the wave equation and the equations governing the slow plasma response can be represented in terms of the energy integral of a classical particle. The analysis of the potential reveals the existence of the localized solutions. The criteria for the latter to occur are obtained. A small-amplitude limit is also discussed.

In the present paper a diagrammatic analysis of the density operator for the evaluation of nonlinear optical quantities is considered. The present approach extends earlier diagrammatic analysis by treating the time evolution of both the wave function and its complex conjugate. Time-ordered graphs result, each of which corresponds to a term in the density matrix. Examples involving the third-order susceptibility are discussed for both monochromatic and pulse excitation. In particular coherent rotational transient birefringence is discussed. The diagrams provide a convenient means by which nonlinear optical processes can be precisely defined and the susceptibility readily evaluated.

A general derivation of non-Markovian Pauli-type master equations is given for systems interacting with pump and relaxation mechanisms. It is shown that the adiabatic-following solutions of Bloch equations, due to Grischkowski and co-workers, are obtained as a special case from Pauli equations of non-Markovian type. Finally, it is proved that for a two-level system the non-Markovian master equation obtained in the Born approximation is also exact.

Resonance fluorescence from a two-level atom is investigated as a problem in nonequilibrium statistical mechanics. The dynamical properties of the atomic steady state are investigated through the principle of detailed balance for open quantum Markovian systems. The saturated atom is shown to be described by a set of equations which obey detailed balance. A Liapounov function is found which guarantees the stability of the atomic steady state for arbitrary values of the driving and damping parameters. Two other Liapounov functions are introduced which are similar in form to the Boltzmann-Gibbs and Prigogine et al. entropy functionals and which reduce to these entropies in the saturation limit. Thus, it is shown that either entropy definition yields an $H$ theorem for the open atomic system where detailed balance obtains.

We apply Lugiato's theory of open systems to the single-mode laser model of Haken and co-workers, in order to investigate the effect on laser dynamics of processes involving one photon and two atoms. A Fokker-Planck time-evolution differential equation is obtained for the field quasiprobability distribution $P(\beta , {\beta }^{*}, t)$, which includes terms proportional to the squared number of atoms $N^2$. A detailed analysis reveals a twofold effect of these terms. The main effect that becomes relevant well above threshold is a broadening of the stationary field-intensity distribution. This broadening is due to a "cooperative noise," whose source is a squared polarization created by the two-atom processes. These processes also give rise to a very weak loss mechanism, which affects the maximum of the stationary intensity distribution in the threshold region, slightly increasing the threshold for the laser emission.

We present here results for the fourth frequency moments of current-correlation functions obtained by simulating a Lennard-Jones system of 256 particles near its triple point. A comparison with the results of Bansal and Pathak based on superposition approximation (SA) for the triplet correlation function $g_3(\overrightarrow{\mathrm{r}}, {\overrightarrow{\mathrm{r}}}^{\prime })$ leads us to a conclusion that the errors involved in the calculation of moments due to use of SA are not of much significance, in contrast to what is generally expected.

Light scattering from a multicomponent fluid mixture, ammonium sulfate-water-ethanol-benzene, has been studied near its tricritical point. From the angular dependence of the scattering intensity, tricritical singularities for the concentration susceptibility and for the correlation length were found to diverge with mean-field-value exponents. Rayleigh linewidths measured both above and below the tricritical temperature were compared with the existing theories.