Theoretical study is made of the transfer between orientation and alignment of excited-state atoms by anisotropic collisions with ground-state atoms. The anisotropy considered is due to the anisotropic velocity distribution of atoms excited by a single-mode laser beam. The transfer rate and relaxation rates for each multipole moment are calculated for the excited state with $J=1\mathrm{}$ as a function of detuning of the laser frequency from the center of an absorption line and mass of perturbing ground-state atoms. Experiments to observe the transfer from alignment to orientation and from orientation to alignment in a weak magnetic field are considered, and corresponding signals are analyzed in terms of the transfer and relaxation rates.

The authors demonstrate special cases for which the resonantly excited $N$-level atom displays particularly simple periodic behavior involving only two levels. The cases, which occur when first and last transitions are weak, have analytic solutions. A striking difference is noted between even-$N$ and odd-$N$, related to the resonance structure of the dressed ($N-2\mathrm{}$)-level atom.

The problem of resonant potential scattering of a charged particle in the presence of a low-frequency laser is analyzed. A method suggested by Krüger and Jung is used and their result is obtained as part of the lowest order in an expansion in $\omega$, the laser frequency. Additional terms are obtained in lowest order and in the next order. No expansion in powers of $\frac{\omega }{\Gamma }$ is made where $\Gamma$ is the resonance width. A modified sum rule for the scattering is obtained.

High-resolution spectra of delayed x rays emitted by fast foil-excited magnesium ions are found to contain a feature at 1321.45±0.74 eV. That energy is in good agreement with previously measured photon energies for the spin-forbidden radiative transitions $\left(1s2\mathrm{}{p}^2\right){}_{}{}^4{}_{}{}^{}P_{}^e{}_{}{}^{}\to \left(1\mathrm{}{s}^{2}2p\right){}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ and $\mathrm{}\left(1s2s2p\right)\mathrm{}{}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}\to \left(1\mathrm{}{s}^{2}2s\right){}_{}{}^2{}_{}{}^{}S_{}^e{}_{}{}^{}$ in the three-electron ion. Time-of-flight decay curves taken at 25- and 50-MeV ion energies yield a 170±13 ps lifetime, in good agreement with a recently published theoretical value of 169 ps for the $\left(1s2\mathrm{}{p}^2\right){}_{}{}^4{}_{}{}^{}P_{\frac{1}{2}}^e{}_{}{}^{}$ state. The authors argue that, for the conditions of this experiment, the $4P_{\frac{1}{2}}^e$ state is produced primarily by a two-step collision process: $2s-2p$ outer-shell excitation followed by $1s-2p$ inner-shell excitation.

The primary objective of this paper is to provide a formalism to predict and characterize the echoes which may be produced in a gaseous sample by an arbitrary sequence of one- or two-frequency laser excitation pulses which successively transfer atomic population between two or more atomic energy levels. The resulting echoes can occur at times which depend on the relative frequencies of the excitation pulses as well as on the times at which the pulses were applied. Using an idealized model of the excitation pulses and the atoms, the authors derive a simple transformation equation which provides the density matrix of a single atom after a general excitation sequence. Equations are derived which utilize the single-atom density matrix to predict the properties of the echoes (if any) which result. The means by which the sample of atoms "remembers" the information necessary to produce different types of echoes is discussed, and it is then shown how a study of the echo can provide information concerning the atomic relaxation processes which tend to destroy this information. It is observed that trilevel echoes can be used to determine the relaxation characteristics of superposition states between energy levels coupled by two-photon transitions. In the case of certain other echoes (such as the three-excitation-pulse stimulated echo) the authors discuss the heretofore unappreciated fact that the sample remembers the "echo information" via a nonthermal velocity distribution of the atoms in one specific atomic state. In these cases a study of the echo behavior can provide information pertaining to the relaxation processes affecting only the one atomic state. The formalism developed is used to predict the properties of several echo effects. First, to provide a connection with previous work, the well-known photon echo is briefly discussed. Then important new properties of the three-excitation-pulse-stimulated echo are described. Finally, three different types of trilevel echo are analyzed. Each of the trilevel echoes discussed has widespread applicability in the study of relaxation processes.

Strengths and Stark widths of the prominent visible PbI and PbII lines are measured in emission by means of a gas-driven shock tube. Absolute ionic line strengths for $7s-7p$ and $7p-7d$ arrays conform well to quantum-mechanical sum rules and agree with theoretical predictions, but $6d-5f$ results differ markedly from central-field approximations. Neutral-line strengths agree satisfactorily with available comparison data. Semiempirical theory predicts the widths of PbII lines with characteristic reliability of better than 25%.

Within the classical path impact formalism, theoretical expressions are derived for the line shape and intensity of the $R$ and $P$ lines of the fundamental band of gaseous HD. These reflect the interplay between the allowed dipole moment and the dipole moments induced during binary collisions. The interference between the allowed and the induced dipoles and between the dipoles induced in different collisions lead to a line shape which is a superposition of a Lorentzian and an anomalous dispersion profile in agreement with experiment.

Photon-echo quantum beats arising from magnetic splitting of the cesium $7P_{\frac{3}{2}}-6\mathrm{}{S}_{\frac{1}{2}}$ transition were observed in a dilute atomic vapor by means of a novel polarization-rotation technique. The quantum-beat spectrum contains frequencies generated by the hyperfine structure of the $7P_{\frac{3}{2}}$ level as well as those due to the Zeeman splitting of both ground and excited levels. Experimental data for both $F=3\mathrm{}$ and $F=4\mathrm{}$ hyperfine components of the $6S_{\frac{1}{2}}$ ground state and for several echo delay times were fitted to calculated spectra, including corrections arising from Faraday rotation of the echo pulses.

The problem of the energy absorption from a weak probe field by a system of atoms driven by a coherent laser field is considered with special reference to the collective behavior of the atomic system. The changes in the nature of the absorption spectra as the intensity of the coherent laser field is changed are examined explicitly for a system of two atoms. Cooperative effects are shown to be important for weak laser fields. For strong fields, it is shown that the absorption spectra under cooperative conditions differ from those without cooperative conditions only by a scale factor.

A theoretical formalism is given for the calculation of electron pair production in a point-Coulomb potential using the method developed by Sud, Wright, and Onley for expressing the radial integrals over the product of Dirac-Coulomb functions in terms of a matrix generalization of the $\Gamma$ function. A partial differential equation in lepton energy satisfied by the $\Gamma$ function is obtained. This partial differential equation can be integrated numerically to obtain the positron spectrum for high-energy photons.

The effect of uniform dephasing and relaxation on the dynamical evolution of the population in a macroscopic volume of three-level molecules is considered where the population is driven optically between the initial ground state and the extreme excited state 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. The authors examine the evolution of collective relaxation between the excited and intermediate levels in the time regime of the pump pulse duration ${\tau }_p$. It is found that in the homogeneously broadened regime, in the mean-field limit, for uniform pumping, and under conditions such that the pump Rabi rate ${\omega }_R$, the characteristic collective relaxation time ${\tau }_R$ and $T_1$ and $T_2$ satisfy the inequalities ${\omega }_R{\tau }_R$, ${\omega }_R{T}_1$, ${\omega }_R{T}_2\gg 1$, collective transverse polarization will evolve if $\frac{{\gamma }_R}{4\gamma }>1\mathrm{}$, ${\omega }_R{\tau }_p\approx \pi$ ($\gamma$ is the uniform dephasing rate, i.e., $\gamma =T_2^{-1\mathrm{}}$). If, on the other hand, the above conditions are met, but $\frac{{\gamma }_R}{4\gamma }<1\mathrm{}$, no collective transverse polarization will evolve during the pump-pulse duration ${\tau }_p$. In the first case super-radiant pulse evolution (classical collective evolution) may evolve after pump-pulse termination. In the latter case it is possible for collective spontaneous relaxation (superfluorescence) to take place if other conditions are satisfied. Further, a convenient algorithm is established whereby results for the super-radiance or superfluorescence model in the mean-field, small-tipping-angle limit are shown to be formally identical to corresponding results for the lethargic, asymptotic regime of swept-gain super-radiance. In the latter case, the equations of motion are with respect to the retarded time frame and the field equations are replaced by Maxwell's equations. It is shown that the mean-field approximation for the case of super-radiance or superfluorescence is formally equivalent to the asymptotic-limit approximation for swept-gain super-radiance. It is found that a solitary pulse will evolve if the gain-to-loss ratio $\frac{{\gamma }_R}{4\gamma }>1\mathrm{}$; if $\frac{{\gamma }_R}{4\gamma }<1\mathrm{}$, no solitary pulse will evolve.

The problem of light scattering from an atomic system under cooperative conditions is analyzed. The atomic correlation function is constructed using the atomic coherent-state representation in a form that is ideally suited for numerical computations. Explicit results are reported for a system of five atoms and the question of the existence of additional side bands is analyzed.

We show that certain properties of superfluorescent pulses radiated spontaneously by a system of many initially excited two-level atoms can be described by means of the classical Maxwell-Bloch equations. The quantum fluctuations which initiate the pulse are random initial polarizations. The radiated fields which arise from different initial polarization distributions vary significantly from pulse to pulse. Such variations represent quantum uncertainties amplified to the macroscopic level. Probability distributions are calculated for various parameters characterizing the shape of the output pulse as well as the mean and the variance of the radiated intensity.

Fluctuations in superfluorescence are investigated. Special attention is given to fluctuations arising from phase disturbances produced by the noise. These are shown to have a signifigant impact on the statistics.

A formalism based on nonrelativistic quantum electrodynamics is developed for the calculation of reaction rates and cross sections for the processes which couple intense fields, such as laser beams, with charged particles in a medium (e.g., plasma). The medium is assumed to be homogeneous, isotropic, and transparent, its linear electromagnetic properties being described by transverse and longitudinal dielectric functions. The Hamiltonian for such a system of charged particles interacting with radiation in the medium is given. The incoming intense fields are described by coherent states, while scattered fields are described by semicoherent states. The theory presented is a diagrammatic perturbation theory for calculating $S$-matrix elements. The Hamiltonian is rearranged by adding and subtracting a single-particle operator (counterterm). A systematic analysis of self-energy structures for charged particles and beam self-energy structures (forward-scattering diagrams of the intense radiation field) is carried out. The self-energy analysis creates a very useful role for the counterterm, endowing it with the ability to renormalize the theory in a specific manner. As an application of the self-energy analysis the counter-term is used to eliminate, to lowest order, the ultraviolet divergence by mass renormalization. Its use in studying beam self-energy structures is also indicated. As an illustration of the formalism, the cross section for Thomson scattering with Doppler shift and the stopping power of a particle generating Čerenkov radiation are calculated.

The photon-number distributions for a laser with a saturable-absorber and a dye laser are obtained by extensions of the Scully and Lamb optical-maser theory. The results are shown to be in correspondence with those of Lugiato et al. for the saturable-absorber laser and with those of Schaefer and Willis for the dye laser. Moreover, they are in a form which clearly shows the relation between the saturable-absorber laser and the dye laser. The thermodynamic potentials for the first-order phase-transition analogy are calculated and are found to be of the form predicted by Scott, Sargent, and Cantrell using semiclassical equations.

Light scattering was used to study phase separation in critically quenched mixtures of isobutyric-acid—water and 2,6-lutidine—water. The measurements spanned the time interval $10\le t\lesssim {10}^3$ s and quench depths from 0.7 to 9 mK. The parameters measured were $k_m\mathrm{}\left(t\right)\mathrm{}$, i.e., the photon momentum transfer at the angle of maximum scattering, and the ring intensity $I(k_m,t)$. The early-stage measurements of $k_m$ vs $t$ are in very good agreement with the calculations of Kawasaki and Ohta and with the coalescence model of domain growth, which gives $k_m\propto t^{-\varphi }$, with $\varphi =\frac{1}{3}$. In the late stage $\varphi$ increases to unity in both systems. This implies that hydrodynamic effects control the rate of growth of the nucleating domains of size $l\simeq k_m^{-1\mathrm{}}$. In both early and late stages, the intensity measurements are consistent with $I(k_m,t)\propto l^3$. The scattering experiments were supplemented by direct observation of domain growth with a microscope.

Conditions under which chaotic solutions persist when dissipation is added to conservative systems are discussed. These solutions will, in general, produce only "transient" chaos in the physical systems since they are not necessarily stable. The analysis shows that, just as in the strictly conservative case, resonant systems are more susceptible to chaos than nonresonant systems.

Energy-transfer equations for a test particle in a fully ionized plasma are presented. The charged particles interact via Lienard-Wiechert potentials and the dominant contribution to the scatterings are from small-angle binary collisions. Asymptotic expansions of the energy rate equations are presented for all cases where either the test or the field particles or both are relativistic. These asymptotic equations are then used to derive equations determining rates of equipartition of energy, from which appropriate equipartition times are deduced. This work represents a relativistic generalization of nonrelativistic binary-collision Coulomb scattering.

A field theory, recently introduced by the authors, whose partition function yields the generating function for the number of configurations of $N_p$ branched polymers containing $N_b$ monomers, $N_{f}f$-functional units, and $N_L$ loops, is used to study the statistics of animals (clusters on a lattice) and the intimately related problem of the statistics of branched polymers in the dilute limit. The number $A\left(N_b\right)$ of animals per site containing $N_b$ bonds grows as ${N_b}^{-\theta }{\lambda }^{N\mathrm{b}}$ as $N_b$ tends to infinity, leading to a singularity in the generating function $\Xi \mathrm{}\left(K\right)\mathrm{}{\Sigma }_{\mathrm{Nb}}{K}^{\mathrm{Nb}}A\left(N_b\right)$ of the form $\Xi \mathrm{}\left(K\right)\mathrm{}\sim {|K-K_c|}^{\theta -1\mathrm{}}$, where $K_c={\lambda }^{-1\mathrm{}}$. Mean-field theory for this and other animal functions is valid above an upper critical dimension $d_c$ of 8. For the related polymer problem, $d_c$ is 8 in good solvents and 6 in $\theta$ solvents. In both cases, the critical behavior of generating and correlation functions depends on the nature of applied constraints. If a special combination of fields corresponding to the natural order parameter of the field theory is held constant, the susceptibility and correlation-length exponents $\gamma$ and $\nu$ obtain their usual mean-field values of 1 and ½ for $d>\mathrm{}{d}_c$. First-order corrections in $d_c-d$ are calculated for these and other exponents. If fugacities are held constant, there is a Fisher-like renormalization of critical exponents leading to animal's exponents $\theta =\frac{5}{2}$, ${\gamma }_a=\frac{1}{2}$, and ${\nu }_a=\frac{1}{4}$ for $d>\mathrm{}{d}_c$; $\theta =\frac{5}{2}$ agrees with exact calculations on a Cayley tree and ${\nu }_a=\frac{1}{4}$ with calculations by Zimm and Stackmayer of the radius of gyration of a branched polymer. For $d<\mathrm{}{d}_c$, $\theta -1=\frac{(3\mathrm{}\gamma -2\mathrm{}{\mu }_3)}{(2\mathrm{}\gamma -{\mu }_3)}$, ${\gamma }_a=\frac{\gamma }{(2\mathrm{}\gamma -{\mu }_3)}$, and ${\nu }_a=\frac{\nu }{(2\mathrm{}\gamma -{\mu }_3)}$, where ${\mu }_3$ is a critical exponent controlling the critical behavior of an irrelevant three-point vertex that is of order $d-d_c$ for $d$ near $d_c$. Both the constant-order-parameter and constant-fugacity theories violate the hyperscaling $d\nu =2-\alpha$, where $\alpha$ is the specific-heat exponent.