For the interaction of coherent radiation with a nondegenerate, homogeneously broadened multilevel system the nonlinear susceptibilities and excitations and their time dependence are evaluated using a perturbation approach to the density matrix up to fourth order. This is done for the "off-resonance" case, ${(\Delta {\omega }^2+{\Gamma }^2)}^{\frac{1}{2}}\gg \frac{1}{\tau }$, as well as for the "on-resonance" case, ${(\Delta {\omega }^2+{\Gamma }^2)}^{\frac{1}{2}}\ll \frac{1}{\tau }$, with $\tau$ being the pulse duration, by taking into account the temporal change of the electric field amplitude and the phase and energy relaxation times, $T_2$ and $T_1$. It is shown that the transient one-photon excitation known as adiabatic following, is not only important for a pulse duration $\tau <T_2$, but may also be important for $T_2\lesssim \tau <T_1$. In addition, expressions for the transient two-photon excitation in a multilevel system are derived. Finally, the two-level limit is evaluated to all orders of the perturbation including damping effects, which gives results valid also for large incident light intensities. For the "off-resonance" case an expression is obtained which describes not only the transient adiabatic following process, but also the usual one-photon absorption including saturation effects giving rise to power broadening.

Third-harmonic generation in phase-matched Rb-Xe mixtures has been produced using 7- and 300-psec pulses of a mode-locked Nd:glass laser with peak powers up to 200 MW. Maximum energy conversion efficiencies of 2.8% have been achieved. A theoretical analysis is given which includes the transient excitations of the system and the linear and nonlinear susceptibilities up to seventh order in the perturbation. Agreement between theory and experiment has been obtained up to the highest input intensities demonstrating the importance of the transient excitation due to the adiabatic following. The phase-matching condition for parallel and focused beams has been investigated showing the influence of density gradients at the boundaries of the nonlinear medium (Rb vapor) and of the field-dependent changes of the refractive index at high input intensities. The limiting processes of self-focusing and multiphoton ionization are discussed.

The possible generation of photon echoes is discussed for a system where the incident radiation resonantly drives two-photon transitions. Use of the adiabatic-vector-model approximation of Grischkowsky, Loy, and Liao allows echo behavior to be calculated in a multilevel system by methods similar to those previously employed for two-level atoms. We find that observation of the double-quantum photon echo requires the presence of a nonresonant probe field at the time of formation of the echo pulse. The echo then radiates at the sum and difference of the probe and two-photon frequencies. As an example, we consider a possible experimental arrangement for the detection of double-quantum photon echoes in Rb vapor.

A density-functional theory appropriate to nonuniform simple classical fluids is developed. Unlike most previous theories, the theory is in principle exact in the linear-response regime. For practical applications a small number of well-defined approximations, including that of Percus and Yevick, are made. Given only the Lennard-Jones 6-12 potential as input, the theory yields surface tensions and profiles in very good agreement with the results of Monte Carlo calculations. For a liquid pressed against a hard wall the expected oscillations in density in the vicinity of the wall are obtained. Comparisons with previous theories are made, and points of possible improvement in the formalism are discussed.

We study the properties of a Ginzburg-Landau-Wilson Hamiltonian in which an order parameter is associated with each wave vector which points from the origin to one of two rings in reciprocal space. The existence of the order parameter breaks the two-dimensional rotational symmetry about the axis of the rings. The Hamiltonian may be interpreted as a simple model of the nematic-smectic-$C$ phase transition of a liquid crystal, if we identify the order parameter with the density of the liquid crystal and the axis with the average direction of the director field. There are no cubic terms present in the Hamiltonian, and the phase transition predicted by mean-field theory is second order. Fluctuations are taken into account by means of a method due to Brasovsky, and the phase transition is found to be of first order.

The nonlinear Kerr susceptibility of an oriented succinonitrile single crystal has been measured throughout the cubic plastic phase. The measurement procedure is described in detail, and the results discussed in terms of an orientational correlation function. Connection with other measurements is also made.

A fluctuation theory for the dynamics of metastable fluid states is presented which relies on a limiting form for the static structure factor $S\left(k\right)\mathrm{}$ previously presented by the authors. The transport coefficients are found to show a divergence in the hydrodynamic regime. In the nonhydrodynamic regime a model is presented which uses an approximate single-particle memory function and a diffusive mode is found; this is compared with fluctuation theory results of other workers. A recent computer experiment has shown numerical agreement with the static model.

The Thomas-Fermi-Dirac theory and one that adds Debye-Hückel interaction between particles are described for mixtures. The differences in the predictions of the two models are evaluated for the mixtures of iron and hydrogen under astrophysical conditions.

Linear, nondispersive ion acoustic wave propagation in an argon-helium plasma is investigated in a double plasma device. The experimental wave patterns show that there exists a range of light ion concentration $\alpha$ where both argon and helium modes can be excited and propagate simultaneously, contrary to a previously published experiment of Nakamura et al. The phase velocity of the mode is only slightly affected by the presence of He ions. In the case of the He wave, it can be described by a reduced mass $M_r=\frac{M_{\mathrm{Ar}}}{[1-\alpha +\alpha (\frac{M_{\mathrm{Ar}}}{M_{\mathrm{He}}}\left)\right]}$, showing that the He and Ar ions follow an adiabatic equation of state. The observed increase in Landau damping of the Ar mode is related to the He resonant ions, whereas the damping of the He mode is mainly due to the reduction in the phase velocity of the wave.

The problem of the first- or second-order nature of the nematic-smectic-$A$ phase change is explored. It is found that couplings between various order parameters, especially the first and second translational ones, are important. General Landau theory for coupled orientational and translational order parameters is developed. Numerical methods and results for translational ordering are presented. The effects of molecular polarity are considered. The relative importance of different couplings is discussed, and some experiments are proposed.

Numerical studies are reported on the exact time evolution of large systems consisting of up to four different kinds of particles that can be transformed into each other via external fields. Topics discussed in detail include the influence of initial conditions on the (generally) oscillatory response of the systems, quantum effects in the weakly and highly degenerate cases, beat phenomena in the density oscillations, and the emergence of longperiod oscillations in multicomponent systems.

The temporal hydrodynamic response of the free surface of a transparent liquid dielectric due to the passage of an intense, focused laser pulse is considered theoretically, and the calculated focal length of the surface lens is in satisfactory agreement with the recent experimental result of Ashkin and Dziedzic. An understanding of this effect is important for answering the question of the momentum of light in a material medium.

We derive quadratic nonlinearities in the viscoelastic stress tensor for nematic liquid crystals, which are necessary for the analysis of observed nonlinear effects in ultrasonic and electrohydrodynamic regimes. An increase in magnitude of the Leslie-Ericksen viscosity coefficients occurs through additive nonlinear terms as velocity gradients increase. The viscous components of the stress tensor are obtained for a nematic liquid crystal as a function of the velocity gradient components. Direct tests for determining the magnitude of single quadratically nonlinear viscosity coefficients are proposed.

Numerical investigations of dynamical systems allow one to give estimates of the rate of divergence of nearby trajectories, by means of a quantity which is usually assumed to be related to the Kolmogorov (or metric) entropy. In this paper it is shown first, on the basis of mathematical results of Oseledec and Piesin, how such a relation can be made precise. Then, as an example, a numerical study of the Kolmogorov entropy for the Hénon-Heiles model is reported.

The kinetics of formation and decay of Cs-Xe molecules in their $\Sigma$ and $\Pi$ bound states produced in Cs-Xe mixtures irradiated with a short-pulse dye laser tuned around the $7P-6S \mathrm{Cs}$ resonance transition has been investigated by fluorescence decay measurements. The time-resolved spectra of the 4600- and 5720-Å molecular fluorescent bands were studied in relation to xenon density, which ranged from 0.9 to 6.9 amagats. Quantitative collisional cross sections are derived from the measured transition rates with peak values around ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$.

It is pointed out that photoelectric counting correlations in an electromagnetic field that are associated with induced and spontaneous emission at the source, and the so-called Hanbury Brown-Twiss effect, are indistinguishable effects. It is shown by examples that interference effects involving the stimulated emission may be regarded as a source of the counting correlations. The results reported in a recent experiment of Scarl and Smith are therefore readily understandable.

A recent measurement of the two-photon counting rate in amplified spontaneous emission showed no time correlations that could be uniquely attributed to stimulated emission. It has been argued that the observed Hanbury Brown-Twiss correlations are associated with the process of stimulated emission. The experimental results can be interpreted in a way that more closely parallels the explanations of other experiments by avoiding specific recourse to stimulated emission as a cause of correlations.

Neon $K$ x-ray spectra produced in 80-keV neon-neon collisions are compared for gas targets and neon atoms implanted in a solid. The "solid target effects" are found to produce an x-ray spectrum which cannot be characterized by a binomial distribution.

Using a laser-cascade fluorescence technique, we have measured the radiative lifetimes of the $n=4\mathrm{to}7 p$ states of Na. The $\mathrm{}(4-7)p$ lifetimes are 125(12) nsec, 345(43) nsec, 0.89(9) μsec, and 1.45(10) μsec. These results are in qualitative agreement with calculated values.

Using solutions to a Hulthèn-like effective potential as variational trail functions we have calculated the energy levels of the nonzero angular momentum states of the static screened Coulomb potential. Our one-parameter results for the $2p$, $3p$, $3d$, $4p$, $4d$, and $4f$ levels are in excellent agreement with earlier, more elaborate calculations. We have also calculated spontaneous emission transition probabilities between several pairs of states and find that our results compare favorably with previous calculations. We conclude that Hulthèn-like trial functions provide better variational energies and wave functions with fewer parameters than hydrogenic or Slater-type functions for screened Coulomb and similar potentials.