A calculation is presented to describe the response of an atomic system subjected to two strong standing-wave field pulses separated in time. One finds a sequence of output pulses following input pulses which is reminiscent of classical photon echoes. A physical picture of the processes involved in echo formation is presented, and connection is made with the classical picture of photon echoes. The application of these techniques to collision studies is emphasized. It is shown that studies of echoes produced by standing-wave fields can prove advantageous for exploring the effects of small-angle scattering on both level populations and atomic coherences.

The authors present for the first time an effective interaction between two ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atoms in a bath of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at temperatures below 0.1 K. This interaction turns out to be, in its long-range limit, an oscillatory function of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ interatomic separation, the oscillations arising essentially from the sharp discontinuity in the momentum distribution at the Fermi surface. In addition, an expression is formulated for the oscillations in the density of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ bath induced by one ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ impurity, as well as a modified Friedel sum rule, which relates the relative amount of matter displaced by this impurity to the phase shifts pertaining to the impurity-${}_{}{}^3{}_{}{}^{}\mathrm{He}$ quasiparticle scattering at the Fermi surface. Finally, the dependence of the results on temperature and on the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ superfluidity gap is discussed.

The results of Brillouin scattering from $p$-cyanobenzylidene-$p$-$n$-octyloxylaniline are reported for the isotropic liquid phase and for monodomains of the nematic and smectic-$A$ phases. For the isotropic phase, the observed temperature dependences of the velocity and the attenuation of sound can be explained well by the temperature dependences of the density, compressibility, and viscosity. In the two liquid-crystalline phases, the velocities of sound are found to depend only weakly on the propagation direction relative to the orientations of the long molecular axes and to vary smoothly with temperature, without irregularities at the nematic-smectic-$A$ transition. The measurements do not reveal the propagating undulation mode (second sound) predicted for the smectic-$A$ phase. The observed directional dependence of the first-sound propagation suggests, however, that second sound exists, but with velocities which are too low for detection in the present experiment. For the isotropic phase, separate measurements were performed on the intensities and widths of polarized and depolarized Rayleigh scattering. These results agree with the predictions of the Landau-de Gennes model. Both the order-parameter relaxation time and the integrated intensities of critical scattering diverge towards the isotropic-nematic transition with a ${(T-T_c^{*})}^{-1\mathrm{}}$ temperature dependence.

The time-dependent behavior of a model spin system which might represent certain properties of alternating copolymers is studied. This model is an extension of the kinetic Ising model of Glauber to a system in which the strengths of interactions between neighboring spins alternate. The exact stationary and time-dependent solutions for the average spin and spin-pair correlations are obtained for this system. It exhibits two relaxation times, in contrast to the Glauber model; this feature may be relevant to the study of the time-dependent relaxation phenomena of the dipole moments in such polymers as ethylene-propylene copolymer.

The angular distribution of scattered light intensity for polystyrene in diethyl malonate was measured along the isochores near the critical concentration. The zero-angle scattered intensity $\frac{I_{c,o}}{T}$ [i.e., ${\lim }_{k\to 0}\left(\frac{I_c}{T}\right)$ and is directly proportional to the isothermal osmotic compressibility ${\chi }_T$] and the correlation length $\xi$ were obtained as a function of temperature and composition. The scaled functions of the $\frac{I_{c,o}}{T}$ and $\xi$ were examined as a function of the scaling parameter. The pseudospinodal generalization was found to be valid for even a macromolecular solution. In addition, some considerations concerning the reduced quantities of $\frac{I_{c,o}}{T}$ and $\xi$ in terms of the scaling laws are reported.

The dynamical correlations and thermodynamic functions for a single spin ½ experiencing a static external field and a linear interaction with phonons in a direction perpendicular to the field are discussed as a function of the spin-phonon coupling in order to study the abrupt transition from a nearly free spin system to an almost self-trapped situation. The theory is based on a mode-coupling approximation which permits the expression of relaxation kernels for the dynamical spin susceptibilities in terms of convolution integrals over the spin-excitation spectra. The thermodynamic functions are obtained from transcendental equations expressing the consistency of the static response with the relaxation dynamics. The relevance of the theory for a description of paraelectric impurities is indicated.

The mobility $\mu$ electrons in methane at $n<\mathrm{}6\mathrm{}\times {10}^{20}$ molecule/${\mathrm{cm}}^3$ is field dependent at $\frac{E}{n}>0.012\mathrm{}$ Td (1 Td = 1×${10}^{-17\mathrm{}}$ V ${\mathrm{cm}}^2$/molecule). The temperature dependence of the thermal-electron mobility in the low-density vapor is $\mu n\propto T^{0.45}$. The threshold field and temperature dependence are much lower than reported previously. In the electron energy region $0.002<\mathrm{}\epsilon <0.2\mathrm{}$ eV the momentum-transfer cross section of methane molecules is well approximated by ${\sigma }_{\nu }=0.014\mathrm{}{v}^{-1.9\mathrm{}}$ ${\mathrm{cm}}^2$. In the low-density gas the electron drift velocity $v_d$ becomes superlinear with field strength at threshold velocity $v_d^{\mathrm{thr}}=c_0$, the speed of low-frequency sound. At $n>\mathrm{}6\mathrm{}\times {10}^{20}$ the value of $\mu n$ in the coexistence gas decreases slightly, while $\frac{d\left(\mu n\right)}{\mathrm{dT}}$, ${\left(\frac{E}{n}\right)}_{\mathrm{thr}}$, and $\frac{v_d^{\mathrm{thr}}}{c_0}$ increase. The effects are due to quasilocation of the electrons by density fluctuations in the dense gas. The entropy $\Delta S^{\prime }$ and enthalpy $\Delta H^{\prime }$ of activation of electron transport correlate with the structure factor $S\left(0\right)\mathrm{}$ of the dense gas: $\frac{\Delta S^{\prime }}{S\left(0\right)\mathrm{}}=19\mathrm{}$ J/mol K and $\Delta H^{\prime }\approx T\Delta S^{\prime }$ near the vapor-liquid coexistence region. At $n>\mathrm{}6\mathrm{}\times {10}^{21}$ there is a rapid increase in $\mu n$ due to conduction-band formation. ${\left(\frac{E}{n}\right)}_{\mathrm{thr}}$ passes through a cusp >0.04 Td at $n=8\mathrm{}\times {10}^{21}$, where $\frac{d\mu }{\mathrm{dE}}$ changes sign, then decreases again to 0.01 Td at $n>\mathrm{}1.0\mathrm{}\times {10}^{22}$ molecule/${\mathrm{cm}}^3$. The threshold $\frac{E}{n}$ in the normal liquid is similar to that in the low-density gas. At low field strengths the electron energy is moderated mainly by elastic collisions in the low-density gas, and by inelastic collisions in the liquid.

A formalism for a time-dependent harmonic oscillator is presented. The quantum-mechanical solution is developed and the Green's function is derived. Particular examples of runaway and dissipative behavior are considered.

An angular momentum of fixed magnitude is studied in the presence of a time-dependent magnetic field by use of a density matrix expanded in multipole moments. The cases of resonant and nonresonant nonadiabatic processes are treated. Application to spin-state-selection experiments leads to oscillations in the magnetic-vector polarization consistent with experiment.

An all-valence-electron self-consistent-field linear-combination-of-atomic-orbitals molecular-orbital procedure including configuration interactions for calculating the magnitude and sign of the nonlinear second-order molecular susceptibility components (hyperpolarizability) for substituted dipolar aromatic molecular systems is reported. Three fundamentally important examples, aniline, nitrobenzene, and $p$-nitroaniline, are considered. Analysis of the microscopic origin of their molecular second-order susceptibilities provides a direct means for understanding the macroscopic nonlinear optical response of organic molecular solids which have already been observed to possess exceptional nonlinear optical properties. The important excited states of aniline, nitrobenzene, and $p$-nitroaniline have been identified and examined in their relationship with the molecular second-order susceptibility-tensor components ${\beta }_{\mathrm{ijk}}$. The detailed nature of the charge separation accompanying these states has been discussed in terms of both the configurations composing the excited states, and also the one-electron molecular orbitals which determine those configurations. These results demonstrate how the bond-additivity approximation is inappropriate for $p$-nitroaniline. Finally, the frequency dependence of the ${\beta }_{\mathrm{ijk}}$ components in each case shows that the Kleinman relations are valid approximations only at relatively low frequencies.

The plasma red shifts of ${\mathrm{H}}_{\alpha }$ and ${\mathrm{D}}_{\alpha }$ were measured in an atmospheric-pressure wall-stabilized arc, which was operated in argon with a small admixture of either hydrogen or deuterium. The measurements have yielded, within the experimental uncertainties, the same red shifts for ${\mathrm{H}}_{\alpha }$ and ${\mathrm{D}}_{\alpha }$, i.e., zero mass dependence.

The authors calculate the radiative opacity of gold under conditions representing particle-beam-pellet fusion targets: solid density and a temperature of 750 eV. It is shown that under these conditions the absorption lines form broad bands due to the combined effects of linewidth, electrostatic splitting, and the existence of a distribution of ionization states in the plasma. As a result, line absorption has a dominant effect on the Rosseland mean free path.

Two different free-energy theories of inhomogeneous fluids have been developed recently. One, the modified Van der Waals theory, requires as input the pair potential and the Helmholtz free-energy density and pair-correlation function of the homogeneous fluid. The other, the approximate density-functional theory, requires the Helmholtz free-energy density and direct-correlation function of the homogeneous fluid. Although formally different, it is shown in this paper that for a liquid-vapor interface in a 6-12 Lennard-Jones fluid they predict similar surface tensions (within 12% of one another) and density profiles. The gradient approximations are a little wider and the tensions about 15% higher than those of the corresponding integral theories. The integral versions are solved variationally with a trial function shown to be accurate by comparison of the exact solutions of the gradient approximations to the variational solutions of the same.

It is shown to within the accuracy of present-day computer-simulation studies that the bridge functions (i.e., the sum of elementary graphs, assumed zero in the hypernetted-chain approximation) constitute the same universal family of curves, irrespective of the assumed pair potential. In view of the known parametrized results for hard spheres, this observation introduces a new method in the theory of fluids, one that is applicable to any potential. The method requires the solution of a modified hypernetted-chain equation with inclusion of a one-parameter bridge-function family appropriate to hard spheres, and the single free parameter (the hard-sphere packing fraction) can be determined by appealing to the requirements of thermodynamic consistency. The assertion of universality is actually demonstrated via the application of this new method to a wide class of different potentials: e.g., hard spheres, Lennard-Jones, an inverse fifth power ($r^{-5\mathrm{}}$) applicable to the helium problem, the Coulomb potential (i.e., the one-component plasma), charged hard spheres, an oscillatory potential proposed for certain liquid metals, and the Yukawa potential.

The general stability conditions of a three-component plasma lead, in addition to the usual critical phenomena, to the appearance of a chemical instability, connected with the multiple solution of the law of mass action. As a result of a first-order transition the system will separate into two phases with different degrees of ionization. As the fraction of highly ionized phase increases, the conductivity of the system becomes metallic. Such a phenomenon can explain the metal-dielectric transition and its connection with such critical phenomena in different systems as weak electrolytes, molten salts, metal-ammonia solutions, and solid-state plasmas.

The equilibrium velocity distribution of classical free particles interacting with random classical radiation is investigated using the model of Einstein and Hopf, and extended to allow relativistic particle velocities. The model considers a massive free particle which has an electric dipole oscillator mounted inside; the oscillator provides the interaction between the particle and the random radiation. In this paper we give the calculations leading to a Fokker-Planck equation for the equilibrium distribution of particle momenta, and evaluate the equation for a number of radiation spectra. We find the following results: (i) If the random classical radiation is the Rayleigh-Jeans law for thermal radiation, then the equilibrium particle distribution follows the Boltzmann distribution only at low temperatures where nonrelativistic particle velocities are involved. The Rayleigh-Jeans law does not lead to the Boltzmann distribution for relativistic free particles. (ii) If the random classical radiation is the zero-point radiation spectrum, then the equilibrium particle distribution is the Lorentz-invariant distribution. (iii) If the random classical radiation is the Planck spectrum with zero-point radiation, then the equilibrium particle distribution goes over asymptotically to the Lorentz-invariant distribution at velocities near the speed of light. Thus no finite number of free particles can form an equilibrium velocity distribution if zero-point radiation is present. The particles will diffuse to velocities ever closer to the speed of light. We conclude that equilibrium for a finite number of particles must involve some explicit mechanism for confinement if classical zero-point radiation is present.

A phase operator for a charged particle in a magnetic field is defined by using the classical connection between the angles in the configuration and the velocity planes (both perpendicular to the magnetic field). Coherent states are used for fixing the center of the orbit. The same states are also used in establishing quantization rules for classical functions containing products of quantities that do not commute in quantum mechanics.

The phase-transition behavior of a hard-core lattice gas with nearest-neighbor exclusion and next-nearest-neighbor attraction on the plane-square lattice has been determined using high- and low-density activity series including double series in the sublattice activities reported here. The model exhibits a line of second-order transition points at high temperature and a line of first-order transition points at low temperature intersecting at a tricritical point. The series for the various thermodynamic functions do not converge equally well at all temperatures, requiring the utilization of a strict criterion (outlined here) for assessing the reliability of numerical results. From the combined behavior of the thermodynamic functions we have determined the radius of convergence of the series at all temperatures, the position of the singularities (in terms of the fugacity) on the real axis approaching the intersection of the unit circle at low temperature. Along the second-order line the critical exponents are estimated to be $\alpha \simeq 0.0$ (logarithmic singularity), $\beta \simeq \frac{1}{8}$, and $\gamma \simeq \frac{7}{4}$. At the tricritical point ${\alpha }_t\simeq 1$ and ${\gamma }_t\simeq 1$ are in agreement with the $\epsilon$-expansion results of Stephens and McCauley for $d=2\mathrm{}$. The density series are poorly behaved, and we can only estimate the phase diagram.

The results of earlier calculations are used to obtain oscillator strengths for high principal-series transitions in cesium, in terms of the coefficients in an interpolation formula for principal quantum numbers $17<n<\mathrm{}\infty$.

It is shown that the functional form for the energies of a parameter-dependent system can be found by minimizing an associated semiclassical energy function in configuration space.