Results on the width of the self-correlation function $\rho \mathrm{}\left(t\right)\mathrm{}$ for liquid argon as determined recently by the method of isotopic mixtures and earlier by the technique of double Fourier transformation are compared and commented on. The excellent agreement found between $\rho \mathrm{}\left(t\right)\mathrm{}$ obtained by the two different methods is used to demonstrate the reliability of the latter technique. The fact that this technique can be applied for practically all monatomic liquids in contrast to the method of isotopic mixtures, is emphasized.

Zwanzig's projection operator and Mori's non-Markoffian generalized Langevin equation methods are applied to the problem of two-level atoms. Time-correlation functions of appropriate variables are calculated in a perturbation scheme.

A single-transverse-mode $Q$-switched Nd-glass laser, which can operate over a number of longitudinal modes variable from 1 to 100, has been used to investigate laser temporal-coherence effects on the 11-photon ionization of xenon atoms. When the laser pulse has an over-all bandwidth of 4 ${\mathrm{cm}}^{-1\mathrm{}}$, the number of ions formed is enhanced by ${10}^{6.9\pm 0.3}$ over that produced by a monomode laser pulse with the same average laser intensity. The observed enhancement in the number of ions due to the change in temporal coherence of the pulse is in good agreement with recent theoretical prediction.

With the aid of machine computation, we investigated the time evolution of nonlinearly coupled Langevin equations with 20 modes as a specific example of nonlinear systems off equilibrium. If the strength of an external excitation, which is restricted to a few particular modes, is sufficiently small, the asymptotic motion observed in the phase space of 20 modes approaches a fixed point while undergoing fluctuations. As the strength exceeds a certain critical value, the motion transits to a limit-cycle-like motion in the phase space. The rate of orbit separation between an arbitrary pair of modes participating in the limit-cycle-like motion is much greater than the similar rate observed in the fixed-point-like motion. The irreversible decay rate of the asymptotic structure decreases as the intensity of random forces decreases, confirming that the most stable structure realized in the asymptotic time limit of a nonlinear system off equilibrium is the one with the least irreversible decay rate.

We present extensive molecular-dynamics (MD) computations of the time-dependent correlation functions of the classical one-component plasma over a wide range of thermodynamic states characterized by the dimensionless parameter $\Gamma =\frac{e^2}{a{k}_{B}T}$, where $a$ is the ion-sphere radius. The computed velocity autocorrelation functions exhibit marked oscillations for $\Gamma \gtrsim 10$ at a frequency close to the plasma frequency, showing the existence of strong coupling between single-particle and collective modes; this is confirmed by a standard memory-function analysis. The dynamical structure factor consists of very sharp peaks near the plasma frequency, up to wave vectors of order $\frac{1}{a}$. The resulting dispersion curve exhibits negative dispersion for $\Gamma \gtrsim 3$. A simple memory-function analysis reproduces the MD data very well. At $\Gamma =152.4\mathrm{}$ our computations also provide evidence of well-defined shear modes. For large wave vectors a second, high-frequency transverse mode appears. From the correlation functions we have finally extracted estimates of the diffusion constant and the coefficient of shear viscosity. Near crystallization the shear viscosity has a value which is unusually large compared with that of simple liquids near the triple point.

A mixture of hard spherocylinders and spheres is studied in a virial expansion. The introduction of spheres into a partially aligned system of spherocylinders induces, via a small two-phase region, a transition to an isotropic phase. The dependence of this transition upon the size of particles is studied.

A system of classical particles, moving in a plane triangular or a plane honeycomb lattice, may be used to represent a statistical-mechanical model for a real substance occurring in fluid, and also in crystalline phases if a suitable particle interaction is chosen. In the case of the triangular lattice, a hard-core interaction between particles at the nearest-neighbor lattice sites and an arbitrary soft-pair interaction with finite, positive or negative, zeroth Fourier component between particles at lattice sites placed at a greater distance from one another, are taken. In the case of the honeycomb lattice, hard-core interactions between particles on nearest- and next-nearest-neighbor lattice sites are assumed, while a soft interaction as for the triangular lattice is again chosen for all other pairs. The hard-core part of the grand canonical partition function $\Xi$ has been calculated by a combinatorial method and that part of $\Xi$ given by the soft interaction by the mean-field approximation. In this case simple state equations can be derived, if one considers in addition to homogeneous particle distributions two further simple periodical distributions, which may be represented by two homogeneously occupied sublattices with, however, different densities. In this way, the existence of three thermodynamically stable phases for the triangular and honeycomb lattices can be proved. These are a gas phase, a liquid phase, and a crystalline phase with triangular and honeycomb periodical structure, respectively. Transitions between the phases can occur. Corresponding phase diagrams which are very similar to those of inert gases for special structures of the soft-particle interaction are drawn.

Measurements are presented of the intensity and lifetime of Rayleigh light scattered from thermally excited twist and splay modes of $p$-cyanobenzylidine-$p-n$-octyloxyaniline (CBOOA) in the nematic phase near the smectic $A$—nematic phase transition. The temperature dependence of the twist and splay elastic constants and viscosities are deduced. The phase transition is continuous ($T_c-T^{*}<3\mathrm{}°$ mK); this contradicts the prediction of Halperin, Lubensky, and Ma that this phase transition would be weakly first order. The critical behavior of the twist elastic constant $K_{22}$ and the twist viscosity ${\gamma }_1$ is consistent with mean-field predictions from 3°mK to 7°K above the transition; these data are inconsistent with the critical behavior predicted by the helium analogy. The splay mode is not renormalized, as expected.

The thermodynamic properties of small clusters of rare-gas atoms are determined from a biased random-walk Monte Carlo procedure. The cluster sizes studied range from $N=3\mathrm{}$ to $N=13\mathrm{}$ atoms. The internal energy is calculated as a function of temperature. Each cluster exhibits an abrupt liquid-gas phase transition at a temperature much less than for the bulk material. An abrupt solid-liquid transition is also observed for $N=11\mathrm{} \mathrm{and} 13$. The entropy of fusion is $S\simeq 1.76$ e.u. For smaller clusters, the solid-liquid transition is more gradual. The bond-length distributions are calculated for each cluster at various temperatures. The fluctuations of bond lengths from their average values increase gradually with temperature until the melting temperature is reached, at which point there is a large, abrupt increase. The indications are that a harmonic normal-mode analysis is applicable only at temperatures substantially below the melting point and even there, the frequency spectrum is temperature dependent. For $N=3\mathrm{}$, the equilibrium structure is an equilateral triangle. An $N=5\mathrm{}$ cluster forms a trigonal bipyramid and for $N=7\mathrm{}$ the form is a pentagonal bipyramid. The nine-particle structure has symmetry $C_{1h}$ and is a pentagonal bipyramid with two additional atoms, and the $N=13\mathrm{}$ cluster forms an icosahedron.

The recent observation by Hasan and Goble of a discrepancy between their numerical results on the specific heat of an ideal Bose gas confined to a thin-film geometry and the earlier analytic calculations of Pathria employing Neumann boundary conditions is shown to be unjustified. In those cases where a true comparison is possible, e.g., under Dirichlet or periodic boundary conditions, the observed deviations turn out to be insignificant if one uses the more recent second-order calculations of Greenspoon and Pathria rather than the original first-order ones of Pathria. For comparison under Neumann boundary conditions, fresh numerical calculations are required. We also present here second-order analytic calculations of the specific heat of this system (i) under mixed boundary conditions (Dirichlet on one wall, Neumann on the other) and (ii) under antiperiodic boundary conditions, and compare them with the relevant numerical calculations of Hasan and Goble.

Thick-target $K$ x-ray yields from Pb + Pb collisions have been measured at two bombarding energies near 100 MeV in order to determine cross sections. The latter fit into a new scaling law for $K$-vacancy production cross sections in symmetric heavy-ion collisions with $Z>\mathrm{}10\mathrm{}$.

It is pointed out that the thermomagnetic force observed to date is a magnetic-field-induced change of the thermal force which is proportional to the first spatial derivative of the temperature. This is in contradistinction to the point of view expressed by Fleming.

The condition for a superradiant phase transition to occur in the Dicke model is shown to be a condition on the atomic density. The transition can only occur for high densities.

We extend our recent work on the causal aspects of two-atom spontaneous decay to the case of nonidentical atoms.

The value of the Coster-Kronig transition probability for $Z=73\mathrm{}$ has been determined by eight variations of the $K-L$ x-ray coincidence technique. The effect of a correction for unwanted $L\eta -K{\alpha }_2$ coincidence events in the $L\alpha -K$ coincidence spectrum is discussed. The value reported for the Coster-Kronig transition probability at $Z=73\mathrm{}$, $f_{23}=0.153\mathrm{}\pm 0.002$, is a weighted average of measurements not involving this correction. This value is in excellent agreement with previous measurements but deviates significantly from theoretical predictions.

The Glauber approximation is applied to excitation of $2{}_{}{}^1{}_{}{}^{}P$ level of helium by proton impact with incident energies from 25 to 1000 keV. The theoretical results for the total excitation cross sections are in good agreement with the experimental data of Park and Schowengerdt and of Hippler and Schartner. Comparison is made with other theoretical models.

It is shown that the generalized optical theorem in quantum mechanics is a useful theorem in the scattering of two coherent beams.

A previous theory of atomic transitions in ultrastrong electromagnetic fields is applied to the problem of the ionization of highly excited hydrogen atoms. The magnitude of the fields necessary for the validity of the theory is greatly reduced by using excited hydrogen in the initial state, and the requirement of only multiphoton ionization limits the application to lowfrequency (microwave) fields. The requirement can probably be satisfied with currently available equipment. A result of the calculation is that the average number of photons absorbed is twice the minimum number.

Cross sections differential in the angle and energy of ejection of the second ionized electron are presented for the collision process ${\mathrm{H}}^{+}+\mathrm{He}\to {\mathrm{H}}^{+}+{\mathrm{He}}^{++}+2e$.

Kr $K$, Kr $L$, and Ar $K$ x-ray yields have been measured for excitation by 36- and 48-MeV fluorine ions in +6 to +9 charge states. The significant decrease in the dependence of the target x-ray yields on the projectile charge state, which is observed as the parameter $\frac{Z_1}{Z_2}$ is decreased, is in agreement with theoretical expectations.