Classical and quantum dynamics in the classically chaotic stadium billiard are compared through studies of the evolving phase-space distributions and expectation values. Good agreement between the two mechanics is found for all distributions other than vertically directed wave packets which contain significant contributions from pseudoregular quantum eigenstates. Despite formal arguments as to the absence ‘‘quantum chaos’’ the quantum dynamics clearly shows a time-averaged relaxation to equilibrium, over the timescale studied, which is consistent with the classical K-system behavior.

The weak-noise limit of Fokker-Planck models with coexisting attractors is analyzed and the nonequilibrium potential defined by the weak-noise limit of the probability density in the steady state is constructed. The nonequilibrium potential is found to be continuous with discontinuities in its first derivatives along certain surfaces in the configuration space, which are created by the coexistence of attractors. The general rules determining the position of these surfaces in configuration space are given. Numerical and approximate analytical results for the nonequilibrium potential of the Brownian motion in a periodic potential subject to an external force are obtained. A comparison with earlier work is presented.

An exact expression for the three-particle direct correlation function, $c_3$, of a general fluid is derived. Exact expressions for the three-particle total correlation function, $h_3$, &, &, and δ$h_2$/δ${\rho }_1$ are also found. The first terms of the black ${\rho }_1$-circle, $h_2$-bonds expansion of $c_3$ and δ$h_2$/δ${\rho }_1$ are explicitly evaluated and, in particular, it is found that the leading term of the $c_3$ expansion is $c_3$=${\prod }_i$,${\mathit{j}=1;\mathit{i}<\mathit{j}}^3$ $h_2$(i,j). The behavior of this term is discussed for several configurations of a Lennard-Jones fluid in the neighborhood of the triple point. A comparatively more complex structure than that of $c_2$ is found. The correction terms are analyzed and it is found that they are small but not negligible: they tend to enhance the excluded-volume effect due to the strong repulsion of the potential. A scheme to obtain the higher-order direct correlation functions is also outlined. The relevance of these results to the modified hypernetted-chain approximation and to the theory of inhomogeneous fluids is briefly discussed.

We have measured the profile of the He i 4471-Å line and its forbidden component at 4470 Å in the plasma of a high-pressure pulsed discharge at an electron temperature of about 1.5 eV, and at electron densities ranging from 0.5×${10}^{17}$ to 2.0×${10}^{17}$ ${\mathrm{cm}}^{\mathrm{-}3}$. Contrary to all preceding experiments performed at higher electron temperatures, in the present experiment better agreement with theoretical calculations is found. A tentative explanation of this improved agreement is offered.

The theory of the extended-ratio method (ERM) and its extensive applications to various lattice models are presented here in detail. We find the following interesting features in contrast with the traditional ratio method (TRM): the results of the ERM very often (except for a very special example encountered among the studied lattice models) appear to be smoother and better or at least comparable to those of TRM; the odd-even oscillations appearing in the loose-packed lattices are reduced greatly; the Neville tables often provide sequences with a faster convergence rate and appear steadier and more reliable; while the computational efforts needed for the ERM are the same as those needed for the TRM.

The fractal dimensionalities have been determined for a variety of random fractals in which the masses of occupied lattice sites or particles are weighted by their probabilities of being contacted by random walkers (harmonic measure) or by particles following linear trajectories (ballistic measure) which are absorbed after their first contact. Using the harmonic measure, fractal dimensionalities ($D_h$) of 0.925±0.05 are found for a variety of two-dimensional random structures with different fractal dimensionalities [percolation clusters (D≃1.89), Witten-Sander clusters (D≃1.70), cluster-cluster aggregates (D≃1.43), and screened-growth clusters (D=1.25, 1.50, and 1.75)]. Using the ballistic measure, fractal dimensionalities of 1.26±0.02 were obtained for Witten-Sander aggregates and 1.17±0.02 for percolation clusters. For screened-growth clusters with fractal dimensionalities of 1.25, 1.5, and 1.75, the fractal dimensionality with ballistic measure was found to be 1.25±0.05, 1.31±0.03, and 1.28±0.03, respectively. Consequently, it seems that the fractal dimensionality associated with the harmonic measures is the same for all two-dimensional objects and has a value consistent with that predicted by the theoretical work of Grassberger.

This paper reports the measurement of the depopulation cross sections of the Rb(ns) and Rb(nd) states by ${\mathrm{ND}}_3$ (23≤n≤50). The experimental data are discussed with reference to previous work done on collisions between Rb(ns) and Rb(nd) states and ${\mathrm{NH}}_3$.

The Burkhardt-Konya-Coulson-March (BKCM) procedure developed by Gadre and Pathak for direct and reverse transformations between atomic-electron density and electron-momentum density has been modified. The modification is based on a work by Allan and March suggesting the use of a square of the Fourier transform of √ρ(r) for obtaining electron-momentum density at small as well as large p values. The new procedure [grafted-BKCM (G-BKCM)] involves an amalgamation of these procedures: the Allan-March procedure being grafted onto the BKCM method for low and high p values. The G-BKCM method has been tested out in direct as well as reverse directions and is seen to lead to extremely good estimates of atomic properties in the conjugate space.

We derive and test a new method for replacing an infinite set of close-coupling equations with only two equations, of the same form but involving an effective coupling potential. The resulting coupling matrix element is entirely expressible in terms of ground-state expectation values. As an example, we test the new method for a model system of electron–hydrogen-atom scattering and find that the calculations involving only ground-state properties do predict results in good agreement with calculations in which excited states are included explicitly.

It is shown that the distorted-wave amplitude for charge transfer can be transformed to a simpler form when one of the nuclear charges is much larger than the other. This amplitude is substituted into the unitarized distorted-wave approximation (UDWA) formula and applied to the process H(1s)+$B^{z+}$→${\mathrm{H}}^{+}$+${\mathrm{B}}^{\left(\mathrm{z}\mathrm{-}1\right)+}$. It is confirmed that the simplified formula is valid down to a few keV/amu for z≥10.

Multiply charged atomic recoil ions up to ${\mathrm{N}}^{6+}$, along with a weak trace of ${\mathrm{N}}^{7+}$ ions, have been observed in 1.05–MeV/amu ${\mathrm{Ar}}^{12+}$-ion impact on molecular targets (${\mathrm{N}}_2$). A shift of the peak positions for these multiply charged atomic ions (${\mathrm{N}}^{\mathrm{j}+}$) toward the high-energy side in charge-energy spectra, compared with those for recoil ions from single-atom targets such as Ar, strongly suggests that these recoil ions (${\mathrm{N}}^{\mathrm{j}+}$) have fairly large initial kinetic energies due to the Coulomb explosion of multiply charged molecular ions produced in the impact of highly charged projectiles. It is believed, therefore, that those multiply charged atomic ions, for example, ${\mathrm{N}}^{6+}$ ions, originate from multiply charged molecular ions, for example, ${\mathrm{N}}_2$${\mathrm{}}^{11+}$, ${\mathrm{N}}_2$${\mathrm{}}^{12+}$, or ${\mathrm{N}}_2$${\mathrm{}}^{13+}$ ions, which dissociate into two atomic ions.

Sodium-containing solids have been bombarded with 80-keV ${\mathrm{Ar}}^{+}$ ions, and the light emitted from sputtered particles has been studied in the wavelength range 200–900 nm. A number of spectral lines, which cannot be identified as previously observed transitions, have been seen. Their origin is discussed, and they are tentatively classified as transitions among core-excited levels in neutral sodium.

A recently proposed two-step method is applied to the quantum-mechanical problem of one-dimensional Morse potential. The method is composed of two steps. In the first step a variational principle is applied to a generalized coherent-state ansatz which in the present case is nothing but a Gaussian with a shifted origin and modified frequency. Correlation corrections are then added in the second step by standard perburbation. The ‘‘rigorous formula’’ for the energy spectrum is derived by a lowest-order perturbation calculation. As a severe test of the theory, we have applied the method to calculate the Frank-Condon factors. The agreement with numerical calculation is excellent over eight orders of magnitude.

Observations of second-harmonic generation in Na vapor with a pulsed laser have been reported. We have checked these observations with a sensitive cw technique at low power. No second-harmonic generation is observed, giving support to proposed mechanisms requiring high-power pulses.

A pair of nonlinear equations is derived which describes the dynamics of the electromagnetic drift oscillations in a nonuniform magnetized electron gas. It is shown that the nonlinear electromagnetic drift modes can propagate in the form of dipole vortices.

For the bound state of three identical lattice bosons interacting via attractive potentials (with strength U, range r, and repulsive core $U_0$) we investigate how its mass depends on U for large U. We find that the mobility of this bound complex depends strongly on r and that for a nearest-neighbor interaction (r=1) it may depend strongly on $U_0$.

For small wave numbers, the half-width and the maximum value of the incoherent scattering function obtained from neutron scattering experiments on liquid sodium at 403, 602, and 803 K approach their hydrodynamic limits in a manner as predicted by the mode-coupling theory.

We present a new method for calculating the dielectric constant of dense systems. The dielectric constant is calculated from the fluctuations in the electric field required to suppress variations in the sample polarization. In our algorithm the conventional roles played by field and polarization are reversed. This has the advantage of eliminating all reaction fields, but may only be useful for systems which do not have large dielectric constants.

We consider the behavior of the dimensionless ratio of the first two cumulants that would be observed in a dynamic light-scattering experiment on a coagulation system of particles. This cumulant ratio evolves with time to a limiting value independent of time representing a self-preserving distribution. The limiting value is a function of the fractal dimension of the clusters.

The influence of an applied field on the thermodynamics of a two-dimensional system of elongated particles is analyzed with use of the transfer-integral formalism. The particles see a local ${\phi }^4$ potential and are subject to elastic interactions with their nearest neighbors. In the strong-coupling regime the resulting Schrödinger-like equation is solved variationally. In particular, the system described here is shown to undergo a first-order phase transition.