Through parametrization of the recent Monte Carlo results as well as those of the dielectric formulation by the present authors, we propose a simple, analytic formula for the static local-field correction which determines the screening function of the degenerate electron liquids at metallic and lower densities. The detailed features of the present theory agree well with the results of the Fermi hypernetted-chain variational calculations. It is shown that the resulting dielectric function satisfies the compressibility sum rule and the self-consistency condition in the short-range correlation significantly better than other existing theories.

Motivated by the experimental findings of the onset time of a supercooled liquid, we extend Suzuki's scaling method to include the case of a time-dependent externally controlled growth rate. The simple application of this modified nonlinear-time-scale transformation leads to the following predictions: the deeper one quenches the sample, or the longer one waits before heating the sample, or the more the heating of the sample, the shorter the onset time of the freezing process. Its inadequacy to explain the quench-rate dependence of the onset time suggests that a similar examination of a two-mode theory may be the key to the behavior of the fusion phenomenon of supercooled liquid.

We develop and compare four expansions for line broadening in simple fluids. The dressed-cluster expansions (DCE) express the line broadening in terms of the dynamics of small clusters (absorber and $p$ perturbers, $p=1,2\mathrm{}\dots$) and at the same time incorporate properly the static $p+1\mathrm{}$ particle distribution functions of the fluid; i.e., the effects of "initial correlations." The hydrodynamic expansions (HE) are perturbative in the line-broadening interaction and express the broadening in terms of dynamical correlation functions of the fluid. Each expansion involves also a renormalization procedure (partial resummation in the appropriate expansion parameter). We use two types of resummation, in the time and frequency domain, denoted POP (partial time ordering prescription) and COP (chronological time ordering prescription), respectively. All four expansions (DCE-POP, DCE-COP, HE-POP, and HE-COP) when truncated at the qth order yield the correct first $q$ moments of the line shape and allow us to use well-known fluid correlation functions in the calculation of collisionally broadened line shapes.

It has been recently shown that equilibrium charge-state distributions (ECSD's) of heavy ions exiting carbon foils are well fitted by the ${\chi }^2$ model, the Gaussian model, and the reduced ${\chi }^2$ model in the low-, intermediate-, and high-velocity regions, respectively. A qualitative interpretation of these statistical distributions is given in the present work, and it is pointed out that the reduced ${\chi }^2$ model is mathematically identical to the ${\chi }^2$ model if the charge state $i$ is replaced by $Z-i$($Z$ is the projectile atomic number) in the probability density function. This equivalence is physically explained by the existence of a charge-state limitation in these two velocity regions. The author discusses also the validity of semiempirical relations giving the mean charge $\overline{i}$ and the standard deviation of the charge $s$ in the different velocity domains. At sufficiently high velocities $\frac{E}{M}\gtrsim 100$ keV ${\mathrm{amu}}^{-1\mathrm{}}$, $Z\lesssim 20$, experimental data available seem to indicate that $\overline{i}$ and $s$ depend monotonically on $Z$ and $v$, but this is not the case at lower velocities where shell effects play a major role. Finally, the author analyzes ECSD's observed for heavy ions, $59\lesssim Z\lesssim 82$, at low energies $\frac{E}{M}\lesssim 7$ keV ${\mathrm{amu}}^{-1\mathrm{}}$) and finds that these ECSD's are also very well fitted by the ${\chi }^2$ model proposed previously for lighter ions, $Z\lesssim 26$, at $\frac{E}{M}\lesssim 20$ keV ${\mathrm{amu}}^{-1\mathrm{}}$. However, for these heavy ions, ECSD's are already Gaussian for $\frac{E}{M}\gtrsim 5$ keV ${\mathrm{amu}}^{-1\mathrm{}}$.

Starting from linearized velocity moment expansions of the first Bogoliubov-Born-Green-Kirkwood-Yvon kinetic equation for one-component plasmas and using the non-linear fluctuation-dissipation theorem, the authors develop a systematic procedure for calculating the dynamical linear polarizability in terms of quadratic ones. This procedure provides insight into the long-wavelength structure of the velocity-average-approximation (VAA) hypothesis invoked by the authors in earlier calculations. At high frequency, the new, more exact polarizability result exactly satisfies the ($\frac{1}{{\omega }^4}$) frequency moment sum rule. Indeed, it is entirely exhausted by the earlier Golden-Kalman polarizability calculated in the VAA.

A space modulation of the self-diffusion coefficient along the pitch axis in a cholesteric phase that has been distorted under the action of an applied external magnetic field is suggested by NMR measurements. A phenomenological equation describing the spatial modulation is derived and applied with good agreement to the measured deuterium NMR spectral patterns. The fittings indicate that the amplitude of the modulation is small, but nonetheless an important factor in fitting the data. Finally, some of the implications of a space-modulated diffusion coefficient are discussed.

We present an analytical method for the evaluation of quantum defects of atoms and ions based on Schwinger's variational principle. The method is applied to a screened Coulomb potential $V$, and expressions for quantum defects as smooth functions of energy are obtained. This function goes through all the Rydberg levels and the lowest bound state. We calculate the quantum defects for $l=0\mathrm{}$, where trial functions with one and two Slater-type functions are used. The results are accurate when the trial function represents the exact wave function in the region where $V\ne 0$.

An irreversible stochastic model for the growth of clusters on a square lattice is formulated and studied by Monte Carlo simulation. The growth rate has a nonlinear nonlocal dependence on the density of occupied sites, qualitatively similar to that of crystallization governed by surface tension and diffusion. The density and Hausdorff dimension of the clusters are estimated. These results are compared with data for percolation clusters and with recent results for diffusion-limited growth.

The validity of nonrelativistic dipole approximation (NRDPA) in predicting forward Rayleigh scattering amplitudes is examined. Gavrila's analytic Coulomb $K$-shell amplitudes are compared with the results of a relativistic numerical calculation based on a multipole expansion of the second-order $S$-matrix element. The real part of the forward amplitude is predicted fairly well in NRDPA at all energies, including the low-energy regime where form-factor approximation fails. The imaginary part of the amplitude is fairly well predicted by NRDPA not too far above threshold, but the prediction fails at higher energies. The dipole contribution to these amplitudes is dominant below and near threshold, but higher multipoles become increasingly important at higher photon energies. The continued usefulness of NRDPA provides another illustration of the cancellation among relativistic, retardation, and higher multipole contributions.

Using the Argonne 100-in.-radius double-focusing mass spectrometer we have searched for long-lived (≥ ${10}^{-5\mathrm{}}$ sec) doubly charged atomic negative ions with the use of electron impact and Penning ionization sources. Our source operating conditions are similar to those of previous experiments which claim the existence of such ions. In contrast to all previous experiments, our mass resolution is sufficient to absolutely identify any impurity ion from its mass defect, and the machine design is such that artifact peaks (Aston peaks), caused by collisional dissociation of molecular negative ions, do not occur. Using a variety of target gases, we set upper limits for the production of doubly charged or singly charged species in electron bombardment and Penning sources of $X^{2-} \mathrm{to} X^{-}<~{10}^{-7\mathrm{}} \mathrm{to} {10}^{-8\mathrm{}}$ and $X^{2-} \mathrm{to} X^{-}<~5\times {10}^{-10\mathrm{}}$, respectively. These results contrast to those of previous experiments which claim positively identified ratios of $X^{2-} \mathrm{to} X^{-}={10}^{-1\mathrm{}} \mathrm{to} {10}^{-2\mathrm{}}$ and $X^{2-} \mathrm{to} X^{-}\approx {10}^{-3\mathrm{}}$, respectively. We find no evidence of any doubly charged atomic negative ion.

It is pointed out that the magnitude of the nuclear-scattering term in the eikonal exchange amplitude is smaller than but not negligible as compared with that of the electronic-scattering term at intermediate energies. It is, therefore, concluded that any approximation scheme which bypasses completely the nuclear-scattering term cannot provide a good approximate value for the eikonal exchange amplitude at intermediate energies especially at larger scattering angles. Comparison is made between these terms (electronic and nuclear scattering) using their exact eikonal forms as well as their various approximate expressions.

A method to calculate the bound-state eigenvalues of the Schrödinger equation is presented. The method uses a new diagonal representation of the Hamiltonian. The variational principle is applied to this diagonal representation and yields closed-form expressions of the form $E_n=E(an+b)\mathrm{}$ for the eigenvalues. Examples are presented for some quark potentials of current interest.

The exact random-phase-approximation dielectric function is used to compute the energy loss and straggling of nonrelativistic charged particles in very dense electron fluids $r_s\le 1$ at any degeneracy and for any velocity ratio $\frac{V}{V_F}$. Relevance to ion-driven inertial fusion is stressed.

The topological equivalence between the hydrogenic system and the free-particle system is established by a homeomorphic embedding of ${\mathrm{R}}_3$ into ${\mathrm{R}}_4$. The oscillator representation of the generators of the dynamical group SO(4,2) is realized for both systems in a unified way. It is shown that the free-particle wave functions form the basis of the unitary irreducible representation D(0,0) of the homogeneous Lorentz group instead of $\mathrm{D}{(0,(-\frac{\frac{1}{2}Z}{E})}^{\frac{1}{2}})$, $E>\mathrm{}0\mathrm{}$, in the case of the hydrogen atom.

The "diabatic" levels responsible for the observation of quasi-Landau resonances in absorption spectra of strongly magnetized atoms obey some scaling laws, valid for the whole range of the magnetic field. This suggests again that it should be possible to find a fully separable approximate model to describe the considered system in a realistic way.

The Jaynes-Cummings model of a two-level system interacting with a single-mode coherent-state field is investigated in a transformed representation emphasizing quantum corrections to the semiclassical Rabi problem. We find an intuitive explanation of the collapse and revivals of oscillations in the population inversion.

The spectrum of single-atom fluctuations in cooperative situations such as in the context of optical bistability and tristability is calculated by applying the method of system size expansion. The correlation functions of the fluctuating forces in quantum Langevin equations for any pair of atoms are found to be of order $\frac{1}{N}$. The relaxation matrix for single-atom fluctuations is shown to have the same structure as in the noncooperative situation but with an effective field determined by the state equation for multistability.

In this Comment we study the resonance fluorescence of a system of two atoms separated by an arbitrary distance $R$ in an on-resonance laser field. The steady-state spectrum is calculated in the strong-field limit both for negligible and for non-negligible dipole-dipole interaction. The singlet state of the system is included throughout, even for small interatomic separations. We show that the so-called "scaling factor," or the enhancement of the integrated fluorescence by $N$ atoms (above the expected factor of $N$), predicted in the literature by many authors, does not, in fact, exist.