Gauss's principle of least constraint is used to develop nonequilibrium molecular-dynamics algorithms for systems subject to constraints. The treatment not only includes "nonholonomic" constraints—those involving velocities—but it also provides a basis for simulating nonequilibrium steady states. We describe two applications of this new use of Gauss's principle. The first of these examples, the isothermal molecular dynamics of a three-particle chain, can be treated analytically. The second, the steady-state diffusion of a Lennard-Jones liquid, near its triple point, is studied numerically. The measured diffusion coefficient agrees with independent estimates from equilibrium fluctuation theory and from Hamiltonian external fields.

We discuss divergences in the density expansion of the mobility of a quantum-mechanical particle moving in either two and three dimensions through a random array of hard-core scatterers. The most important divergences at low temperatures are of quantum-mechanical origin and involve the ratio of the de Broglie wavelength of the moving particle to its mean free path. When these divergent contributions are resummed they lead to both of the following: (1) logarithmic terms in the virial expansion of the mobility and (2) long-time tails in the integrand of the Green-Kubo formula for the mobility. In $d$ dimensions the long-time tails have the form $-\frac{{\alpha }^{\mathrm{}\left(d\right)\mathrm{}}}{t^{\frac{d}{2}}}$, where ${\alpha }^{\mathrm{}\left(d\right)\mathrm{}}$ is a positive constant. For $d=2\mathrm{}$, the long-time tail is not integrable and the implications of this are discussed. Similar results have been obtained by Abraham et al. For $d=3\mathrm{}$, the long-time tails lead to corrections to the zero-frequency mobility of $O\left({\omega }^{\frac{1}{2}}\right)$, where $\omega$ is the frequency. This result should be detectable in electron-mobility experiments in gases at low temperatures.

Faraday rotation (FR) has a nonlinear part which can be excited by a strong elliptically polarized electromagnetic wave in a plasma, even in the absence of a static magnetic field. It is due to the different dispersion rates of the strong left- and right-circular polarization components of the wave (the corresponding refractive indices are denoted by $n_L$ and $n_R$) and induces weak nonuniformities in a magnetized plasma. As a result the study of the nonlinear characteristics requires the WKB type of nonlinearly correct first-harmonic field solutions. This nonlinear evolution problem has been investigated in this paper. The new results, depending on both the field intensity and the nonlinearly induced spatial inhomogeneity, are (1) the nonlinearly correct expressions for $n_L$ and $n_R$, (2) the amplitude evolution equations in which the coefficients are slowly varying with respect to $x$ (the Cartesian coordinate parallel to the direction of propagation) and their WKB solution, (3) the expression for the nonlinearly correct FR angle, and (4) a numerical estimation on the interaction of a plasma with a C${\mathrm{O}}_2$ pulsed laser in which it has been shown that the nonlinear increment of FR is opposite in sign to the value found in the linearized approximation of the field equations. The new results have been discussed in some special cases and some comments are given on enlarging the scope of further work on the FR of strong waves.

Green's functions and transition self-energies of dissipative quantum-mechanical many-body systems are formulated in terms of operator-basis expansions of Heisenberg equations of motion in Liouville space. Matrix elements of the Liouvillian with respect to arbitrary nonorthogonal operator bases play a primary role in the analysis. The self-energies are expressed as functionals of initial statistical ensemble averages which are presumed known and not restricted to systems at or near equilibrium; this provides a first-principles approach to use of spectral line shapes as a diagnostic of the nonequilibrium state of a dense gas, plasma, and/or radiation field. A perturbation expansion of the self-energy is derived and the general term is interpreted in terms of a subtraction of reducible parts. A separation into resonant and nonresonant contributions plays a crucial role in the analysis. The first-order resonant contribution yields a generalized statistical Hartree-Fock approximation, whereas the second-order contribution generalizes the Weisskopf-Wigner theory of decaying states to include thermal and, more generally, nonequilibrium environmental effects on transition-energy shifts and widths. Off-diagonal contributions to the self-energy are shown to be essential for inclusion of environmental contributions.

The general method of the preceding paper is applied to the theory of spectral line shape. Illustrative calculations of the transition-energy shift and width are carried out for a twolevel atom interacting with the quantized electromagnetic field. In the thermal-equilibrium case, explicit results are given in terms of the digamma function and Bose-Einstein distribution, generalizing the standard Lamb-shift and Weisskopf-Wigner natural width results to nonzero temperature. In the nonequilibrium case expressions are obtained which exhibit the influence of nonequilibrium photon distributions on the shift and width. A general theory of the time-dependent power radiated in the decay of an excitation is developed for systems not necessarily at or near equilibrium, in terms of appropriate generalizations of the Liouvillian Green's functions of the preceding paper. This approach is illustrated by calculation of the time-dependent radiated power for the same two-level model.

This paper presents an investigation of the interaction of a high-power Gaussian electromagnetic beam in ordinary mode with the electrostatic modes of the plasma and the resulting Raman and Brillouin scattering process. Taking into proper account the nonuniformity of the pump Gaussian beam, we have derived the expressions for the spatial amplification factor and temporal growth rate within the WKB and paraxial-ray approximations for stimulated Raman and Brillouin scattering. The effect of the nonuniformity of the pump is seen to affect the scattering phenomena significantly.

Modified Saha ionization theory has recently been used to obtain the dominant pressure and thermal ionization effects in the "intermediate" region (0.5-10 TPa) of the equation of state. The present work is aimed at providing the justification for the use of this theory in the presence of interactions. The valence charges at 0 K at normal density as determined using this theory are in very good agreement with their normal valence charges for a number of elements. The equation of state as computed from it is also in good agreement with the Thomas-Fermi-Dirac equation of state. Finally the theory is shown to simulate the valence transition under pressure in Eu and Yb.

Liquid alkali metals are treated as a system of charged hard spheres (CHS) in the background of interacting electrons. Such a system of CHS in a uniform background of electrons has been solved exactly by Palmer and Weeks in a mean spherical approximation. With the use of this model as a reference, the effect of responding electrons is taken into account in a linear-response approximation. The resulting expression for the structure factor involves the CHS diameter as the only free parameter and is very simple to compute. It reduces to the familiar Ashcroft-Lekner model when the charge on the hard spheres is taken to be zero. The results obtained for the static structure factor of all the alkali metals at different temperatures are in excellent agreement with the experimental data.

A detailed presentation of the Landau theory of the cholesteric blue phase (BP) is given with emphasis on the comparison of model predictions with reported experimental data. The basic model, which is asymptotically exact in the high-chirality limit, leads to the prediction of a body-centered cubic (bcc) $O^5 \mathrm{}\left(I432\mathrm{}\right)\mathrm{}$ structure for the BP. However, the model can be systematically extended to physical chiralities and used to calculate the free energies of more complex cubic structures. In particular, bcc $O^8 \left(I{4}_{1}32\right)$ and simple-cubic $O^2 \left(P{4}_{2}32\right)$ structures are analyzed and their optical and thermodynamic properties, as well as those of $O^5$, are compared with those reported for the two observed phases, BPI and BPII. It is shown that, in general, the known properties of these phases are consistent with a structure assignment of $O^8$ for BPI and $O^2$ for BPII. Some promising lines for future investigation are indicated.

It is observed that the Feynman path summation for the one-dimensional Dirac equation can be projected into three spatial dimensions to yield a path-summation formula for physical spin-½ particles of nonzero mass. Since the three-space projection matrix is independent of time and does not involve the particle's mass, relativistic motion governed by the Dirac equation has an underlying one-dimensional aspect.

Ab initio self-consistent-field calculations with large polarized basis sets have been used to determine the optimized geometry of an isolated nitrite ion. Similiar calculations, performed for a nitrite ion interacting with either one or two sodium ions, suggest that only modest differences in geometry will occur when a nitrite ion is placed in an interactive environment. This finding appears to contradict an analysis of the absolute photodetachment spectrum of N${\mathrm{O}}_2^{-}$ which indicates that in the gas phase the N-O bond length is 8% shorter than in the sodium nitrite crystal.

Charge-transfer cross sections in collisions of completely stripped ions of boron and carbon with the ground state of atomic hydrogen have been calculated in the framework of the continuum-distorted-wave approximation. The total charge-transfer cross sections have also been evaluated by applying $n^{-3\mathrm{}}$ law from $n=6\mathrm{}$ levels. The present calculated results for total cross sections are found to be in better agreement with the experimental results as compared to the existing theoretical results over the entire energy region considered.

The stopping-power data given by Khandelwal and Merzbacher have been reevaluated because, according to Choi, their expressions for the $M$-shell form factors were in error. Present results are (20-45)% smaller. In addition, the coefficients for the asymptotic expression were calculated.

A semiclassical core-polarization-penetration model is used to parametrize the $6snh-6sni$ and $6sni-6snk$ intervals in Ba I which were recently measured by Gallagher, Kachru, and Tran. The parametrization represents the existing data to within experimental uncertainties, and extrapolative predictions along these Rydberg series are presented.

Spectral features of the radiation emitted by autoionizing states in the presence of a strong laser field are calculated under the condition of multiple photon absorption and emissions. The method is based on the exact solution of the master equation for the recycled system. The decay spectra are found to exhibit sharp maxima at the laser frequency and, for large values of the Fano $q$ value, sidebands which are reminiscent of the triplet which one finds in the context of a two-level atom.

The time-dependent theory of the Stark quenching of $2S$ states in hydrogen and helium is developed for high electric fields, fields for which the Stark matrix element is large compared to the state separations. The metastable $2S$ state of an atom is mixed with two $P$ states by the field, and the subsequent decay is described.

The zero-core-contribution method is extended to study the photodetachment of heteronuclear diatomic molecules. Total photodetachment cross sections are calculated for the ions O${\mathrm{H}}^{-}$, S${\mathrm{H}}^{-}$, and Se${\mathrm{H}}^{-}$. The anisotropy factor $\beta$ is also calculated for O${\mathrm{H}}^{-}$. The agreement with measured values of these quantities is good.

In this report we calculate ${\Gamma }_5$, the rate for orthopositronium to decay to five photons. We find that ${\Gamma }_5=[0.0189(11\left)\right]{\alpha }^2{\Gamma }_{\mathrm{Lo}}$, where ${\Gamma }_{\mathrm{Lo}}$ is the lowest-order orthopositronium decay rate. The relevance of our result to the experimental situation is discussed.

Oscillator-strength measurements have been calibrated against the radiative lifetime for the $4s-4p$ transition of potassium. This yields a value of (8.1±0.5)×${10}^{-21\mathrm{}}$ ${\mathrm{cm}}^2$ for the photoionization cross section at the series limit, and implies a value for the cross-section minimum in good quantitative agreement with that calculated by Seaton.

The simple analytical model of Burch et al. for the calculation of $K$ x-ray and Auger energy shifts resulting from an additional vacancy in the $2p$ orbital is extended to arbitrary defect configurations. The energy shifts for $K$, $L$, and $M$ x-ray series of ${}_{}{}^{86}{}_{}{}^{}\mathrm{Rn}$ are calculated for vacancies in $1s$, $2p$, $3d$, and $4f$ orbitals. The relative importance of inner- and outer-shell vacancies in producing the x-ray shifts is discussed.