The concept of a ray path in a fluctuating environment is examined and found to result in a nonlinear equation of motion for the unit vector everywhere tangent to the ray path. The equation of evolution for the probability distribution describing how the fluctuations in the ray path fill phase space is constructed using a projection-operator technique. Approximations to this general equation and the solutions thereof are discussed.

A two-stage scheme is presented to study structural perturbations of the sine-Gordon equation. Although the method is based upon the inverse scattering transform, detailed knowledge of this technical apparatus is not necessary in order to effect the calculations. In the first stage, slow modulations of speeds and positions for the soliton components are computed. The radiation resulting from the acceleration of the solitons is then calculated as a first-order correction through an easily constructed radiative Green's function. The method is exemplified by using it to study several outstanding problems that arise in applications of the Josephson transmission line. In particular we consider: (i) the pinning of flux quanta by microshorts, (ii) the quantum flux shuttle, (iii) annihilation conditions for fluxon-antifluxon collisions, (iv) breather decay, and (v) radiation from a moving fluxon.

An analysis of the potential and field profiles in low-dielectric constant liquids, where ions are thermally generated and recombine bimolecularly under applied voltage, is presented. The forced-diffusion model, which is described by a set of nonlinear differential equations, is solved numerically for a symmetrical case where the parameters of the positive and negative ions are equal. The solutions show a significant departure from the geometrical-potential distribution and the boundary conditions used lend themselves easily to generalization, which can include ion-injection and electron-transfer mechanisms.

A general perturbation method, founded on the multiple-space-scales technique, is applied to the kinetic analysis of the nonlinear effects generated by continuous transverse electromagnetic waves of finite amplitude propagating in warm and partially ionized plasmas. The collisional and weakly collisional cases are successively studied for a typical ordering of the significant parameters. In each case, it is first shown that the zero-order electron distribution function is determined by a set of two coupled equations and that it becomes inhomogeneous and generally non-Maxwellian under the effect of the collisional heating due to the wave absorption in the medium. The electron distribution function and the electric field inside the plasma are then completely determined up to second order in terms of the zero-order quantities by exact formulas which allow discussion of the influence of the microscopic interaction law on the nonlinear behavior of the medium. Some other applications of this method are outlined, particularly for the case of amplitude-modulated electric fields.

A theoretical model of the magnetohydrodynamic (MHD) motion and radiation emission characterizing dense laser-heated exploding-wire plasma has been developed which solves (numerically) the set of MHD equations coupled with a set of atomic rate equations describing the ionization and radiation dynamics of the plasma. The model has been applied to study the use of a high-powered laser to ionize and heat an aluminium-exploding-wire plasma. Particular attention has been directed towards the radiation emission from such a plasma which includes free-free (bremsstrahlung), free-bound (radiative recombination), and bound-bound (line emission) contributions. Included in the line emission are hard x rays produced by excited-level-to-ground-state transitions in the heliumlike and hydrogenlike ion species. The simulation model does not presently contain reabsorption or transport of the radiation. Laser absorption efficiency and laser energy-to-x-ray conversion efficiencies are studied as functions of laser pulse width, laser intensity, and initial wire diameter. It is found that the x-ray emission depends critically on the laser energy deposition, the plasma density profile, and hydrodynamic motion at the time of laser interaction, and the strength of the plasma current and its subsequent self-consistent, confining magnetic field.

The modified self-consistent scheme of Singwi et al. (STLS) for the calculation of static structure of classical liquids is used to calculate equilibrium properties of liquid sodium and rubidium. First, the effect of the attractive part of the potential on the static structure factor is studied. Using the theoretical results for pair correlation function $g\left(r\right)\mathrm{}$ we compute internal energy, pressure equation of state, high-frequency shear and bulk moduli, Einstein-frequency and second-frequency moments of the longitudinal- and transverse-current correlation functions. The corresponding expressions are also calculated by using the experimental $g\left(r\right)\mathrm{}$ for liquid sodium and molecular-dynamics data for liquid rubidium. These results agree reasonably well with the theoretical predictions of the modified STLS theory. Disagreement in pressure and bulk modulus is due to the fact that the theory yields too high a compressibility.

The effect on the dynamical structure factor $S\left(k\omega \right)$ due to coupling to temperature fluctuations and to the self-motion is investigated. For this purpose a phenomenological equation for the one-particle phase-space correlation function is presented and is used for explicit calculations. The equation gives for $k\to 0$, $\omega \to 0$ the correct hydrodynamic results and for large values of $k$ it gives correctly the single-particle motion. Detailed comparisons with experimental and molecular-dynamics results are presented for liquid argon and rubidium.

We present an approximation to the linearized collision operator or memory function of the exact kinetic equation obeyed by the correlation function of the phase-space density of a classical one-component plasma. This approximate collision operator generalizes the well known Balescu-Guernsey-Lenard (BGL) operator to finite wavelengths, finite frequencies, and finite coupling constants. It, moreover, satisfies the necessary symmetry relations, leads to appropriate conservation laws, and fulfills its first sum rule exactly. Next we use this operator to compute the shear viscosity $\eta$ for a series of coupling constants spanning the whole fluid phase. For weak coupling we make contact with the BGL theory, while for strong coupling we confirm, at least qualitatively, the results of Vieillefosse and Hansen, who predicted a minimum in $\eta$ as a function of temperature. We also demonstrate the important role played by the sum rules in the quantitative evaluation of a transport coefficient such as $\eta$.

The continued-fraction equation which determines the quasienergy of a two-level system in an external monochromatic field is derived by a simple semiclassical argument. The perturbation expansion of the quasienergy is extended to tenth order in the coupling constant.

The importance of the rigorous treatment of photon angular momentum in molecular-collision processes occurring in the presence of intense radiation is investigated. An alternate approximate treatment, which essentially neglects the angular momentum coupling between the photon and the molecular degrees of freedom by averaging over the angular dependence of the interaction matrix elements, is presented and applied to a model calculation. The degeneracy-averaged results of this calculation compare remarkably well with the results of a rigorous calculation, from which we conclude (with reservation) that the explicit consideration of photon angular momentum coupling in molecular-collision problems is unnecessary.

It is pointed out that the fixed-scatterer approximation (FSA) does not underestimate the $e^{-}$-H scattering cross section near the forward direction. The FSA result rather suffers from a logarithmic divergence in the forward direction which comes, as is well known, from the double-scattering term.

$1s-2p$ excitation cross sections of hydrogenlike ions by electron impact in the Coulomb-Born (CB) and Coulomb-Born-Oppenheimer (CBO) approximations have been evaluated in a straightforward manner, avoiding the use of partial-wave analysis. Results for different hydrogenlike ions, with $Z=2, 3, 6, 10, \mathrm{and} 50$ are thus obtained up to an incident electron energy of ten times the excitation threshold, with little computational effort. The results for ${\mathrm{He}}^{+}$ ions are compared with available experimental data.

A theoretical study of low-energy collisions of ${\mathrm{He}}^{2+}$ with He has been made. Potential curves are obtained using generalized valence-bond wave functions for the $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state formed from ${\mathrm{He}}^{+}$ + ${\mathrm{He}}^{+}$ and the $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and $E{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ states formed from ${\mathrm{He}}^{2+}$ + He. The predominant mechanism for single charge transfer is a radiative transition. The dipole transition moment connecting the $B$ and $X$ states is calculated using the ab initio wave functions. The radiative collision problem is formulated in terms of a complex potential and solved in the JWKB approximation. Cross sections are presented for energies from 0.001 to 10 eV. A rate constant of 3.6 × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^3$/sec at 300 K is obtained. This value is in satisfactory agreement with the recent experimental result and there is some evidence that the remaining discrepancy is due to the effect of tunneling and shape resonances, which have been estimated to increase the rate to 4.4 × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^3$/sec. The splitting of the asymptotically degenerate $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and $E{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ states is also examined and a conflict with a recent prediction of the asymptotic splitting is resolved.

The mobility of $\alpha$ particles in helium gas is calculated using the zeroth-order Viehland-Mason theory with interaction potentials recently computed by Cohen and Bardsley. The results show a dependence on field strength similar to the measurements of Johnsen and Biondi but are lower in magnitude by about 5%.

Using the $J$ matrix method, diagonalization of $H_0+V$ in certain finite $L^2$ basis sets is shown to generate a Gauss quadrature of the continuum. Explicit formulas for the corresponding weight function and orthogonal polynomials are given. This leads to a particularly simple expression for the Fredholm determinant and to the equivalence of the $J$ matrix and Fredholm equivalent-quadrature methods. Consideration of the asymptotic behavior of the polynomials for large degree results in a proof of Heller's derivative rule relating the spacing of pseudostate eigenvalues to the relative normalization of pseudostate and continuum matrix elements, and providing an alternative to Stieltjes imaging for the solution of the classical moment problem. Applications include an accurate quadrature of the sum over a complete set of intermediate states in perturbation expansions.

When electrons of moderately high energy collide with multiply stripped ionic targets, the predominant mode of collision is the impact excitation of outer-shell electrons, which subsequently decay by radiative emission. As the degree of ionization increases, the strength for inner-shell excitation becomes comparable with that for the direct-impact ionization of outer-shell electrons. The inner-shell vacancy thus created may decay by emission of an electron [Auger ionization (AI)] or a photon [excitation fluorescence (EF)]. For highly charged ionic targets, it is shown that the Auger ionization contributes significantly to the total ionization cross section, and becomes dominant over the direct-impact ionization in some cases (${\mathrm{Mo}}^{24+}$). The excitation probabilities, both to discrete and continuum states, have been calculated for the inner- and outer-shell electrons, using the improved Bethe approximation and the semiclassical projection operator. The result shows the drastic decrease in the relative transition strength to the continuum as the degree of ionization $Z_I$ increases. The branching ratios for the Auger ionization and fluorescence decay are fitted as functions of $Z_I$ for ionized targets. The AI and EF cross sections are compared with the corresponding direct processes.

The asymmetry parameters $q$ in the Van der Waals potentials $V=-\mathrm{A}{\mathrm{R}}^{-6\mathrm{}}(1+q{cos}^2\Theta )$ describing the interaction between LiF and the various inert gases were determined. A polarized, velocity-filtered LiF beam in the $J=1\mathrm{}$ state was scattered from inert gases contained within a scattering cell. The ratios of the total scattering cross sections for different states of LiF polarization relative to the beam direction were measured. From these data the asymmetry parameters were found to be 1.72±0.35, 1.05±0.10, 1.01±0.10, 1.12±0.10, and 1.28±0.10 for He, Ne, Ar, Kr, and Xe, respectively. These values, except for He, are in good agreement with calculations based on the pertinent electrical properties and excitation energies of the atoms and the molecule, insofar as they are known or may be estimated.

We present a method for including a variational correction in the discrete-basis-set method for electron-molecule scattering introduced by Rescigno, McCurdy, and McKoy. Our prescription for variationally corrected partial-wave $K$-matrix elements is based on Kohn's formula for the variationally stable scattering amplitude in three dimensions. The method is applied to $e^{-}$-${\mathrm{H}}_2$ scattering in the static-exchange approximation, and the effect of choosing different trial basis sets is shown. Our results are in good agreement with the results of other accurate calculations.

An electron in a high-Rydberg state will experience the Coulomb $R^{-1\mathrm{}}$ potential and the polarization $R^{-4\mathrm{}}$ potential. For $R$ large compared to $\frac{a_0}{\alpha }$, where $\alpha$ is the fine-structure constant—$\frac{a_0}{\alpha }$ is very large—it will also experience a retardation polarization $R^{-5\mathrm{}}$ potential. We here show that at very large $R$ the nonrelativistic $R^{-6\mathrm{}}$ nonadiabatic potential which it experiences beyond a few Bohr radii is cancelled by retardation (or, better, vacuum fluctuation) effects.

The power-dependent Bloch-Siegert effect has been observed in the Ramsey separated-oscillatory-field technique using slow neutrons. The variation of the shift with oscillatory power shows good agreement with previously determined theory. It should be noted that the explicit form of the shift in the Ramsey technique is quite different from that predicted for the simple Bloch-Siegert effect.