The energy, wave function, and radial parameters of the low-lying triply excited resonances of the lithium atom are calculated using a saddle-point technique. A total of eleven resonances with ${}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{},{}_{}{}^4{}_{}{}^{}P_{}^e{}_{}{}^{},{}_{}{}^2{}_{}{}^{}D_{}^e{}_{}{}^{},{}_{}{}^2{}_{}{}^{}S_{}^e{}_{}{}^{},{}_{}{}^2{}_{}{}^{}P_{}^e{}_{}{}^{}$, and ${}_{}{}^2{}_{}{}^{}D_{}^o{}_{}{}^{}$ symmetries are investigated. These results are used to identify the observed Auger spectra of Rødbro, Bruch, and Bisgaard. If the identifications suggested here are correct, then the agreement between the results of the present work with those of the experiment is excellent. The oscillator strengths and transition energies of these resonances in an optical absorption or emission process are calculated. In order to compute these oscillator strengths, the energies and wave functions of the Li $1s2s2p{}_{}{}^4{}_{}{}^{}P,1s2p2p{}_{}{}^2{}_{}{}^{}P$, and $1s2s2s{}_{}{}^2{}_{}{}^{}S$ states are also tabulated. The energies of the two bound states agree to within 0.013 eV with the highly accurate results in the literature. The result for the ${}_{}{}^2{}_{}{}^{}S$ resonance agrees with the more recent experiments and lies well within the quoted experimental error.

This paper deals with the strongly nonlinear regime of the atom and field interaction which arises for both high cw input intensities and large absorption. The intensity of the light inside the medium is then highly nonlinear with respect to the incident one, the order of magnitude of the nonlinearity being approximately $\alpha 1$, for a cell of length $l$ and an absorption length ${\alpha }^{-1\mathrm{}}$. The transverse effects related to such a regime are analytically treated. They are shown to induce self-focusing, blooming, and also spatial ringing. These features strongly depend on the distance of the screen from the cell, on the detuning between the incident wavelength and that of the atomic transition, and on the input intensity. For self-focusing, analytical expressions of the focal point, of the waist, and of the maximum intensity are given. This model for transverse effects in strong nonlinear propagation of pulses would contribute to explain recent anomalous observations.

The two-photon process with continuum intermediate states is investigated. The line shape is found to be a singlet rather than a doublet as in the case of discrete intermediates (Autler-Townes doublet). The ionization line shape is a doublet and exhibits oscillations as a result of the coherence and the interference between the yields from the initial and final states.

In strongly coupled, degenerate plasmas, the electron collision frequency has been described by the Ziman formula with the ion-ion correlations modeled by the classical one-component plasma (OCP). However, this model fails to reproduce the correct quantum Lenard-Balescu result in the weak-coupling limit. It is demonstrated here that a recently obtained correlation-function expression for the collision frequency reduces to the Ziman and Lenard-Balescu results in the appropriate limits. In addition, it is shown that an extension of the Lenard-Balescu result to include strong coupling can be interpreted as the Ziman collision frequency with the OCP structure factor replaced by the ion-ion structure factor for a two-component system. Numerical estimates of this structure factor are used to calculate the electrical conductivity in moderately coupled ($\Gamma \le 2$) hydrogen plasmas.

We evaluate the low-frequency-component microfield distribution for a one-component classical gas of ions interacting through an effective potential. The screening of the ions is a way to account approximately for the effect of the electrons. In this paper the ion-ion effective interaction is calculated by a quantum-mechanical treatment of the electrons. We compare our results for the low-frequency microfield distributions with theories using a classical Debye-Hückel treatment of the electron screening of the ions.

We present a theoretical treatment of optical-field-induced molecular reorientations and quantitative experimental verifications of the associated nonlinear-optical processes in the nematic phase of liquid crystals. Explicit analytic expressions are obtained in the small-angle linearized approximation of the Euler-Lagrange equation describing the molecular reorientation. It is found that optical-field strengths much lower than the so-called optical Freedericksz transition threshold can create substantial molecular reorientations and generate easily observable nonlinear-optical effects such as self-focusing and degenerate four-wave mixings. The theoretically predicted dependences on the scattering geometry, the optical intensities, and the nematic thicknesses are in excellent agreement with experimental data. The relative contribution of thermal effect is also determined.

X rays from 1 to 25 keV emitted by the Alcator $A$ device have been collected with a Si(Li) detector and pulse-height-analysis system. Under normal operating conditions, spectra are thermal, indicating clean ($Z_{\mathrm{eff}}\sim 1$), Maxwellian distributions. Temperature profiles are provided. When $\frac{v_d}{v_{\mathrm{th}}}\gtrsim 0.03$, the x-ray spectra become nonthermal, reflective of non-Maxwellian distributions. The observed nonthermal behavior increases with minor radius and poloidal symmetry, is correlated with poor energy confinement, and cannot be accounted for by classical electric-field-driven perturbation theory. Radial electron diffusion is discussed.

A recursive method is described for generating the Helmholtz free energy and paircorrelation function of a nonuniform fluid, in powers of the Kac inverse-range parameter $\gamma$. The results agree with earlier calculations using graphical and functional-integral methods. The ordering of the free energy is functionally consistent with a similar ordering of the density profile. The lowest-order or "van der Waals" theory is equivalent to a mean-field average of the attractive intermolecular energies and use of local thermodynamics in a reference hard-sphere fluid. The next level of approximation is the "random-phase approximation," which is shown to produce logarithmic anomalies in the free energy and density profile similar to those expected on the basis of capillary-wave theory. The occurrence of these anomalies results from the existence of a longwavelength divergence in the transverse Fourier transform of the lowest-order paircorrelation function.

A Hamiltonian system of nonlinear dispersive waves is used as a basis for generalizing the test-wave model to a set of resonantly interacting waves. The resonant test field (RTF) is shown to obey a nonlinear generalized Langevin equation in general. In the Markov limit a Fokker-Planck equation is obtained and the exact steady-state solution is determined. An algebraic expression for the power spectral density is obtained in terms of the number of resonantly interacting waves ($n$) in the RTF, the interaction strength ($V_k$), and the dimensionality of the wave field ($d$). For gravity waves on the ocean surface a $k^{-4\mathrm{}}$ spectrum is obtained, and for capillary waves a $k^{-8\mathrm{}}$ spectrum, both of which are in essential agreement with data.

Nonlinear corrections to the density-density correlation function are calculated for a nonturbulent fluid subjected to both a temperature gradient and a shear flow. Linear corrections vanish in the chosen geometry.

It is suggested that the interface free energy between bulk phases with a macroscopically flat interface can be estimated from the variation of certain probability distribution functions of finite blocks with block size. For a liquid-gas system the probability distribution of the density would have to be used. The method is particularly suitable for the critical region where other methods are hard to apply. As a test case, the two-dimensional lattice-gas model is treated and it is shown that already, from rather small blocks, one obtains results consistent with the exact solution of Onsager for the surface tension, by performing appropriate extrapolations. The surface tension of the three-dimensional lattice-gas model is also estimated and found to be reasonably consistent with the expected critical behavior. The universal amplitude of the surface tension of fluids near their critical point is estimated and shown to be in significantly better agreement with experimental data than the results of Fisk and Widom and the first-order $4-d$ renormalization-group expansion. Also the universal amplitude ratio used in nucleation theory near the critical point is estimated.

A study is made of a series-expansion procedure which gives the leading terms of the $n$-particle distribution function $p^{\mathrm{}\left(n\right)\mathrm{}}(1,2,\dots ,n)$ as explicit functionals in the radial distribution function $g\left(r\right)\mathrm{}$. The development of the series is based on the cluster-expansion formalism applied to the Abe form for $p^{\mathrm{}\left(n\right)\mathrm{}}$ expressed as a product of the generalized Kirkwood superposition approximation $p_K^{\mathrm{}\left(n\right)\mathrm{}}$ and a correction factor $\exp \left[A^{\mathrm{}\left(n\right)\mathrm{}}\right(1,2,\dots ,n\left)\right]$. An ordering parameter $\mu$ is introduced to determine $A^{\mathrm{}\left(n\right)\mathrm{}}$ and $p^{\mathrm{}\left(n\right)\mathrm{}}$ in the form of infinite power series in $\mu$, and the postulate of minimal complexity is employed to eliminate an infinite number of possible classes of solutions in a sequential relation connecting $A^{\mathrm{}(n-1\mathrm{})\mathrm{}}$ and $A^{\mathrm{}\left(n\right)\mathrm{}}$. Derivation of the series for $p^{\mathrm{}\left(n\right)\mathrm{}}$ and many other algebraic manipulations involving a large number of cluster integrals are greatly simplified by the use of a scheme which groups together all cluster terms having, in a certain way, the same source term. In particular, the scheme is useful in demonstrating that the nature of the series structure of $p^{\mathrm{}\left(3\right)\mathrm{}}$ is such that its three-point Fourier transform $S^{\mathrm{}\left(3\right)\mathrm{}}({\overrightarrow{\mathrm{k}}}_1,{\overrightarrow{\mathrm{k}}}_2,{\overrightarrow{\mathrm{k}}}_3)$ has as a factor the product of the three liquid-structure functions $S\left(k_1\right)S\left(k_2\right)S\left(k_3\right)$. The results obtained to order ${\mu }^4$ for $A^{\mathrm{}\left(3\right)\mathrm{}},p^{\mathrm{}\left(3\right)\mathrm{}}$, and $S^{\mathrm{}\left(3\right)\mathrm{}}$ agree with those derived earlier in a more straightforward but tedious approach. The result for $p^{\mathrm{}\left(4\right)\mathrm{}}$ shows that the convolution approximation $p_c^{\mathrm{}\left(4\right)\mathrm{}}$, which contains ${\mu }^3$ terms, must be supplemented by a correction of $O\left({\mu }^3\right)$ in order to be accurate through third order. The $\mu$-expansion approach is also examined for the cluster expansion of the correlation function in the Bijl-Dingle-Jastrow description of a manyboson system, and then compared with the number-density expansion formula by using the Gaussian model for $g\left(r\right)-1\mathrm{}$ to evaluate cluster integrals. A testing procedure based on the requirement $p^{\mathrm{}\left(3\right)\mathrm{}}\mathrm{}(1,2,2)=0\mathrm{}$ is developed to study accuracy of the $\mu$-ordered approximations for $p^{\mathrm{}\left(3\right)\mathrm{}}$. Numerical results obtained to orders ${\mu }^2,{\mu }^3$, and ${\mu }^4$ with the Gaussian model indicate substantial improvements with each increase in the order of truncation in the power series of $p^{\mathrm{}\left(3\right)\mathrm{}}$. A brief discussion is presented concerning the asymptotic behavior of $g\left(r\right)\mathrm{}$ in the context of equilibrium statistical mechanics.

A class of exactly solvable nonlinear stochastic models with multiplicative Gaussian white noise is here solved by a method of linear imbedding. The models describe a continuous instability with fluctuations of the bifurcation parameter. The method of solution is a generalization of an idea, originally introduced by Carleman for the solution of deterministic rate equations. Our application of this method to the stochastic models studied here provides further insight into the applicability of the method. The solutions we find are compared with results, which have been obtained earlier by Fokker-Planck methods. Complete agreement with the Fokker-Planck results is found, contrary to recent claims by Brenig and Banai and also in disagreement with recent results of Suzuki et al. The method presented here also allows us, for the first time, to obtain solutions in a domain of parameter space where the Fokker-Planck equation has not been solved as yet.

The force acting on a Clausius-Mossotti fluid in an electromagnetic field is evaluated microscopically. Owing to the modification of the two-particle density by the electric field, an additional mechanical force $\Delta {\overrightarrow{\mathrm{f}}}^{\mathrm{}\left(M\right)\mathrm{}}$ is found. When this is added to the electrical force ${\overrightarrow{\mathrm{f}}}^{\mathrm{}\left(E\right)\mathrm{}}$, the total force in the static case becomes identical to that deduced macroscopically by Helmholtz. The analysis is extended to various time-dependent cases, and it is pointed out that $\Delta {\overrightarrow{\mathrm{f}}}^{\mathrm{}\left(M\right)\mathrm{}}$ essentially assumes its static value on time scales longer than $T_c$, the relaxation time of the two-particle density, but is otherwise negligibly small. Thus Peierls's theory of the momentum of light is valid only for pulses much shorter than $T_c$; the necessary correction due to $\Delta {\overrightarrow{\mathrm{f}}}^{\mathrm{}\left(M\right)\mathrm{}}$ in other cases is given and discussed.

The validity of three approximate treatments of the exchange interaction in low-energy $e-{\mathrm{CO}}_2$ scattering is assessed by comparing approximate and exact static-exchange eigenphase sums in the resonant ${\Pi }_u$ symmetry and the nonresonant ${\Sigma }_g$ and ${\Sigma }_u$ symmetries. Of the approximations studied—orthogonalized static, free-electron-gas model potential, and orthogonalized model potential—the latter has yielded results in best agreement with those of the exact treatment of exchange. Newly calculated static-exchange-polarization cross sections for energies from 0.1 to 2.0 eV are presented.

The use of some further simplifications in the usual impulse-approximation scheme provides a simple computational method for the evaluation of ejected-electron cross sections. Except for very low energies of incoming and ejected electrons, our treatment also exhibits the usefulness of Compton profiles for the description of ejected electrons. As an illustration, the case of helium has been investigated here. The proposed treatment appears to give a standard representation for the comparison of a whole set of previous experimental and theoretical results.

The vortex viscosity of a model diatomic fluid is calculated using both equilibrium and nonequilibrium molecular dynamics. The two calculations agree within statistical uncertainties. The results show that vortex viscosity does not have a conventional Kubo-Green relation. An argument as to why this is so is presented.

An error in an old but often quoted paper by Bethe on the cross section for an atomic transition caused by the magnetic moment of the projectile is corrected by comparing it with the generalized Rosenbluth's formula.

Measurements have been made of total cross sections for the scattering of electrons by lithium-diatomic molecules over the electron energy range 0.5 - 10 eV, with the use of the molecular-beam recoil technique. The total cross sections in units of ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ are 541 (0.5 eV), 307 (1 eV), 199 (2 eV), 160 (3 eV), 135 (6 eV), and 100 (10 eV). The uncertainty in these results is ± 16%.

We have evaluated numerically the first-order terms in the $h$-bond expansion for triplet correlations as given by Abe for Lennard-Jones fluids using a technique developed by Barker and Monaghan. Results are obtained for a range of fluid densities and comparisons are made to data obtained through Monte Carlo simulations by Raveche, Mountain, and Streett. These comparisons indicate that the first-order term is inadequate near and beyond the triple point of the system.