A large-amplitude high-frequency modulated wave launched by an external source significantly changes the plasma equilibrium. The adiabatic Vlasov distribution function of the electrons is found for one-dimensional initial-and boundary-value problems. The nonlinear dispersion relation is derived to all orders in the electric-field amplitude. A new nonlinear mode below the electron plasma frequency exists. In this state the plasma is described by a double-humped distribution function.

The correlated-basis-functions method of Feenberg and the coupled-cluster formalism of Coester and Kümmel are joined to form a new ground-state many-body method combining the advantages of both older methods and avoiding their disadvantages. From the point of view of the correlated-basis-functions method, coupled-cluster theory is used to sum the perturbation series partially to arbitrary order. From the point of view of the coupled-cluster method, correlated basis functions are used to take out the repulsive core of the two-body interaction in order to allow more efficient truncation schemes. It is found that powerful renormalizations are possible. Explicit equations are given for the two-body subsystems embodying generalized Bethe-Goldstone and random-phase equations summing, in the correlated basis, ladder and ring diagrams to arbitrary order.

The shear viscosities and surface tension of a liquid crystal CBOOA (cyanobenzylidene octyloxyaniline) were measured by the use of the technique of generating and detecting surface waves (capillary waves) developed by the authors. For the wave propagation perpendicular to the direction, the surface tension $\sigma$ decreased sharply upon entering into the smectic-$A$ phase. When the waves propagate parallel to the director, the attenuation due to the diverging viscosity ${\eta }_3$ near the nematic to smectic-$A$ transition became so large that measurements in the smectic phase were not possible. The viscosity ${\eta }_3$ was found to diverge as ${(T-T_c)}^{-\nu }$, where $\nu =1.0\mathrm{}\pm 0.1$ at 200 Hz and $\nu =0.83\mathrm{}\pm 0.15$ at 400 Hz.

The Navier-Stokes equations for incompressible and compressible fluids are generalized by inclusion of viscous stress relaxation, as required by kinetic theory. Two initial-boundary-value problems of the nonlinear generalized Navier-Stokes equations are solved analytically, which describe the propagation of transverse or shear waves due to temporal and spatial velocity pulses $\overrightarrow{\mathrm{v}}\mathrm{}(0,t)\mathrm{}$ and $\overrightarrow{\mathrm{v}}\mathrm{}(x,0\mathrm{})\mathrm{}$, respectively. It is shown that transverse perturbations propagate in the form of a discontinuous wave with a finite wave speed due to viscous stress relaxation, whereas the conventional Navier-Stokes equations result in nonphysical solutions, suggesting a diffusion process covering the entire fluid with infinite speed.

Following up a new method for solving a many-body Bose gas proposed by Wong and Fung previously, we extend our study to summing all terms relating to the three-body correlation function in the canonical-transformation matrix representation. It was found that only a certain class of interaction potential will allow for an analytic representation of the one-to-one linear transformation matrices. However, the variational method based on construction of the basis correlations does not have such mathematical restriction.

A system with a chemical reaction behaves like a system with a smaller number of components which, in turn, results in growth of the critical indices.

Electromagnetic sawtooth waves, supposedly generated in pulsar environments, have been the subject of numerous publications. These waves are of such magnitude as to drive all plasma particles with relativistic velocities. We show analytically that such waves are subject to fast instabilities that destroy them in a time comparable to the oscillation period. They are stabilized in the presence of a strong magnetic field.

It is proved that the solutions to the Enskog equation for an $N$-component gas enjoy the nice properties that are known in the context of the Boltzmann equation, to indicate its compatibility with thermodynamics, provided some restrictions are imposed on the functions $\chi$. The functions $\chi$ are introduced in the Enskog equation in order to account for correlations among particles.

An Enskog-like kinetic equation for chemically reacting fluids is introduced phenomenologically. It is proved that the suggested dynamical theory is compatible with thermodynamics (it includes the proof of an $H$ theorem) provided one compatibility condition restricting the choice of the phenomenological quantities introduced by the proposed Enskog-like theory is satisfied. This work follows closely the similar discussion in Part I (preceding paper), where the inert fluids were discussed.

The covariant path integral with a quadratic Lagrangian in curved space will be evaluated using a Fourier-series analysis of smooth paths in Riemannian normal coordinates. The present treatment replaces an earlier one.

Misunderstandings concerning earlier work are clarified. The crucial role attributed to noncoincidence of the polarization states of the counterpropagating waves in a saturated gas laser is questioned.

Through analyses of the Monte Carlo data on strongly coupled fluids such as the classical one-component plasma, we demonstrate that the excess internal energy $U$ may be expressed to a good degree of accuracy by a lattice-model formula, $\frac{U}{N{k}_{B}T}=\alpha \Gamma +\frac{3}{2}$, near the crystallization point, where $\Gamma$ is the coupling constant and $\alpha$ takes on a value close to the Madelung constant of the corresponding crystalline lattice.

Five predicted but formerly unlocated energy levels in the $5p^{5}5d$ configuration of Cs II are reported. Transitions involving these new levels and previously known levels allow the classifications of 19 lines in the spectrum of Cs II which have been observed but not classified prior to this time.

The two-photon absorption initiated by two coherent beams is considered. It is shown that the resonance fringe variation, which appeared in the Doppler-free two-photon absorption of pulsed laser beams, can also be observed in absorption with a Doppler shift.

The asymptotic behavior of the coefficients $a_n$ in the expansion of the ground-state energy of the hydrogen molecular ion in terms of the inverse powers of the internuclear separation is found to be $a_n=-(n+1\mathrm{})!2^{-n}{e}^{-2\mathrm{}}[1+2\mathrm{}{n}^{-1\mathrm{}}-20\mathrm{}{n}^{-2\mathrm{}}-45\mathrm{}{n}^{-3\mathrm{}}+O(n^{-4\mathrm{}}\left)\right]$. The first two terms of this numerically obtained expression agree with the "asymptotic conjecture" involving the lowest excitation energy of $\mathrm{H}_2^{}{}_{}{}^{+}$

The wave functions for the hydrogen atom are determined in the momentum representation, using momentum variables $p_r$, $p_{\theta }$, $p_{\phi }$ which are associated with the spherical polar variables $r$, $t(=e^{i\pi cos\theta })$ and $v\left(e^{i\phi }\right)$. The functions may be written as $\left\{{\phi }_{n,l,m}\right(p_r,p_{\theta },p_{\phi })={\alpha }_{n,l}(p_r\left){\beta }_l^m\right(p_{\theta }\left)\delta \right(p_{\phi }+m),\}\left\{{\alpha }_{n,l}\right(p_r)={\left(\frac{n}{i{p}_0}\right)}^{3l+z}\Sigma \stackrel{n-l-1\mathrm{}}{k=0\mathrm{}}\left(\{n-l-1\mathrm{}\}\left\{k\right\}\right)\frac{2^{k-l+1\mathrm{}}}{\mathrm{}(2l+k+1)\mathrm{}(2l+k)\mathrm{}\cdots \mathrm{}(l+k+2\mathrm{})\mathrm{}}{\left(\frac{\frac{i{p}_0}{n}}{p_r-\frac{i{p}_0}{n}}\right)}^{l+k+2\mathrm{}},\}\left\{{\beta }_l^m\right(p_{\theta })=\Sigma \stackrel{E\left(\frac{l}{2}\right)}{j=E\left(\frac{m}{2}\right)}{a_j{p}_{\theta }}^{-\frac{\mathrm{}(m+1\mathrm{})\mathrm{}}{2}}{J}_{\frac{j-(m-1\mathrm{})\mathrm{}}{2}}\left(p_{\theta }\right),\}$ where $\delta$ is the Dirac delta function and $p_0=Z{a}_0^{-1\mathrm{}}$ ($a_0$ is the Bohr radius). $J_{\nu }\left(p_0\right)$ are Bessel functions of integer or half-integer order. The radial functions are shown to have poles up to order $n+1\mathrm{}$ at $p_r=i\frac{p_0}{n}$.

$g_J$-factor corrections for the ground states of the first-row atoms and sodium are calculated by use of spin-extended Hartree-Fock (SEHF) wave functions. The present results are compared with Hartree-Fock values and experimental $g_J$ factors. The theoretical SEHF $g_J$ factors show a deviation from the experimental ones which increase very regularly from lithium to fluorine. these discrepancies are believed to arise from the neglect of correlation effects, and they indicate that the previous success of the Hartree-Fock theory in the cases of oxygen and fluorine is fortuitous. Hartree-Fock values are also presented for the $g_J$-factor corrections of the ground states of the second-row atoms, and for potassium, rubidium, bromine, and iodine.

Radiative corrections generate shifts in the Rydberg levels of "murium," the system composed of an electron bound by its image charge to a plane wall, which are proportional to the fine structure constant $\alpha$; if the wall is perfectly conducting and impenetrable the shift in the ground-state energy is 0.2%, extraordinarily large for a radiative correction. (The difference from the usual hydrogenic Lamb shift, which goes roughly as ${\alpha }^3$, originates in the fact that the vacuum fluctuation fields near the wall differ from those in free space, so that on renormalization the leading terms are not completely canceled.) The absolute shift is greatly reduced for a realistic wall.

The cross sections for the formation of excited ${\mathrm{Mg}}^{+}$ states in 20-500 keV ${\mathrm{Mg}}^{++}$-Mg collisions have been measured by optical spectrometry in order to test the validity of the model proposed by Horsdal-Pedersen et al. Phys. Rev. Lett. 41, 1541 (1978) to explain a pronounced structure in the experimental cross section for resonant double-charge transfer in ${\mathrm{Mg}}^{++}$-Mg collisions. The present ${\mathrm{Mg}}^{+}3p$-formation cross sections support the basic assumption in the model, that the interaction between two molecular states, separating into the atomic configurations ${\mathrm{Mg}}^{++}-\mathrm{M}\mathrm{g}3s^2$ and ${\mathrm{Mg}}^{+}3p-{\mathrm{Mg}}^{+}3s$ at large intermolecular distances, plays a dominant role in the collision. An extended version of the model is needed to account for the observed formation of ${\mathrm{Mg}}^{+}3d$ and ${\mathrm{Mg}}^{+}4s$ states, the population of the ${\mathrm{Mg}}^{+}3p$ state from the projectile and target, separately, and the polarization of the ${\mathrm{Mg}}^{+}(3p\to 3s)$ emission.