We show that with some weak assumptions molecular expressions for Frank elastic constants of nematics, containing the direct correlation function, are equivalent to such expressions obtained from the theory of hydrodynamic fluctuations.

We present and discuss representative dynamical-correlation functions of the variables of the Lorenz model. The chaotic properties correspond to the asymptotic decay of the time correlations. The global features of the corresponding spectra can be explained by calculating a memory representation, in particular, by summing the continued fraction to infinite order. Details of the spectra can be understood only in part, even if a resonant mode is coupled by standard procedures. Interesting open questions about the statistical physics of and its applicability to this pseudostochastic system remain.

In view of the importance of the equivalence between the prior-interaction and post-interaction forms for the validity of distorted-wave Born-approximation (DWBA) studies in reactive scattering, we present a comparison study between the two forms by illustrating a reactive atom — diatomic-molecule system. Our DWBA method presented earlier is found to satisfy the condition of the equivalence remarkably well.

We discuss the extension of the Lewis-Riesenfeld technique of solving the time-dependent Schrödinger equation to cases where the invariant has continuous eigenvalues. The extension is carried out for a general Ermakov system. We also discuss extensions to $N$-dimensional systems and the calculation of the propagator for a general Ermakov system.

Previously published theoretical formulas for the mean wavelengths and spectral widths of unresolved transition arrays are applied to transitions of the types $3d^{N+1\mathrm{}}-3\mathrm{}{d}^{N}4p$ and $3d^{N+1\mathrm{}}-3\mathrm{}{d}^{N}4f$ observed in highly ionized spectra of Mo and Pd. Agreement with experiment is excellent and opens the way to the quantitative interpretation of the intensities.

The three-center atomic expansion method for ion-atom collisions first described by Anderson et al. (1974) is reexamined and applied to a broader energy range to study the role of united-atom orbitals in a close collision. In this method the electronic wave function is expanded in terms of traveling atomic orbitals around the two moving centers as well as united-atom orbitals around the center of charge. For the symmetric resonant ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collision, it is found that electron-capture probabilities at small impact parameters are changed substantially with the addition of united-atom orbitals at the third center for low-velocity collisions ($v\le 0.5$), whereas there is almost no such change at higher velocities ($v\sim 1$). This illustrates the velocity range in which the relaxation of electronic orbitals occurs toward the united-atom orbitals in a close collision and implies the velocity range where an adiabatic molecular-orbital expansion becomes inappropriate.

Recently, a new Thomas-Fermi model was proposed that attempts to better describe the outer regions of the atom. We here report a test of the new model, a calculation of the diamagnetic susceptibilities of the inert gases. Although the results of the new theory are considerably better than those of the Thomas-Fermi model, the predictions are still significantly in excess of the experimental values.

Numerical stabilization procedures are developed for solving the coupled integral equations that arise in connection with the separable treatment of exchange interactions in electron-molecule scattering. Stabilization is important for maintaining numerical accuracy in treating target molecules that produce strong-coupling potentials, especially at low collision energies. The techniques we have developed are reliable and do not add significantly to the computation times.

It is shown that the general form of the longitudinal correlation function $f$ implies the fluctuation-dissipation relation ${\left(\frac{\delta K}{\delta f}\right)}_{f=1\mathrm{}}=\frac{4}{9}B[1+(0.13507\left)\mathrm{}\ln B\right]\epsilon$, where $K$ is the inertial-transfer term in the Kármán-Howarth equation, $B$ is the quasiconstant "broadness" parameter, and $\epsilon$ is the time-dependent dissipation rate. This result suggests that Kolmogorov scaling can only be "universal" to within dimensionless factors that depend on $B$.

The $K$-shell ionization cross section for Hg by electron impact has been calculated in the nonrelativistic and relativistic plane-wave Born approximations. The latter is calculated both with a Coulomb and a Møller interaction. The investigation indicates that it is important to incorporate both relativistic dynamics and the Møller interaction in the treatment at incident energies greater than a few times the ionization energy. In addition, a calculation for Au has been performed to illustrate the difference in the calculation of the cross sections for Au and Hg targets. These calculations have been compared with experimental data for Au.

An earlier result of the expansion of hydrogenic wave functions is generalized.

The theory of electron transport in semiconductors has been used by Paranjape to discuss the drift velocities of electrons in gases, especially the onset of nonlinear dependence on field strength. The same problems are here discussed in terms of existing gas theory, and apply to ions as well as electrons. The effect of inelastic collisions is stated more explicitly, in terms of a ratio of thermally averaged cross sections.

Acoustic surface waves can be generated along the plasma column in pressure equilibrium with a gas blanket in the presence of the uniform axial magnetic field. Unlike the case of volume-acoustic-wave generation in the magnetoplasma reported recently, the threshold magnetic field required for the generation of acoustic surface waves increases with increasing gas pressure.

Recombination and impurity attachment in liquid argon have been separated using a gridded ionization detector with adjustable cathode to grid distance. Recombination effects with an electron source and an $\alpha$ source were studied in the range 0.07 to 10 kV/cm. In contradiction to other recent results, our data do not support geminate recombination theory.

The phenomenal accuracies achieved for the spectroscopy of single charged particles suspended in Penning traps has prompted this study of the imperfect Penning trap. The principal result is a new prescription for the cyclotron frequency in terms of the observable eigenfrequencies of the imperfect trap. The new prescription is completely insensitive to a misalignment of the magnetic field direction with the axis of the Penning electrodes, and it is also insensitive to the most significant imperfections in the electrostatic potential. These systematic effects can therefore be completely circumvented in measurements of the anomalous magnetic moments of the electron and positron, and also in experiments on protons and heavier ions where the effects are much larger.

Isotope shifts of even Ba isotopes in transitions to $6sns{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and $6snd{}_{}{}^{1,3}{}_{}{}^{}D_2^{}{}_{}{}^{}$ Rydberg states have been used to study systematically the change in electron density at the nucleus. For $n>~11$ the total charge density at the origin approaches that of ${\mathrm{Ba}}^{+}$. Local perturbers strongly effect the electron density, and admixture coefficients can be derived which are in quantitative agreement with those from multichannel quantum defect theory.

Resonant four-wave mixing in coupled three-level systems is theoretically studied including high pump-field intensities. A new destructive interference between two contributions to the optical coherent response of the atomic system, leading to total signal cancellation at the onset of the Rabi regime, is predicted.