It is shown that a cholesteric liquid crystal, between parallel confining plates of spacing $2L$, prepared in the "storage mode" (helix axis parallel to plates) undergoes a transition to the nematic state when $L$ is decreased to a critical value $L_c$. For $0<\mathrm{}\frac{(L-L_c)}{L_c}\ll 1$ the pitch of the cholesteric helix diverges as $\ln (L-L_c)$.

Fluctuation phenomena occurring in a system of 216 water molecules, studied by molecular dynamics at 1 g ${\mathrm{cm}}^{-3\mathrm{}}$ and 10 °C, indicate that (i) transverse currents persist in the form of propagating collective coordinates even for a wavelength of about 20 Å, with indications that the same will happen for much longer wavelengths. The velocity of propagation is 1.05 × ${10}^5$ cm ${\sec }^{-1\mathrm{}}$. In the region of 20 Å the lifetime of the fluctuation appears to increase linearly with increasing wavelength. (ii) Density fluctuations at 20 Å are found to be propagating but only marginally; the corresponding velocity of sound is 1.8 × ${10}^5$ cm ${\sec }^{-1\mathrm{}}$. (iii) The spectrum of density fluctuations exhibits a secondary maximum at a much higher frequency than the normal frequency of sound propagation and it is suggested that experiments should be directed to the region of this "high-frequency sound."

A method is presented for calculating the pair-correlation functions for a high-density quantum-mechanical plasma of protons and electrons. The Slater sum is approximated in the form of a classical Boltzmann factor with the Coulomb potentials replaced by effective potentials. The effective potentials contain the classical potential plus quantum corrections. The quantum effects may be separated into symmetry effects, diffraction effects, and coupling between the two. This method is exact at infinite temperatures and is tested here down to temperatures at which there is about 40% ionization. The pair-correlation functions are obtained from a Monte Carlo calculation. The fraction of electrons in the ground state of an atom is also calculated; an approximate formula for this fraction is $\left(\frac{1}{2}\right)[1-\mathrm{erf}(\frac{b\ln T}{T_0}\left)\right]$, where $b$ and $T_0$ are simple fitted functions of the density.

A light-scattering investigation of Brownian motion in the critical mixture nitroethane-isooctane is reported, along with a theory to explain the results. The diffusion constant of $0.3-\mu$ Teflon particles was measured by autocorrelation spectroscopy, at various values of scattering wave vector $\overrightarrow{\mathrm{K}}$. The experimental results exhibit a $K$ dependence stronger than can be accounted for by a simple dynamic scaling approach to the shear viscosity. The theory presented takes into account the nonlocality of the shear viscosity and its effect on the diffusion of small material particles. In addition, we develop a theory to explain the effect of a specific interaction between the particles and the two fluid components. Defining an effective viscosity as ${\eta }_{\mathrm{eff}}\equiv \frac{k_{B}T}{6\pi \mathrm{RD}}$, where $D$ is the diffusion coefficient, the theoretical results may be expressed as ${\eta }_{\mathrm{eff}}=\eta \left({\xi }_1\right)+G{\alpha }^2{\xi }_2^2[\frac{1}{2}-(\frac{R}{{\xi }_2}\left)K_1\right(\frac{2R}{{\xi }_2}\left)\right]$, ${\xi }_1^{-2\mathrm{}}\equiv {\mathrm{}(0.94R)\mathrm{}}^{-2\mathrm{}}+{\xi }^{-2\mathrm{}}+a^2{K}^2$, ${\xi }_2^{-2\mathrm{}}\equiv B\alpha +{\xi }^{-2\mathrm{}}+a^2{K}^2$, where $\eta \left(\xi \right)$ is the viscosity expressed as a function of the correlation length $\xi$, $a$ is the dynamic scaling parameter ($a=1.12\mathrm{}\pm 0.1$), and $K_1\mathrm{}\left(x\right)\mathrm{}$ is the Bessel function of imaginary argument. The parameters $G$ and $B$ are nonadjustable and depend on the particle size $R$, the intermolecular spacing, and the Ornstein-Zernike parameter. The parameter $\alpha$ is a measure of the surface interaction between the particles and the fluids. The resulting expression fits the data within the experimental error of 1%.

The relaxation rate, resulting from the order-director fluctuation, of the dipolar energy of benzene proton-spin pairs in a liquid crystal was calculated. For this mechanism the ratio $\frac{T_1}{T_{1D}}$ is 3. Proton-spin-lattice relaxation times, $T_1$, $T_{1X}$, and $T_{1D}$, as well as the transverse and longitudinal magnetization, were measured in the liquid crystals para-octyloxybenzoic acid and para-azoxyanisole (PAA). Since the spins on one liquid-crystal molecule are isolated from spins on other molecules, each molecule represents an independent small ensemble. Although the macroscopic thermodynamics applies to a large sample of these small ensembles, the spin-temperature concept should only be applied to such systems with care. In both liquid crystals, the spin-relaxation processes were analyzed using the concept of spin temperature. It is shown that in PAA the relaxation of Zeeman energy in the rotating frame is influenced by the proton-to-nitrogen relaxation.

A detailed theory of traveling-wave electronic Raman lasers is constructed, which applies in particular to the spin-flip Raman lasers of Patel and others. Ten equations are set up describing explicitly the behavior of the Stokes field, the anti-Stokes field, the input laser field, and the electronic system. Solutions of these equations are obtained in the sinusoidal steady-state limit. Depletion of the input laser field is accounted for in an approximate but novel fashion in the form of photon-number conservation. We are able to express the steady-state output power in terms of the system parameters and the boundary pump excitation alone. Analytic formulas are given for the linear gain, the threshold pump power, and the Stokes as well as the anti-Stokes power output. They describe, among other things, the saturation and fluorescence behavior of the electronic Raman laser. Various intuitive interpretations are provided for the analytical results. Our detailed predictions are in good agreement with experiments.

It is shown that the critical indices corresponding to (0, $l$ perturbations can be calculated by a Feynman-diagram method. At order ${\epsilon }^2$, the results are consistent with the special cases $l=1,2, \mathrm{and} 4$ obtained previously. There is also general agreement to order $\epsilon$ with the exponents calculated from Wilson's recurrence relation.

Atomic form factors and incoherent scattering functions for boron and singly ionized carbon have been calculated with analytic Hartree-Fock (HF) wave functions and with configuration-interaction (CI) wave functions containing up to 35 terms. Agreement between values of the form factor obtained with the HF wave functions and the largest CI wave functions is to within 0.5%. Values of the incoherent scattering function calculated with the HF wave function differ from the CI values by as much as 27% for boron and 31% for singly ionized carbon.

The recent theoretical results of Kroll and Watson concerning charged-particle scattering in the presence of an intense electromagnetic wave are rederived by using the solution of the Schrödinger equation of a charged particle coupled to a plane-wave electromagnetic field in the dipole approximation and by utilizing the Born approximation.

The energy dependence in interatomic potentials is shown to be expressible as angular momentum dependence of the potential. This means that a potential determined by scattering for a given partial wave can also be used to analyze the question of the existence of a bound state in the same partial wave. This procedure is not available for the problem of the existence of ${\mathrm{He}}_2$ because of the lack of experimental data. However, it is shown that scattering experiments of He + He have been done at sufficiently low energy so that the extrapolation of the potential in energy necessitated by its energy dependence is too small to affect the existence of the bound state.

Previous semiempirical determinations by Fitzsimmons et al. of the asymptotic form of the potentials $V_g$ and $V_u$ for the helium molecular states ${}_{}{}^3{}_{}{}^{}\Sigma _{g,u}^{+}{}_{}{}^{}$ are refined to include new experimental data. The resulting potentials yield cross sections for elastic scattering, diffusion, and metastability exchange in $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)-\mathrm{H}\mathrm{e}\left(1\mathrm{}{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)$ collisions in agreement with various experiments from 15 to 500 °K.

The collisional-excitation method is used to excite autodetaching states of ${\mathrm{Br}}^{-}$ and autoionizing states of Br. The autodetaching states are identified as $4p^4\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)5\mathrm{}{s}^2$, $4p^4({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ or ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{})5\mathrm{}{s}^2$, and $4p^4\left({}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}\right)5\mathrm{}{s}^2$. The autoionizing states are assigned inner-shell-excited configurations: $4s4p^5\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)5s$, $5p$, and $4d$, and $4s4p^5\left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)5s$. Other peaks in the electron spectrum may be due to doubly excited states.

The Ne $K$ x-ray spectrum following bombardment by 30-MeV ${\mathrm{O}}^{5+}$ and 35-MeV ${\mathrm{O}}^{6+}$, ${\mathrm{O}}^{7+}$, and ${\mathrm{O}}^{8+}$ beams has been resolved into nine lines corresponding to $K{L}^0$ through $K{L}^7$ transitions. Using a curved-crystal spectrometer, relative intensities for the previously unresolved $K{L}^0$, $K{L}^1$ and $K{L}^2$ transitions have been extracted despite the overlap of the H-like oxygen-beam x rays. For ${\mathrm{O}}^{5+}$ and ${\mathrm{O}}^{7+}$ bombardment, the measured relative intensities of the remaining lines disagree with a previous measurement.

A study of doubly excited Feshbach states of the negative ions of carbon and oxygen has been performed using the method of configuration interaction. Dominant two-particle excitations considered include $2p^2\to 3s^2$, $3s3p$, $3p^2$, and $4s^2$ for both ${\mathrm{C}}^{-}$ and ${\mathrm{O}}^{-}$ systems. Four states of ${\mathrm{C}}^{-}$ and twelve states of ${\mathrm{O}}^{-}$ have been located. No experimental results are as yet available for ${\mathrm{C}}^{-}$. Six of the states of ${\mathrm{O}}^{-}$ reported here have been detected experimentally.

In view of further determination of shielded homonuclear and heteronuclear diatomic orbitals, the problem of one electron in the field of two fixed nuclei and a cylindrically symmetric parametric potential is investigated. The simultaneous resolution of the separated equations, in prolate-spheroidal coordinates, is performed by a matricial technique using a Newton-Raphson scheme; as the orbitals are expanded in terms of orthogonal functions only symmetric band matrices are involved. Calculation of monoelectronic and bielectronic integrals is described.

The determination of shielded diatomic orbitals (SDO) is investigated from the exact resolution, in prolate-spheroidal coordinates, of the two-center problem with an effective parametric potential. This potential, which is cylindrically symmetric in order to preserve the separability of the Schrödinger equation, is obtained either by classical electrostatic considerations or by a variational procedure. Calculations are carried out for two-electron diatomic systems, i.e., ${\mathrm{H}}_2$, $\mathrm{He}_2^{}{}_{}{}^{2+}$, and He${\mathrm{H}}^{+}$ in their ground state. From the results and also from theoretical considerations, these SDO appear to be close to self-consistent-field orbitals. Extension to the $N$-electron problem is considered.

We present the first observations of resonant states in atomic oxygen using an electron-impact technique. We verify the existence of several doublet resonant states located previously by other techniques, and observe for the first time resonant states whose multiplicity is different from that of the ground state of ${\mathrm{O}}^{-}$. To one such state located at 8.80 eV we assign the configuration [$2p^3\left({}_{}{}^4{}_{}{}^{}S\right)3\mathrm{}{s}^2\left({}_{}{}^4{}_{}{}^{}S\right)$] and to another at 14.06 eV we assign the configuration [$2p^3\left({}_{}{}^2{}_{}{}^{}D\right)3\mathrm{}{p}^2$].