Deuterium NMR spectra from a set of cholesteric materials differing in pitch length have been interpreted in terms of a biaxial ordering of the molecules. It is found that, in these materials, the biaxiality in the cholesteric phase is a universal function of the reduced temperature (independent of pitch length) only when there is a blue phase present in the material. In contrast, when the cholesteric phase transforms directly into the isotropic phase without the presence of a blue phase the biaxiality on a reduced-temperature plot is strongly pitch-length dependent. By the study of different deuterated sites of the same molecule, the mechanism for biaxiality is examined. Deuterium NMR spectra are also used to measure the pitch dependence of the self-diffusion constant. Finally, the NMR technique of measuring biaxiality in the cholesteric phase is discussed and a critique made. The materials used in the study were selectively deuterated 4-methoxybenzylidene-4′-butylaniline (MBBA) twisted by the addition of chiral 4-methoxybenzylidene-4′-[(+)-2-methylbutyl]aniline (MBMBA) in various weight percentages to obtain samples of different pitch lengths.

We study by computer simulation the behavior at low energy of a two-dimensional Lennard-Jones system. The dynamics of the system are analyzed by computing the mean value of the energies of the normal modes, their autocorrelation and cross-correlation functions, and their Fourier spectra. When the energy is lowered the system undergoes a stochastic transition, made evident by qualitative changes occurring in the dynamics. The autocorrelation functions exhibit a twofold behavior: a rapid exponential-like decay which dominates at high energy and a slow decay which dominates at low energy. The Fourier spectrum appears to be continuous at high energy and becomes discrete at low energy. At the lowest energy considered by us, normal modes no longer exhibit a trend toward energy equipartition, at least within the times of our simulation; this fact is due to the onset of selection rules for the energy exchanges among modes. These phenomena occur in a physically significant energy range. For the sake of comparison we have performed a similar analysis on the Hénon-Heiles model, obtaining a relevant concordance.

With the use of the two-particle distribution function calculated in a preceding paper, some thermodynamic functions (energy, free energy, pressure, specific heat, compressibility, and the speed of sound) are calculated for a two-component, classical dilute, and slightly relativistic plasma up to order $\frac{\mathrm{kT}}{{\mathrm{mc}}^2}$. The results are discussed and compared with previous work of other authors.

A generalized mean-field theory, incorporating the "classical" mean-field theories but having a richer structure, is formulated. Thermodynamic consistency is established for this generalized theory. As an application of the formalism, a treatment of coupled orientational and translational order-disorder transitions is presented, resulting in self-consistency equations requiring no numerical integration but exhibiting the essential features of the isotropic-nematic-smectic transitions in liquid crystals.

Detailed experimental investigations are performed on the oblique collision of plane ion-acoustic solitons in a double-plasma-type plasma device. Many of the observed phenomena of inelastic collisions of solitons are found to be similar to those of resonance interactions described by nonlinear ion-acoustic waves, and the virtual states produced after the interaction are well defined.

When the two-particle periodic Toda lattice is perturbed by a time-dependent external field, we find that the external field creates resonance zones in the phase space of the Toda lattice. These resonance zones cause the energy of the lattice to undergo large fluctuations. Interaction of resonance zones causes the motion of the Toda lattice to become "chaotic." A theory is developed which describes the emergence of resonance zones for a small-amplitude applied field. Computer studies are presented which verify this theory.

Variational perturbation calculations with various soft inverse-power potentials as reference demonstrate that the equation of state (EOS) for a wide variety of physically conceivable pair potentials, in the strong-coupling (dense-fluid) regime, may be characterized by a universal scaled pair distribution function of the form $g(r{\rho }^{\frac{1}{3}},\frac{s^E}{N{k}_B})$. This universality, which has been already conjectured by the examination of various applications of the hard-sphere perturbation theory, is equivalent to a statement of additivity of EOS's if the density $\rho$ and the excess entropy $s^E$ serve as the independent variables. With the use of "additivity" with the inverse powers as the basis set of potentials, simple conditions for the validity of a Grüneisen-type scaling EOS are obtained, based on general features of the effective pair potential for the material.

The general theory of nuclear-spin relaxation induced by translational self-diffusion in liquid crystals, developed in previous papers, is applied to the crystalline-$B$ and hexatic-$B$ phases of smectics by taking into account their characteristic features concerning molecular positional ordering, the inter-and intralayer molecular jumps, and the correlation in the layer stacking. The evaluated anisotropy and dispersion of $T_1$ and $T_{1\rho }$ are presented graphically for a variety of parameters. It is shown that in most cases $T_{1\rho }$, due to translational diffusion, has a characteristic anisotropy and dispersion while $T_1$ is expected to be nearly isotropic and with ${\omega }^2$-type dispersion at usual NMR frequencies. The relaxation study cannot discriminate between various types of the interlayer and intralayer correlations occurring in the crystalline-$B$ and hexatic-$B$ phases of the smectics except in the case when relative layer motions are fast compared to the diffusion. The comparison of the theoretical relation and experimental data enables the determination of diffusion constant $D_{\perp }$ in the smectic-$B$ phases while the ratio $\frac{D_{\perp }}{D_{\parallel }}$ could be determined only via precise study of the $T_{1\rho }$ angular dependence. With the application of the theory to available $T_1$ data of the smectic-$B$ phase of N-[4-($n$-dodecanoyl) benzylidene]-4′-aminoazobenzene (${\mathrm{C}}_{12}$BAA) and of the smectic-$B_c$ phase of terephthal-bis(4-$n$-butylaniline) (TBBA), the corresponding $D_{\perp }$ are estimated.

A model of a magnetic lattice gas is presented in which the gas particles possess magnetic moments of randomly distributed values. Possible types of phase diagrams for such systems in arbitrary dimension are discussed qualitatively, under the assumption that the magnetic interactions can be described in the molecular-field approximation.

The cubic iterative equation $x_{n+1\mathrm{}}=a{x}_n^3+(1-a)\mathrm{}{x}_n$ has two critical points, and in the periodic regime it displays a dependence on the initial condition. This dependence results from the presence of two critical points and leads to two attractors and a "split bifurcation" not found in maps with one critical point. We determine the sequence and patterns of the periodic orbits; these differ from those observed for maps with a single critical point. We note that a conjugacy principle divides the periodic windows into two distinct categories. Also, we observe a correlation between crises of the attractors and the locations of unstable orbits.

We compute the branching ratios for parapositronium and orthopositronium into four and five photons, respectively. We find $\frac{\Gamma (p-\mathrm{P}\mathrm{s}\to 4\gamma )}{\Gamma (p-\mathrm{P}\mathrm{s}\to 2\gamma )}=0.274\mathrm{}{\left(\frac{\alpha }{\pi }\right)}^2\simeq 1.48\times {10}^{-6\mathrm{}}$ and $\frac{\Gamma (o-\mathrm{P}\mathrm{s}\to 5\gamma )}{\Gamma (o-\mathrm{P}\mathrm{s}\to 3\gamma )}=0.177\mathrm{}{\left(\frac{\alpha }{\pi }\right)}^2\simeq 0.96\times {10}^{-6\mathrm{}}$. We also describe the energy spectra of photons from these decays.

Expansion of the Dirac operator in a finite basis set in analogy to the current matrix eigenvalue approach in nonrelativistic molecular quantum mechanics leads to unpleasant results known as "variational collapse." This is avoided if one first performs a Foldy-Wouthuysen transformation to the free-particle part of the Dirac operator, then constructs the matrix representation, and transforms back "on matrix level." The matrix representation so obtained has the correct "Schrödinger limit" for $c\to \infty$ and furnishes very accurate relativistic corrections, even for moderate basis sets. This is illustrated by numerical calculations for the one-electron atom ${\mathrm{O}}^{7+}$, the $\mathrm{H}_2^{}{}_{}{}^{+}$ ion, and by relativistic Hartree-Fock calculations for He and Be.

The derivation of the first nonadiabatic correction in a model potential for one or more electrons outside a spherically symmetric core is considered. Previous derivations of this term employed an additional appeal to perturbation theory. It is shown that this is not an essential restriction. Earlier conclusions that no three-body (two electrons plus core) term of this type exists are confirmed. An alternative derivation of this term, with the same conclusion, is sketched. The question of the appropriate normalization of the eigenfunctions of the model Schrödinger equation is also addressed.

Energy shifts due to the core penetration by Rydberg-state electrons in alkaline-earth atoms are usually small. It is pointed out, however, that they can be underestimated by a factor of 10, if the correct core potential is not used. We compare with previous calculations on Ca I, Ca II, Na I, and Cl XIV.

We propose a simple model wave function for $\mathrm{H}_2^{}{}_{}{}^{+}$, which shares three important properties with the exact wave function. It leads to good approximations for the energies of $\mathrm{H}_2^{}{}_{}{}^{+}$ and for the density at the nuclei.

Unimolecular and collision-induced dissociation of $\mathrm{Ar}_2^{}{}_{}{}^{+}$ produced by electron-impact ionization of ${\mathrm{Ar}}_2$ were studied quantitatively with a double-focusing mass spectrometer. The occurrence of the metastable dissociation process $\mathrm{Ar}_2^{}{}_{}{}^{+*}$ → ${\mathrm{Ar}}^{+}$ + Ar is interpreted qualitatively in terms of potential-energy curves calculated recently using quantum-mechanical methods.

First measurements of proton stopping powers in gaseous ${\mathrm{Cl}}_2$ and ${\mathrm{Br}}_2$ are reported for the energy range between 50 and 750 keV with statistical and systematical errors of about 1% each. In the stopping-power maximum the experimental values are higher than those predicted by the Andersen-Ziegler tables; moreover, lower peak energies are found. Experimental shell corrections were deduced from the proton stopping cross sections and adjusted to the theoretical predictions of Bonderup, whereby higher-order $Z_1$ correction terms were included. Within this procedure semiempirical values for the mean ionization potentials of 174 eV for ${\mathrm{Cl}}_2$ and 363 eV for ${\mathrm{Br}}_2$ were obtained.

The newly discovered excited states of ${\mathrm{Li}}^{-}$ are examined from a many-body point of view. Our result for the ${}_{}{}^5{}_{}{}^{}S_{}^o{}_{}{}^{}$ lifetime includes the contribution of radiative autoionization. This removes one-third of the previous discrepancy between theory (our value = 2.7 ns) and experiment (= 2.3 ns). The first predictions of the hyperfine structures (hfs) of the ${\mathrm{Li}}^{-}$ ${}_{}{}^5{}_{}{}^{}S_{}^o{}_{}{}^{}$ and ${}_{}{}^5{}_{}{}^{}P$ states are made, and the change in the hfs parameters as $p$ electrons are removed is studied.

The $K-L$—virtual-transition contribution in the dispersion relation for the soft—x-ray Rayleigh scattering amplitude is significant for carbon and other light elements. The correction to recent tabulations due to this contribution is estimated.

Interaction potentials for the $X{}_{}{}^2{}_{}{}^{}\Sigma$ and $A{}_{}{}^2{}_{}{}^{}\Pi$ states of NaHe obtained by the quasistatic inversion technique are utilized in quantum-mechanical calculations of intensities in the red wing of the sodium resonance line. The results are in good agreement with the experimental data from which the potentials were derived. We conclude that the potentials produced by the quasistatic method are accurate for NaHe and that the method is applicable to systems of low reduced mass.