The Van der Waals model of a binary mixture in which $b$ is constant and $a$ depends quadratically on the composition possesses a global phase diagram in a space of five thermodynamic fields. The salient features of this phase diagram are worked out and compared with those found previously in a three-component model.

The ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ quadrupole coupling constant and asymmetry parameter $\eta$ have been measured (using a double-resonance technique) as a function of temperature in the smectic $A$, smectic $C$, and smectic $H$ phases of achiral TBBA and chiral TBACA, as well as in the smectic $\mathrm{VI}$ and the solid phase of TBBA. In the low-temperature smectic $H$ and smectic $\mathrm{VI}$ phases of achiral TBBA the results clearly demonstrate the existence of bipolar orientational ordering $〈cos2\varphi 〉\ne 0$ whereas they show the existence of polar orientational order $〈cos\varphi 〉\ne 0$ in the smectic $H$ phase of chiral TBACA. Here $〈cos\varphi 〉\propto {(T_c-T)}^{\beta }$ with $\beta =0.33\mathrm{}\pm 0.02$. In the smectic $C$ phase of both systems the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ nuclear-quadrupole-resonance spectrum is mainly determined by anisotropic fluctuations in the long molecular axis and the orientational order parameters can be only roughly estimated.

A self-consistent scheme is discussed for calculating the pair potential of simple classical liquids from a knowledge of the zeroth and fourth frequency-moment sum rules of the coherent scattering function $S(q, \omega )$. The procedure is tested by using molecular-dynamics data on a liquid-argon-like system interacting through a Lennard-Jones (6-12) potential. A detailed investigation of the propagation of error in the potential due to uncertainties in the measurement of the data has been made which should serve as a guideline to the experimentalist.

The relaxation kinetics of the optical Kerr effect of succinonitrile [${\left(\mathrm{C}{\mathrm{H}}_2\mathrm{C}\mathrm{N}\right)}_2$] is measured in the liquid and plastic-crystal phases. The Kerr intensity decay profile of the plastic crystal indicates that more than one relaxation mechanism is operative. The temperature-dependence study of succinonitrile's relaxation time in the plastic-crystal phase yields an activation energy of 2.6 kcal/mole.

A double decomposition of phase space into both wave-number bands and spacially localized wave packets is used to derive model equations for an averaged time-dependent velocity or vorticity amplitude localized in both real and Fourier space. Intermittency develops in time, and correlation functions scale as the wave number to a universal power. Energy cascades to infinite wave number in a finite time in a series of self-similar pulses that propagate down our hierarchy of equations. A number of subgrid parametrizations are also examined.

A simple formulation i presented for the analysis of nuclear quadrupole spectra in biaxial liquid crystals based on orientational order parameters. The analysis contains no tilt angle or other model-dependent parameters not directly measured in NMR experiments. The observability and effect of various order parameters on the asymmetry of the electric field gradient $\eta$ is discussed. It is shown that $\eta$ is insensitive to rotational freeze-out of the variety expected to be observed in some biaxial phases. Nuclear quadrupole resonance experiments are described which are expected to yield rotational freeze-out parameters.

A repeated-ring kinetic theory is derived to describe the thermal motion of a tagged particle of arbitrary size and mass immersed in a fluid. In the spirit of the fully renormalized kinetic theory developed by Mazenko, systematic approximations are made in the exact equations of motion for the tagged-particle phase-space correlation function to cast the dynamics of the system in terms of the two-body Enskog collision operator. In addition to Enskog (uncorrelated collisions) and ring (two correlated collisions) events, we include repeated-ring (3,4,...correlated collisions) events. The theory is applied to the calculation of the velocity autocorrelation function and diffusion coefficient of a large hard sphere immersed in a dense fluid of smaller hard spheres. The accepted long-time behavior of the velocity auto-correlation function $t^{-\frac{3}{2}}$ is obtained and the diffusion coefficient is found to have the same functional form as in the Stokes-Einstein law of hydrodynamics. It is suggested that the theory be applied to study self-diffusion in a dense hard-sphere fluid.

The equilibrium statistical mechanics of the sine-Gordon chain is studied using transfer-integral techniques. Implementation of formally exact expressions for the free energy, equilibrium averages, etc., rests upon solution of the transfer-integral (TI) problem. Away from the continuum limit the solution to the TI problem contains features that must be examined with some care. Several approximate schemes for solving the TI problem are described and subjected to numerical verification. The appropriate thermodynamic variables for describing the sine-Gordon chain are found to be temperature and phase; the mechanical variable conjugate to phase is torque. Examination of the Helmholtz free energy, torque, equilibrium averages, etc., shows that as $T\to 0^{+}$ the chain with nonzero phase is described by a gas of noninteracting solitons. At $T=0\mathrm{}°$K the chain with nonzero phase corresponds to a kink lattice. At $T=0^{+}$ this lattice "melts" although the phase evolution continues to occur locally on the chain as solitons.

It is shown that the magnetic radiative energy shift derived from the relativistic-Lamb-shift expression of Erickson and Yennie reduces in the nonrelativistic limit to a formula given by Grotch and Hegstrom, which was derived starting from the nonrelativistic theory. This clears up a discrepancy between those two approaches. The corresponding correction to the $g$ factor, which exists only for states with $l\ne 0$, is estimated to be $-0.24\mathrm{}{\alpha }^3$ for the $2P$ state of hydrogen.

The observations of magnetic fields as a function of position and time during a pulse reported in a recent Letter by Nishida, Hirose, and Skarsgard imply turbulent heating substantially less than that inferred from the diamagnetic signals. The inferences of heating and penetration are therefore doubtful.

It is shown that (a) the energy content calculated by Gentle is consistent with that reported in the Letter and (b) the stray capacitance of the toroidal coil system is negligible in the diamagnetic measurement for the frequency range of the experiment.

The variation of field-ionization thresholds due to the $m_l$ quantum number is calculated using a classical model. Results are compared to the $\left|m_l\right|$-dependent field-ionization thresholds of sodium Rydberg states. An approximate solution and scaling laws are presented.

The values of $S\left(1\right)\mathrm{}$ and $L\left(1\right)\mathrm{}$, i.e., quantities related to straggling of particles given by Dehmer, Inokuti, and Saxon [Phys. Rev. A 12, 102 (1975)], are inaccurate within the Hartree-Slater model used in that work. Those values are too large by as much as several percent because of an overestimation of contributions from high excitation energies. Revised values of $S\left(1\right)\mathrm{}$ and $L\left(1\right)\mathrm{}$, accurate to about 1%, are presented and discussed in greater detail. They are now in closer agreement with other values of N, O, Ne, and Ar found in the literature. All the other $S\left(\mu \right)$ and $L\left(\mu \right)$ values given by Dehmer, Inokuti, and Saxon remain unchanged.

The dependence of the polarizabilities ${\alpha }_0\mathrm{}\left(R\right)\mathrm{}$ and ${\alpha }_2\mathrm{}\left(R\right)\mathrm{}$ [or equivalently ${\alpha }_{\parallel }\mathrm{}\left(R\right)\mathrm{}$, ${\alpha }_{\perp }\mathrm{}\left(R\right)\mathrm{}$] on the internuclear separation $R$ has been synthesized for the ${\mathrm{N}}_2$ molecule in its ground (${\Sigma }_g^{+}$) state. The significance of this dependence for a previous calculation of $e$-${\mathrm{N}}_2$ vibrational excitation is indicated.

A theoretical stopping-power formula for nuclei and antinuclei is presented. It is estimated to be valid in the regime specified by $\beta >0.3\mathrm{}$, $\gamma <50\mathrm{}$, and $\left|\frac{Z_1}{\beta }\right|<\mathrm{}100\mathrm{}$ at the ± 3% level of accuracy.

A new approach to the direct determination of excitation energies and various attachment or detachment energies, such as electron affinities and ionization potentials, is presented. It is based on the coupled-cluster ansatz for the trial wave function, generalized to the open-shell excited or ionized states in a way which enables a variation principle to be used, assuming that the closed-shell ground-state coupled-cluster wave function is known. The conditions for the applicability of this approach are discussed, and the basic formalism is derived. A technique enabling a systematic elimination of disconnected clusters in a general open-shell case is presented and used. An example pertaining to ionization processes is worked out in some detail. Finally, the relationship of the presented approach to configuration-interaction and perturbative Green's-function approaches is briefly outlined.

An extensive configuration-interaction calculation for the $\mathrm{}\left(1s2s3s\right)\mathrm{}$ ${}_{}{}^4{}_{}{}^{}S$ state of neutral lithium has been carried out in an effort to establish absolute term values for the low-lying quartet states with a few ${\mathrm{cm}}^{-1\mathrm{}}$ of accuracy. The lowest quartet state, $\mathrm{}\left(1s2s2p\right)\mathrm{} {}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$ is found to be 57.4128 (10) eV above the ground state $1s^{2}2s$, in apparent disagreement with a recent experimental value of 57.4420 (40) eV obtained from Ritz formulas applied to the ${}_{}{}^4{}_{}{}^{}D$ states of even and odd parity. The positions of all identified quartets have been recalculated from raw experimental data and new theoretical results.

Configuration-interaction calculations for the lowest ${}_{}{}^4{}_{}{}^{}S$, ${}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}P$, ${}_{}{}^4{}_{}{}^{}D_{}^o{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}D$, ${}_{}{}^4{}_{}{}^{}F_{}^o{}_{}{}^{}$, and ${}_{}{}^4{}_{}{}^{}F$ states of neutral lithium have been carried out with a basis of $10s8p8d6f3g2h1i$ Slater-type orbitals. The nonrelativistic-energy upper bounds converge to within 4-45 ${\mathrm{cm}}^{-1\mathrm{}}$ of the expected nonrelativistic energies. An explanation is given for the fact that transitions from ${}_{}{}^4{}_{}{}^{}F$ states have not been observed in beam-foil experiments. Some aspects involved in the assessment of the reliability of calculated oscillator strengths are discussed, and the calculated mean lifetimes for electric dipole decay are compared with experiment.