We present a Landau theory of the smectic $A$ to helicoidal smectic $C$ phase transition which has recently been discovered. We analyze qualitatively the molecular interactions between chiral molecules in order to explain the appearance of a twisted smectic $C$ phase. Using an expansion of the free energy, we show how a second-order transition takes place. We also study the properties of the system near the phase change: (i) the behavior of the dielectric susceptibility and piezoelectric coefficient; (ii) the transition to a regular smectic $C$ phase by means of an electric field. Comparison is made with the available experimental results.

The nonlinear equation governing low-frequency drift waves is considered. Utilizing the linear dispersion relation for such waves, it is shown that there exists a parameter range for which the drift waves are governed by a modified Korteweg-de Vries equation having a solitary solution in one and two dimensions. The one-dimensional solitons are unstable with respect to perturbations in the direction perpendicular to their motion.

The influence of Earth's gravity on measurements of the Rayleigh linewidth $\Gamma$ of a simple fluid near its critical point is investigated in detail. Special attention is given to the scaled linewidth ${\Gamma }^{*}$. From a number of different viewpoints it is found that gravity significantly affects linewidth measurements in the critical region. Small errors in beam centering render available experimental data useless for the purposes of distinguishing between modern theories, as variations in beam height split the universal curve of the scaled linewidth into a single-parameter family. The mode-mode coupling and decoupled-mode theories, which in the gravity-free case predict slightly different results for $\Gamma$ and ${\Gamma }^{*}$, predict qualitatively different behavior in the dependence of $\Gamma$ on height and scattering angle when gravity is taken into account. When the relative deviation of ${\Gamma }^{*}$ from its gravity-free uniform fluid value is plotted versus the reduced correlation length, it exhibits distinct patterns characterizing the different theories used to compute it. By comparing these patterns with the results of carefully controlled experiments, gravity should prove to be a useful tool for eventually selecting a correct theory.

Scattering from a multielectron target by a heavy particle is approximated in terms of amplitudes for scattering from individual target electrons. By treating the motion of the projectile classically and ignoring correlations, the wave function for the system is expressed as a product of single-electron wave functions. The probability amplitude for scattering into specific states is then a product of single-electron scattering amplitudes. In this approximation, cross sections for excitation and ionization involving many electrons are expressed in terms of a binomial distribution of single-electron probabilities. The standard connection of this amplitude for multiple excitation and ionization, $A^{\mathrm{if}}\mathrm{}\left(B\right)\mathrm{}$, to the corresponding scattering amplitude, $f\left(\theta \right)$, is given, and the validity of this approximation is discussed.

The thermodynamic properties of the quantum-mechanical one-component plasma are calculated at all temperatures for four densities at the high-density end of the metallic region. The Slater sum (diagonal density matrix) is obtained by using a nonzero-temperature variational principle with the simplest credible approximations. The Slater sum is approximated as the product of the ideal Fermi-gas Slater sum and a product of pair functions. Various methods for calculating thermodynamic quantities are investigated with the main emphasis on the pressure. In calculating the thermodynamic properties, the effects of Fermi statistics are included in a nonperturbative manner using Lado's method. The hypernetted-chain approximation is used to compute the pair correlation functions. Three different approximations are used for the three-body correlation functions so that errors may be estimated. The free energy is calculated by integrating the energy over temperature, while holding the volume fixed. Differentiating the free energy with respect to volume was found to yield more accurate pressures than using the virial theorem. Tables of the excess energies, pressures, and free energy are given for four densities and 20 temperatures.

The Zwanzig-Mori theory is applied to the study of dielectric behavior of polar liquids in the far-infrared spectral range. The basic dynamical variables on which the calculation is based are the macroscopic dipole moment $\overrightarrow{\mathrm{M}}\mathrm{}\left(t\right)\mathrm{}$ of the liquid sample and its time derivatives. The return to transparency and the excess absorption are analyzed in detail. It is shown that the spectral behavior of pure liquids can be described by the same formulas as those applicable to analyze diluted solutions provided microscopic time parameters of the latter theories are replaced by new macroscopic time parameters chosen in an appropriate way.

The fact that a finite-diameter incident beam samples a range of fluid densities is found to have little effect on light scattering except extremely near the critical point. This finding disagrees with the results of Splittorff and Miller, and Leung and Miller, because their geometry differs from the usual experimental arrangement.

In asserting that gravity plays an insignificant role in light-scattering experiments using a horizontal geometry, Cannell has only considered gravity-induced deviations from the predictions of the classical Ornstein-Zernike theory of light scattering for a uniform fluid. He has not addressed himself to the important problem of using light-scattering experiments to help distinguish between modern theories of the pair correlation function. In particular, the nonvanishing of the critical exponent $\eta$ is only experimentally manifest very close to the critical point where, depending on its value, gravity may obscure its measurement. A vertical beam geometry is suggested as an alternative for light-scattering experiments performed very close to the critical point, since it utilizes the large density gradient to reduce sharply the problems of multiple scattering and beam bending (due to refraction) inherent in current experimental designs.

Using the exact equation of state for the two-dimensional one-component plasma, asymptotic static longwavelength limits and compressibility sum rules are derived for the linear and quadratic polarizabilities.

Cross sections for the collisional $l$ mixing of $\mathrm{Na}\left(n{}_{}{}^2{}_{}{}^{}D\right)$ states from $n=5\mathrm{} \mathrm{to} 14$ by ${\mathrm{N}}_2$ and CO have been measured by time-resolved laser fluorescence and calculated in a two-state approximation by assuming the perturbing gases are spherically symmetric. For both CO and ${\mathrm{N}}_2$ the experimental cross sections rise sharply from $n=5\mathrm{}$ to $n=10\mathrm{}$ and remain constant for $n>\mathrm{}10\mathrm{}$. The theoretical calculations overestimate the experimental cross sections by a factor of 3 from $n=10\mathrm{} \mathrm{to} 12$, but are in good agreement for the smaller $n$ values.

Absolute C $K$ x-ray production cross-section measurements using 18-26-MeV protons on thin carbon foils extend the range of previous measurements in the asymptotic region. These measurements permit extraction of the two main parameters of the asymptotic theory, viz., $M_{\mathrm{tot}}^2=0.84\mathrm{}$ and $C_{\mathrm{tot}}=8.2\mathrm{}$, which are in good agreement with those obtained in previous work at lower energies. The ionization cross sections extracted from these measurements are compared with the predictions of the asymptotic theory as well as the binary-encounter, semiclassical, and plane-wave Born approximation theories.

It is shown that application of the global nonlinear crossover equation of state to fluids leads to a simple analytical expression with crossover between critical and mean-field regimes. This expression gives the same structure as the Wegner correction-to-scaling terms and provides a new insight into the theoretical character of such terms. Additional analysis of our Xe coexisting density data shows that this nonlinear crossover expression does not represent as good a fit to the data as a single power law with a non-Ising exponent.

By using the concept of degree of coherence of quantum optical fields, the properties of fields which can be modulated at a complex rate are studied.

By recasting the Bethe-Salpeter equation in a more general form, the natural ensuing bound-state perturbation theory accounts for the anomalous ${\alpha }^6\ln {\alpha }^{-1\mathrm{}}$ contribution of the fourth-order vacuum polarization to the ground state of the positronium hyperfine structure as a binding correction of a two-photon diagram. Viewed as such, this contribution is not anomalous. Another two-photon diagram, in which such a binding correction makes it a candidate for an ${\alpha }^6\ln {\alpha }^{-1\mathrm{}}$ contribution, is found. By using the Bethe-Salpeter equation recast in the more general form and the perturbation theory associated with it, the formal connection with the external field approximation is given.

Helium atoms in highly excited Rydberg states are produced by electron impact and are detected by electric field ionization. The principal quantum numbers $n$ are determined to lie in the range $20\lesssim n\lesssim 80$ by ionizing the excited He atoms in a uniform, swept electric field. The absolute excitation cross section for 100-eV incident electrons is found to be $(9\mathrm{}\pm 5)\times \frac{{10}^{-17\mathrm{}}}{n^3}$ ${\mathrm{cm}}^2$. This expression predicts a value for $n=4\mathrm{}$ that agrees with the optically measured $n=4\mathrm{}$ cross section. The 108-μsec time of flight requires that the high Rydberg He atoms have lifetimes much longer than those calculated for low-angular-momentum ($l\le 2$) states, those expected to be populated by electron impact. The proposed explanation is that the excited He atoms suffer collisions with electrons and/or ground-state He atoms causing longer-lived higher $l$ states to be populated. This explanation is supported by measurements of signal as a function of incident-electron energy, electron current, and He pressure. The cross section for $l$-changing collisions between electrons and high Rydberg helium atoms is given by ${\sigma }_{\Delta l}^e\cong 5\times {10}^{-(15\mathrm{}\pm 0.3)}\frac{\ln \left(100E{n}^2\right)n^4}{E}$ ${\mathrm{cm}}^2$.

Using an electrostatic ion-storage device and a microwave state-selection technique, we have measured the hyperfine structure $\Delta {\nu }_2$ of the $2s$ state of ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$. Our result is $\Delta {\nu }_2=1083.354\mathrm{}9807\left(88\right)\mathrm{}$ MHz (the equivalent uncertainty is 0.009 ppm). When combined with the $1s$-state hyperfine structure $\Delta {\nu }_1$ to make the quantity $D_{21}\equiv 8\Delta {\nu }_2-\Delta {\nu }_1$, we obtain $D_{21}\left(\mathrm{experiment}\right)=1.189\mathrm{}979\left(71\right)\mathrm{}$ MHz. Current theory produces $D_{21}\left(\mathrm{theory}\right)=1.189\mathrm{}801\left(1\right)\mathrm{}$ MHz. The 178(71) Hz difference may arise from a combination of quantum-electrodynamic and nuclear structure effects which remain to be treated theoretically.

Using the generalized oscillator-strength formulation of the Born approximation, electron ionization cross sections were calculated for 20 elements with $19\le Z\le 54$. For Kr and Xe, good agreement (30%) is found for the total ionization cross section above 300 eV. Comparison with measured cross sections for producing various charge states in Kr and Xe showed significant discrepancies, which arise from neglect of configuration interaction. Comparison with measured total cross sections for other elements show limited agreement, though the agreement improves as one goes to higher $Z$.

The results of extensive calculations on cross sections for electron ionization of atomic subshells are presented in a scaled form. In general, the scaling is nonclassical, i.e., does not vary inversely with the square of the ionization potential. Comparison is made of the scaled $2p$ ionization cross section with measurements on Ar and Au, and good agreement is found. Comparison is made with measurements on cross sections for electron ionization of positive ions. The conclusion reached is that for ions with outer shells of low ionization potential, the scaled atomic cross sections are inaccurate, and that for such ions the cross sections are better described by the classical scaling law.

The frame-transformation theory has been employed to extend first-principles studies of electron-molecule collisions to heteronuclear diatomic systems. The Wigner-Eisenbud $R$ matrix has been introduced at the boundary point of the molecular-core radius—which defines the inner region—in a molecule-fixed frame of reference in the fixed-nuclei approximation. The solutions of the scattering equations in the outer region, where rotational motion of the nuclei is taken into account, are continued by transforming the $R$ matrix to the space frame of reference. This procedure has been applied to a model calculation of thermal-energy electron scattering from CO. The dependence of the rotational transition cross sections on the core radius has been studied. A general methodology has been developed for adapting the single-center pseudopotential method to the proposed amalgamation of the $R$-matrix and frame-transformation theories in order to perform a fundamental calculation of the interior problem. A comprehensive study of $e^{-}$-CO scattering is carried out on the basis of this methodology. In the present application the dipole term in the multipole expansion of the static potential, computed from the ground-electronic state wave functions of the CO molecule, has been renormalized so that it reproduces, asymptotically, the experimentally measured magnitude of the dipole moment of carbon monoxide. The calculated momentum-transfer cross section is in good agreement with the experimental measurements for thermal-energy $e^{-}$ scattering from CO. The rotational excitation and deexcitation, and total scattering and momentum-transfer cross sections computed from this method also reproduce the 1.75 eV ${}_{}{}^2{}_{}{}^{}\Pi$ resonance; while those obtained from an extension of the model calculation mentioned above fail to do so. In particular, it is found that for rotationally inelastic scattering in the resonance region the cross sections for 0→4 and 1→3 transitions are the largest among those which start from the ground and first rotational states of CO molecule, respectively. The angular distributions for various electron impact transitions in CO have also been computed.

A new method is proposed to approximate the exchange-correlation potential in the Hartree-Fock equations for a many-electron atom. The exchange-correlation potential is separated into a self-interaction term and a characteristic exchange term. The self-interaction term is evaluated exactly, while the exchange term is approximated in a manner similar to Slater's statistical average method using a previously obtained theoretical exchange parameter $\alpha$. In the present method different potentials are used for different spin orbitals instead of the average potential used in the Hartree-Fock-Slater (HFS) scheme. The separation of the exchange-correlation potential into a self-interaction plus exchange terms removes all the major defects of the HFS potential, such as the wrong asymptotic behavior at large $r$ values and the underestimation of the self-interaction. The accuracy of the present method is demonstrated by calculations on the first-row transitionmetal ions ${\mathrm{Cu}}^{+}$ and ${\mathrm{Mn}}^{+2\mathrm{}}$. The results for exchange potentials, one-electron eigenvalues, spin density distribution, and contact hyperfine interaction agree excellently with Hartree-Fock values. The relative importance of the self-interaction and exchange terms for various electron shells are discussed. Computationally, the method is as simple as the Hartree-Fock-Slater scheme.