We show that the analysis of the electroclinic effect in a chiral smectic liquid crystal made by Garoff and Meyer is not correct in the very vicinity of $T_c$. We propose an analysis based on the Landau theory and conclude that the electroclinic coefficient and electric susceptibility do not diverge, but can take large values.

Very near the chiral smectic-$A$—smectic-$C$ phase transition, the correlation length of the fluctuations in the smectic-$A$ phase is larger than the pitch of the helical structure within the fluctuations. Above this temperature regime near the transition, the electroclinic coefficient is a good approximation to the generalized susceptibility of the chiral smectic system. Present indications are that this temperature regime is on the order of 20 mK in extent.

Our experimental data indicate that for metallic targets the self-generated magnetic field consists of two parts, one part originating from a laser-driven electron current, and the second due to the plasma-surrounding gas interaction. These conclusions differ from those suggested recently by Drouet et al. We believe our model for the origin of these fields to be an accurate description of the processes taking place.

The sharing of vacancies in the $3d\sigma$ molecular orbital between the $K$ shells of chlorine and argon projectiles and $2p_{\frac{3}{2}}$ and $2p_{\frac{1}{2}}$ $L$ subshells of tin, antimony, and xenon targets has been studied. Projectile energies varied from 1 to 16 MeV. The vacancy-sharing ratios deduced from experimental results are interpreted in terms of a long-range exponential-coupling model.

Geometrical and computational interpretations are offered for configuration-mixed $\alpha \left(1\mathrm{}{s}^{d}2s^{2}2p^m\right)+\beta \left(1\mathrm{}{s}^{d}2p^{m+2\mathrm{}}\right)$ (where $d=0\mathrm{} or 2$) valence states based on new profiles of $L$-shell mixing coefficients, correlation energies, and pair-function angular distributions for both ground and excited states. When viewed for species having the same degree of ionization $Z-N$, the profiles constructed for the internal and semi-internal "nondynamical" correlation energies computed by Sinanoğlu's "non-closed-shell many-electron theory" are found to display a striking, approximate particle-hole symmetry with respect to total $L$-shell occupancy. Near-degeneracy-type correlation energy for ${}_{}{}^3{}_{}{}^{}P$ and ${}_{}{}^1{}_{}{}^{}D$ levels of C-like atoms becomes exactly degenerate when the same radial functions are used for both states. The mixing structure for all $L$-shell states is described accurately by an $N$-electron operator $\Lambda \mathrm{}\left(N\right)={\Sigma }_{i<j}{(A_i-A_j)}^2$ with single-particle SO(4) generators $A_i$ like the Runge-Lenz vector. $\Lambda \mathrm{}\left(N\right)\mathrm{}$ represents an approximate "correlation invariant" for $L$-shell mixings.

The long-range behavior of the electronic charge density of ground-state atoms is considered. A rigorous upper bound to this function is derived and is found to be an exponentially decreasing function, which depends on the ionization potential and an effective nuclear charge.

A self-consistent-field approximation is employed to treat bound states in spinor electrodynamics. The proposed method avoids the classical self-interaction of bound quanta arising in variational approximations based on coherent trial states. Relativistic Hartree-Fock equations are obtained and implications for the calculation of atomic structures are discussed.

Static quadrupole and mixed dipole-octupole polarizabilities are calculated from correlated wave functions for the ground states of the first-row atoms with estimated uncertainties of less than 3%. The following mean quadrupole polarizabilities are obtained for the atoms Li through Ne (in atomic units): 1428; 301.8; 145.7; 64.20; 30.72; 21.20; 12.69; 7.726. Correlation contributions are found to range from -12% (Be) to +20% (O).

We study here level-degeneracy effects in super-radiance, using the quantum "small-system" model whose interest and limitations are discussed. First, we show that this model allows one to understand the physical origin of these effects and to describe their qualitative influence on the properties of the emitted light. We also present and analyze numerical results obtained for the case of a dipole transition between two degenerate levels of angular momenta ½. We show that in this particular case one can define a basis of collective states which is well adapted to the invariance properties of the master equation. It is then possible to solve the master equation and to compute expectation values for the radiated field (intensity radiated with a given polarization, quantum fluctuations of this intensity) for various initial conditions and for small but already significant values of the number of individual systems. A detailed analysis of these results and a comparison with analogous calculations in the case where the degeneracy is supposed to be removed allows us to estimate the individual influence of the different types of effects (interference effects and the two sorts of competition effects, inhibition and initiation). We also compare the total intensity radiated to the intensity radiated by the same number of two (nondegenerate) level atoms. This comparison can be simply understood if one studies the partition of the population of the collective energy levels between the different states of these levels, and it appears that the most populated states are these which are able to radiate the most. Finally, it is shown how level degeneracy affects the quantum fluctuations of the intensity.

On the basis of model calculations, we argue heuristically that the dilatation-transformation method is applicable to all potentials, even those that are not dilatation analytic. In particular, we show that resonances are converted into bound (localized) states on the nonphysical sheet of the complex energy plane under the action of a dilatation transformation.

The ($3s^{2}3pnd$) ${}_{}{}^1{}_{}{}^{}D_{}^o{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}D_{}^o{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}F_{}^o{}_{}{}^{}$, and ${}_{}{}^3{}_{}{}^{}F_{}^o{}_{}{}^{}$ Rydberg series of the silicon atom are investigated by a restricted Hartree-Fock calculation and configuration interaction (CI) calculations of various levels. The relative energies with respect to the ionized level $\left(3\mathrm{}{s}^{2}3p\right){}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ given by the largest CI calculation in the present work are -2.63, -1.46, -0.85, -0.55, -0.38, and -0.28 eV, respectively, for the first six members of the ${}_{}{}^3{}_{}{}^{}D_{}^o{}_{}{}^{}$ series, while the experimental values are -2.56, -1.45, -0.85, -0.55, -0.38, and -0.27 eV. The agreement between the two is excellent. The configuration $\left(3s3\mathrm{}{p}^3\right){}_{}{}^3{}_{}{}^{}D_{}^o{}_{}{}^{}$ is predominant in the first member of the ${}_{}{}^3{}_{}{}^{}D_{}^o{}_{}{}^{}$ series, and it also acts as a strong series perturber in the rest of the series. For the ${}_{}{}^1{}_{}{}^{}D_{}^o{}_{}{}^{}$ series the relative energies with respect to ${}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ by the largest CI calculation are -2.27, -1.16, -0.70, -0.46, and -0.32 eV, respectively, whereas the experimental values are -2.31, -1.17, -0.70, -0.47, and -0.34 eV. In this series, $\left(3s3\mathrm{}{p}^3\right){}_{}{}^1{}_{}{}^{}D_{}^o{}_{}{}^{}$ acts as a series perturber just as $3s3p^3$ does in the ${}_{}{}^3{}_{}{}^{}D_{}^o{}_{}{}^{}$ series. At any levels of the approximations, $\left(3s3\mathrm{}{p}^3\right){}_{}{}^1{}_{}{}^{}D_{}^o{}_{}{}^{}$ is not found below the ${}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ state. The ($3s^{2}3pnd$) ${}_{}{}^1{}_{}{}^{}F_{}^o{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}F_{}^o{}_{}{}^{}$ series are found to be pure Rydberg series.

The electronic structure of the ($3s^{2}3pns$) ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$ and $\left(3\mathrm{}{s}^{2}3pnd\right) {}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$ Rydberg series of the silicon atom is investigated by configuration interaction (CI) calculations of various levels. For example, the calculated energies relative to the ionized state $\left(3\mathrm{}{s}^{2}3p\right){}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ for the first five members of the $\left(3\mathrm{}{s}^{2}3pnd\right){}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$ Rydberg series by the largest CI calculation in the present work are -1.91, -1.17, -0.75, -0.50, and -0.35 eV and the experimental ones are -1.91 -1.15, -0.74, -0.50, and -0.36 eV. The $\mathrm{}\left(3pnd\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$ series is strongly perturbed by $\left(3s3\mathrm{}{p}^3\right){}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$, and the perturber $\left(3s3\mathrm{}{p}^3\right){}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$ is almost completely smeared out over the series. The $\mathrm{}\left(3pns\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ and $\mathrm{}\left(3pnd\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ series are found to perturb each other.

A variety of results are reported for the ground state ($X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$) of the hydrogen molecule. They include improved Born-Oppenheimer calculations, a study of the convergence of energies with basis-set size, adiabatic calculations, and the first successful ab initio nonadiabatic calculation. The latter, which treats ${\mathrm{H}}_2$ as a four-body problem, leads us to predict that the dissociation energy of ${\mathrm{H}}_2$ is 36117.92 ${\mathrm{cm}}^{-1\mathrm{}}$. This value may be compared with 36 117.8±0.4 ${\mathrm{cm}}^{-1\mathrm{}}$ (the value derived from the experimental ionization potential), with 36118.6±0.5 ${\mathrm{cm}}^{-1\mathrm{}}$ (the value derived from the experimental vibrational levels of the $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state), or with 36118.3 ${\mathrm{cm}}^{-1\mathrm{}}$ (the upper-bound value derived from the experimental absorption limit).

The solution of the Stark effect in hydrogen to arbitrarily high orders of perturbation theory is made feasible by the explicit formula for the $N\mathrm{th}$-order energy in terms of the separation constants through $N\mathrm{th}$ order, derived here. The $N\mathrm{th}$-order separation constant ${\beta }_i^{\mathrm{}\left(N\right)\mathrm{}}$ is shown to be a polynomial of total degree $N+1\mathrm{}$ in the parabolic quantum number $n_i$ and the magnetic quantum number $m$. The polynomial coefficients have been tabulated through seventeenth order and are listed here through tenth order. Similarly, the $N\mathrm{th}$-order energy is a polynomial in the quantum numbers $n_1$, $n_2$, and $m$. The polynomial coefficients (which are more numerous than for ${\beta }_i^{\mathrm{}\left(N\right)\mathrm{}}$) have been tabulated through seventeenth order and are listed here through seventh order. Seventeenth order is high enough to permit a clear numerical demonstration of the asymptotic character of the perturbation series, and a "maximum useful field strength" is defined and illustrated. Energies calculated by perturbation theory for specific states are shown to be in excellent agreement with energies calculated nonperturbatively.

The eikonal amplitude for a fixed molecular orientation is used in the framework of the adiabatic approximation to calculate pure elastic excitation (0→0 and 1→1), pure rotational excitation (0→2 and 1→3), and average elastic cross sections of the hydrogen molecule in its ground electronic and vibrational states using electrons as incident projectiles. Both differential and integral cross sections are reported at electron energies 20-200 eV. For elastic processes, the effects of target polarization and electron exchange are considered, while for inelastic processes only the effect of the target polarization is taken into account. Results obtained are compared with those of other theoretical and experimental workers. It is found that pure elastic and pure rotational excitation cross sections are comparable at intermediate and large scattering angles, and that they depend on the initial rotational state $J$ of the molecule in such a way that the average elastic cross sections remain independent of $J$.

We show that an internally consistent determination of both the emitter velocity and directional anisotropy of continuum x radiation from heavy-ion collisions provides an important method with which quasimolecular emissions can be identified and distinguished from various backgroumd sources of continuum x rays. These features are illustrated with measurements on the Ni + Ni and Ni + Nb collision systems utilizing the observation of the forward-backward Doppler shift of the continuum x rays to determine the emitter velocities as a function of photon energy.

Argon $K\alpha$ x-ray satellites produced by ion collisions have been analyzed in high resolution. Ions of H, C, N, O, F, Si, and Cl with energies in the range 1-5 MeV/amu were used to bombard argon contained in a gas cell. This study is the first systematic study of $K$ x-ray satellites from free-atom targets with $Z>\mathrm{}10\mathrm{}$. The relative satellite intensities and satellite energies are tabulated and their projectile dependence is qualitatively discussed. The average number of $L$-shell vacancies formed in single-$K$-vacancy-producing collisions is determined from a model calculation based on theoretical decay rates. This model includes (i) the variation in fluorescence yield, and (ii) the variation in $L$-shell rearrangement with the number of $L$-shell and $M$-shell electrons. The averages obtained from the model calculation are nearly the same as the $〈l〉$ values obtained by weighting the x-ray satellites equally. A universal scaling of $〈l〉$ in $Z_1$ and projectile velocity is obtained on the basis of an increased binding effect. This is the first successful demonstration of a scaling law for multiple ionization by heavy ions.

Multichannel electron scattering by atomic hydrogen is studied by using a complex optical potential. Real and virtual excitation and ionization of the target system as well as electron-exchange effects are included in the calculation. A free-particle Green's function is used as an approximation for the propagator in intermediate states. The contributions of the excited and ionized states to the nonlocal optical potential are examined separately. Ionization and excitation cross sections are calculated exactly without further approximation for electron energies greater than 1 Ry. The calculations are in good agreement with recent experimental measurements of differential cross sections.

A numerically tractable technique is derived for computing inelastic cross sections for a single channel by using the microscopic-optical-model potential for elastic scattering. It is assumed that a distorted-wave approximation is used in computing the elastic optical potential. No further approximations are made.

Measured cross sections for electron-impact ionization of ${\mathrm{C}}^{3+}$ and ${\mathrm{N}}^{4+}$ are reported for collision energies between threshold and 500 eV. The measurements were performed with crossed electron and ion beams. The peak cross sections obtained are 2.3 × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ near 200 eV for ${\mathrm{C}}^{3+}$ and 1.5 × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ near 400 eV for ${\mathrm{N}}^{4+}$ with good-confidence absolute uncertainties of ± 11% and ± 15%, respectively. Comparisons of present data with the available theoretical estimates range from good agreement to discrepancies of a factor of two. At the highest energies of the present measurements, near 500 eV, the cross sections have not yet begun to decrease as predicted by all the available theories. It is postulated that inner-shell-electron excitation followed by autoionization is contributing to the measured ionization cross sections at these energies. Ionization-rate coefficients are derived from the data and compared with those measured in plasmas. The agreement in ionization rates is satisfactory in the ${\mathrm{C}}^{3+}$ case, but discrepancies of nearly a factor of two exist for the ${\mathrm{N}}^{4+}$ case.