A new analysis of the Ag $L$-series x-ray spectrum has been performed, based on relaxed-orbital relativistic transition-energy calculations. Satellite energies were computed in intermediate coupling. It is found that satellites arising from $\mathrm{LN}$ double-hole states generally fall within the natural width of the parent diagram lines. Contrary to previous assumption, the observed high-energy satellites are due to $\mathrm{LM}$ double-hole states produced by $L_1-L_3{M}_{4,5}$ Coster-Kronig transitions and by shakeoff. The observed peak structure in the satellite spectrum is due to multiplet splitting of the initial and final double-hole states. Theoretical $L_1-L_3{M}_{4,5}$ transition rates based on the new Coster-Kronig energies are closer to experiment than previous results, but still are too large by a factor of ∼2, indicating an as yet undetected flaw in the theory.

X-ray energies, Auger, and radiative decay rates and fluorescence yields have been computed in intermediate coupling for the various states of the $1s2s3s$, $1s2s3p$, $1s2p3p$, $1s2p3s$, and $1s2p3d$ configurations of ${}_{10}{}^{}{}_{}{}^{}\mathrm{Ne}_{}^{7+}{}_{}{}^{}$ to supplement recent experimental work on these transitions.

A Foldy-Wouthuysen transformation is obtained for use in the field theory of quantum electrodynamics. The gauge invariance of quantum electrodynamics and the fact that the transformation function depends on time only through the photon field are essential for the success of this transformation. Transition operators which include leading relativistic corrections beyond $\overrightarrow{\mathrm{p}}·\overrightarrow{\mathrm{A}}$ are obtained. It is shown that the ${\overrightarrow{\mathrm{A}}}^2$ term in the interaction Hamiltonian contributes. Applications are made to the spin-forbidden and spin-allowed transitions in heliumlike systems.

The lifetimes of the $7s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$, $6d{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$, and $6d{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$ states of singly ionized Ba have been measured. The lifetime of each state was determined by direct observation of the decay of the fluorescence emitted from the excited state, following selective excitation by two-step, dye-laser excitation. The values obtained for the lifetimes were $\tau \left(7s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)=7.91\mathrm{}\pm 0.56$ nsec, $\tau \left(6d{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\right)=5.56\mathrm{}\pm 0.34$ nsec, and $\tau \left(6d{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\right)=4.99\mathrm{}\pm 0.33$ nsec.

Energies and widths of $M\alpha$, $M\beta$, amd $M\zeta$ x rays and energies of $N_4$ to $N_7$ levels have been determined for Np by the photoelectron technique, and energies of $M$ and $N$ levels have been calculated by the Dirac-Fock method. Theoretical and experimental energies agree satisfactorily, with the largest difference occurring for the $4p$ subshell, and thus for $M\zeta$ x rays. Present predictions and those of Huang et al. are in good accord, as are our experimental data and Porter and Freedman's evaluation. Experimental values of linewidths are found to compare well with theoretical Hartree-Slater values.

The photon energy dependence of the partial photoionization cross sections and branching ratios for CO and ${\mathrm{N}}_2$ have been measured using the continuum radiation produced by an electron storage ring. These measurements were conducted over the photon energy range of 14 to 50 eV. The partial photoionization cross sections in the energy region of the photoionization continuum are in good agreement with recent calculations where both the theory and experiment exhibit scattering resonances for specific states of the ion. The continuously variable photon energy source was utilized to examine the effect of autoionization on the partial photoionization cross section, showing in several cases quite different structure depending upon the final state of the ion.

A density-matrix calculation of the line shape for a Doppler-broadened two-level system subjected to a plane-standing-wave laser field with a Gaussian intensity profile is presented to fifth order in perturbation theory. The primary new result is that, for fixed pressure and intensity, the power-broadening contribution to the linewidth is at a minimum when the beam radius is approximately equal to the mean free path. In addition, an analytic solution for the linewidth in the collision-dominated regime is presented for general collision parameters.

The problem of a nonrelativistic free charge interacting with radiation is considered from the theoretical viewpoint. In particular the scattering of light and the energy shifts associated with radiation are discussed using both quantum electrodynamics and the semiclassical theory. It is shown that the multipolar form of the Hamiltonian gives results identical to those of the conventional "$e\overrightarrow{\mathrm{p}}·\overrightarrow{\mathrm{A}}$" type of Hamiltonian. Comparisons are also made with calculations based on the space-translated Hamiltonian.

New tableau formulas are derived which allow mixed configuration Russell-Saunders states to be expressed in terms of products of their pure configuration constituents. Using these and other simple tableau formulas, matrix elements for spin- and orbit-dependent operators can be easily evaluated for mixed configurations without the use of recoupling or fractional-parentage coefficients.

Spontaneous emission from a multilevel atom is studied from the viewpoint of quantum beats. The master equation describing the atomic dynamics is shown to have some parameters that oscillate at the beat frequencies, and because of this a Pauli type of master equation for the diagonal elements of the density matrix is not obtained. As a result, the transition rates in the atomic system show the characteristic beats. The relation of the rate of change of the energy of the atomic system to the total power radiated in the far zone is also established. The normally and antinormally ordered correlation functions of the spontaneously emitted radiation are calculated under the approximation that the level widths are much smaller than the beat frequencies. The contribution arising from the interference of the free field and the source terms to antinormally ordered correlations is carefully evaluated. The nature of beats present in normally and antinormally ordered correlations is discussed, and their detection from the viewpoint of causing transitions in another atom is considered. The change in the nature of beats due to atomic collective effects is studied. Finally, it is shown that because of quantum effects, intensity correlations do not show any beats.

Results are presented of calculations on the photoionization of neon and argon based on a recently developed many-body theory of atomic transitions. The results of our calculation demonstrate that this approach is capable of providing a reliable theoretical estimation as well as studying the individual contributions of various many-body effects associated with the atomic transitions.

The dielectric breakdown intensity threshold, the critical power for self-focusing, and the power threshold for the production of spectral superbroadening have been measured in ${\mathrm{H}}_2$O and ${\mathrm{D}}_2$O. For bandwidth limited pulses of 30 psec duration at 1.06 μm, and 21 psec duration at 0.53 μm, the superbroadening in water always required power levels sufficient for catastrophic self-focusing and intensities equal to the electric breakdown threshold.

A theory for the nonlinear (with respect to the electric field) Faraday effect has been developed and applied to a simple model. Within the framework of this model, our analysis shows that the ratio of the nonlinear Verdet constant to the linear Verdet constant is proportional to the intensity of the incident light and depends on the frequency of light, the excitation energy of the model molecule, and the temperature of the medium. This ratio is small under ordinary conditions. However, under certain circumstances it may become large enough for experimental observation.

In order to study the cooperative emission of radiation from an extended system of $N$ two-level atoms, we use the master-equation approach within the Born and Markov approximations. All the properties of the emission of radiation can be deduced from the diagonalization of the coupling matrix $\Gamma$, where an element ${\Gamma }_{\mathrm{jk}}$ gives the coupling between the atoms labeled $j$ and $k$ via the electromagnetic field. We choose a pencil-shaped volume and study analytically the coupling matrix in the limit for small and large Fresnel numbers. For Fresnel numbers of order unity numerical methods are used. Thus we prove that, for the pencil-shaped geometry, any elaborated model must take into account the interaction of the atoms with the infinity of electromagnetic field modes lying inside two small solid angles about the axis of the largest linear dimension, which we label the $z$ axis. In other words, the intensity of radiation emitted by any atom of the system depends on its position with respect to the others and this "propagation effect" cannot be neglected when interpreting superradiance experiments. For small Fresnel numbers the $z$ dependence predominates, in the opposite case the ($x, y$) dependence does, while for Fresnel numbers of order unity the dependence of all three components must be taken into account. Preliminary calculations are given for which only the $z$ dependence is considered; for Fresnel numbers of magnitude of order unity or smaller, the effect of propagation along the $z$ axis displays large delays for the appearance of superradiance with respect to the time at which the superradiant pulse is maximum when the "propagation effects" are neglected (one-mode model).

Formal expressions are given for the elements of the density matrix of an $n$-level quantum system interacting with a polychromatic electromagnetic field and coupled to the modes of a photon reservoir. The interaction with the polychromatic field is treated in both the semiclassical and quantum approaches, and the expressions obtained for the density matrix in the two cases are compared. It is shown that in most physical situations one can use equivalently the semiclassical or the quantum approach with a simple form of the density matrix of the field at initial time.

Up to now, the problem of the influence of level degeneracy on superradiance has been neglected. We describe here a first approach to this problem, in the frame of "small system" quantum model, generalized to the case of a collection of atoms with two degenerate levels of angular momenta $j$ and $j^{\prime }$ connected by an electric or magnetic dipole transition. The differences between this case and the well-known case of two (nondegenerate) level atoms are of two types. The first type is due to the competition between different transitions sharing a common state: superradiant emission on a transition inhibits or initiates superradiance on transitions with smaller transition probability, depending upon which state, upper or lower, is the common one. This effect does not come from the equality of the different wavelengths and would also appear with the same states even if the degeneracy were removed; its qualitative influence on the features of the superradiant pulse can be easily estimated. The second type of differences is quite specific to level degeneracy and consists in interferences between the transitions of the collective system having the same frequency and polarization. In analogy with the description of collections of two-level atoms as spin-½ systems, a group-theoretical description of the considered collection of atoms is found suitable; the problem of the determination of a basis of collective states and its group-theoretical implications are discussed; in particular, it is found that the isotropic character of spontaneous emission allows us to use tensorial formalism and simplifies the formal description of the problem.

In a recent paper we carried out a rigorous, asymptotic analysis of the low-temperature behavior of a Bose gas confined to a finite cubic geometry and subjected to periodic boundary conditions. That analysis is now extended to Dirichlet, Neumann, and antiperiodic boundary conditions. As before, the thermogeometric parameter $y$ and the condensate fraction $\frac{N_0}{N}$ are studied as functions of temperature and are evaluated explicity for cubes with $\frac{L}{\overline{l}}=40\mathrm{} \mathrm{and} 100$, where $L$ is the edge length of the enclosure and $\overline{l}$ the mean interparticle distance in the system. The finite-size corrections to the condensate fraction under Dirichlet or Neumann boundary conditions turn out to be qualitatively different from those under periodic or antiperiodic boundary conditions. This difference becomes manifest when one tries to express these corrections in a form consistent with the standard scaling theory for finite-size effects.

Measurements of rotational viscosity in the various liquid crystalline phases of TBBA (terephthal-bisbutylaniline) are reported. The quantity measured is the viscous energy dissipation in the liquid crystal as it oscillates in a magnetic field. This dissipation varies greatly in the different smectic phases. It is small in the $A$ and $B$ phases, but large and strongly temperature dependent in the $C$ phase. This behavior is explained in terms of the structure of these phases. The smectic $A$ to smectic $C$ transition is of second order, and the dissipation increases dramatically at the transition point. The critical behavior is found to fit mean-field theory, rather than a predicted heliumlike behavior.

This paper is concerned with the generalized kinetic equation for the motion of a test particle in a weakly-coupled classical fluid. The distribution function for the test particle satisfies a generalized Fokker-Planck equation in velocity. The equation has "memory" and a diffusion tensor that is time and velocity dependent. We study the case of the relaxation of a spatially uniform distribution in considerable detail. In particular, we find that the coupling of interaction, velocity, time, and mass ratio make questionable the traditional methods of solution by expansion in a small parameter.

Stripe domain patterns have been observed in a nematic liquid crystal film excited by ultrasonic waves propagating in a sandwiched glass-nematic-glass medium. The effect was found to be due to molecular reorientation induced by acoustic streaming in the nematic film. Based on a simple fluid dynamical model, we calculated the propagating acoustic modes, their nonlinear mixing which causes acoustic streaming, and the resultant shear flow reorientation of the director which produces the birefringent stripe patterns. Our calculations show quantitative agreement with the measured acoustic modes and the observed stripe domain patterns.