A form of quantum electrodynamics is developed which allows us to treat a number of problems involving dielectric and conducting surfaces, the presence of which leads to a number of new observable effects. A number of suitably defined response functions play a basic role in the present approach, as these in conjunction with the fluctuation-dissipation theorem lead to electromagnetic field correlation functions, which describe physical effects such as lifetimes, frequency shifts of the excited states, dispersion forces, etc. The quantization of the electromagnetic field is only implicitly used. A large part of the present paper is devoted to the calculation of the response functions involving different geometries and various types of dielectrics. Both spatially dispersive and spatially nondispersive dielectrics are considered. The response functions are calculated using Maxwell's equations and the usual boundary conditions at the interface adjoining the two mediums. As a first application of the present approach, the black-body fluctuations in finite geometries and the influence of surfaces on its temporal and spatial coherence are studied. An interesting theorem is also proved which enables us to calculate the normally ordered (antinormally ordered) correlation functions from the symmetrized correlation functions.

The different kinds of response functions introduced in a previous paper are used to calculate the dispersion forces. An exact expression for the interaction energy in a system of harmonic oscillators interacting with a second-quantized radiation field is obtained in terms of appropriate response functions. The radiation field may be either the field appropriate to entire free space or the field altered by the presence of the dielectric. The result is valid for arbitrary geometries involving dielectric and conducting surfaces. An expansion of our result in powers of $e^2$ leads to the results of other authors. The calculation of the dispersion force for the case of excited states is also briefly discussed. Next the problem of the dispersion force between macroscopic bodies is considered. Lifshitz's expression for the dispersion force is rederived using the response functions and the two methods are compared. The role of surface modes in the determination of dispersion force is discussed. Finally the dispersion force between a spatially dispersive and spatially nondispersive dielectric is calculated exactly. When the spatial dispersion is weak, then it is found that the first-order term is repulsive in nature, in contrast to the zeroth-order term which is attractive. As a by-product of our analysis, surface-polariton dispersion relations are obtained.

In this paper the physical entities such as transition probabilities and the density of states are related to appropriate electromagnetic-field correlation functions and to appropriate response functions. Such response functions have already been computed in a previous paper and therefore these can be used to obtain surface-dependent corrections. It is shown how the density of states and hence Planck's law depends on the presence of surfaces. I explicitly calculate the correction terms for the case of a small blackbody bounded by two plane conducting surfaces. An appreciable correction occurs if the linear dimensions of the blackbody are of the order of a wavelength. Next electric-dipole-type transitions in atomic systems are considered and a straightforward perturbation theory is used to obtain one-photon transition probabilities in terms of the surface-dependent response functions. As an illustration of the surface-dependent terms, the transitions in presence of a conducting surface are considered. The transition probabilities show a marked increase or decrease depending on whether the dipole transition is parallel or perpendicular to the surface. Both stationary and nonstationary fields are considered. As a special case of nonstationary fields, the transitions in a coherent field are considered in detail. It is also shown how the coherent radiation field in presence of dielectrics can be realized. It is found that if the radiation field, in arbitrary geometries, is initially in vacuum state then at later times it would be found in a coherent state if perturbed by an external ($c$-number) electromagnetic field.

Transition probabilities for the $3p-3s$ array of Ne i have been measured in emission from a glow discharge containing a He-Ne-Ar mixture. The neon spontaneous emission at 632.8 nm ($3s_2-2\mathrm{}{p}_4$) was taken as the reference line and the emission intensities of the $2p_i-1\mathrm{}{s}_j$ lines were compared with it to obtain the relative transition probabilities $\frac{A(2\mathrm{}{p}_i-1\mathrm{}{s}_j)}{A_{632.8}}$. The discharge condition was carefully controlled so that the ratio of the populations of the $3s_2$ and a given $2p_i$ level was precisely equal to the ratio of the statistical weights of the energy levels: $\frac{N\left(3\mathrm{}{s}_2\right)}{N\left(2\mathrm{}{p}_i\right)}=\frac{g\left(3\mathrm{}{s}_2\right)}{g\left(2\mathrm{}{p}_i\right)}$, eliminating two population unknowns encountered in an ordinary gas discharge. The relative $A$ values were then converted to the absolute values by means of the accurate value of $A_{632.8}$, which was obtained in our recent measurements. The results were subjected to extensive comparisons with other experimental data of Bridges and Wiese, of Bennett and Kindlmann, and the intermediate coupling calculations by Mehlhorn and by Feneuille et al. Excellent agreement was observed throughout between these data sets and our results. The following has been found: Our results are more consistent with the $J$-file-sum rule than any other experimental data; our relative line strengths are in excellent agreement with the theoretical calculations of Feneuille et al.; our radial transition integral ${\sigma }^2$ exhibits least variations over different $2p$ levels—its weighted average has been found to be 6.66±0.02 (a.u.) on an absolute basis, which is very close to the value obtained from the Coulomb approximation; and our transition-probability sums are in excellent agreement with those evaluated from the intermediate coupling calculations combined with the Coulomb approximation. Based on these findings and the error analysis, we estimate the uncertainty of our $A$ values, except for a few weak lines, to be 2% on the relative scale and 6% on the absolute scale. Also, a discussion is given concerning the extent of configuration interaction on the $2p^{5}3p$ states.

The exact solution for the ground state of the quantum one-dimensional $N$-boson problem with attractive $\delta$-function two-body potentials is compared with the (exact) self-consistent solution of the corresponding variational Hartree problem.

A high-temperature expansion is obtained for the density-independent part of the radial distribution function (pair-correlation function) for a quantum-mechanical gas of hard spheres. Explicit expressions are given for the first five terms in this series. Comparison with the numerical values obtained by Larsen shows that our expansion is accurate for all values of the radial distance at moderately high temperatures.

Self-induced transparency in an absorbing neon discharge has been observed on the nonresonance transition $2s_2\mathrm{}(J=1\mathrm{})-2\mathrm{}{p}_4\mathrm{}(J=2\mathrm{})\mathrm{}$. Since linearly polarized light pulses excite two dipole moments differing by only 18%, the absorber is virtually nondegenerate and superior in simplicity to molecular absorbers. Light pulses, generated from the output of a cw single-frequency 1.15-μm He-Ne laser oscillator by a pulsed Ne laser amplifier, were transmitted through the absorber. Comparison of the oscilloscope traces of input and output pulses indicated the occurrence of pulse retardation, peak amplification, and pulse breakup. Complete pulse reshaping to the predicted hyperbolic-secant envelope has been observed. The periodicity of transmission versus pulse power, which provides direct evidence of optical nutation, is in agreement with the results of a pulse-area-pulse-energy model.

The master equation describing the relaxation of a ($2J+1$)-level system is analyzed in the diagonal representation for the density operator using the coherent atomic states as a basis. The $c$-number quasiprobability functions corresponding to the density operator are found to satisfy a second-order partial differential equation on the surface of the Bloch sphere. This equation is solved in the steady-state limit, and a few moments of interest of the atomic operators are calculated in terms of classicallike integrals in the phase space of the atomic variables. In the high-temperature approximation the partial differential equation is solved exactly for all time by a simple eigenfunction expansion procedure. For the special case of a two-level system an exact solution is also available for arbitrary values of the reservoir temperature.

Processes affecting the charge neutralization of intense relativistic electron beams injected into low-pressure neutral gases are investigated. Processes examined include electron impact ionization, electron avalanching, ion impact ionization, ion avalanching, charge exchange, precursor ionization effects, secondary-electron escape, recombination, diffusion, and attachment. Cross sections and analytic estimates are given for each process. The ion avalanche-like process is apparently new and unique to intense relativistic electron beams. Although omitted in past research, the ion ionization effects discussed here can play dominant roles in the charge neutralization process. Pressures of the order of 0.1 Torr ${\mathrm{H}}_2$ are considered specifically, but the results should apply at least qualitatively to even higher pressures and, with appropriate cross sections, to gases other than ${\mathrm{H}}_2$. The results should have immediate relevance to the problems of collective ion acceleration with drifting intense beams, ion loading for the electron ring accelerator, and intense relativistic electron beam propagation in low-pressure neutral gases.

A moment solution to the Boltzmann equation is considered for the initial-value problem of a weakly ionized rarefied gas, or gas mixture, in a uniform electric field. No restrictions are placed on the smoothness of the initial data or the mass ratio between the ions and the neutrals although the theory converges fastest for heavy ions in a light gas. A principal result of this theory is the prediction of shock-wave phenomena in pulsed drift tubes. The result is most persistent for heavy ions in a light gas. For instance ${\mathrm{U}}^{+}$ ions in He can be significantly affected by sharp initial conditions for ${10}^4$ collisions. Comparison is made with the results of asymptotic theories to smooth initial data.

A quantum theory of nonlinear phenomena is considered in which account is taken of all contributions from electric and magnetic multipoles, without any multipolar approximation. Exact closed analytical expressions for the multipoles are first obtained from quantum electrodynamics by applying a generalization of the Power-Zienau transformation. The standard procedure is invoked to calculate general electromagnetic susceptibility tensors ${\chi }_{\mu \nu {\alpha }_1{\beta }_1\cdots {\alpha }_n{\beta }_n}^{\mathrm{}\left[n\right]\mathrm{}}$ (${\omega }_1, \dots , {\omega }_n$). Such a tensor is a shorthand for the electric and magnetic susceptibilities as well as mixed susceptibilities. By considering a relativistic theory based on the Dirac equation, the spin susceptibilities are automatically included. The formalism in this way allows for the computation of a wide range of electro- and magneto-optical effects to any order of perturbation and to any order of multipolar approximation.

The results of neutron scattering experiments with scattering vectors $0.06\le Q\le 0.14$ ${\mathrm{\AA }}^{-1\mathrm{}}$ and $0.27\le Q\le 1.50$ ${\mathrm{\AA }}^{-1\mathrm{}}$ are discussed in terms of hydrodynamics. It is found that the small-$Q$ data, at low densities, exhibit a distinct Brillouin triplet, describable by hydrodynamic theory. At larger $Q$, and at higher density, a hydrodynamic description is still possible with simple $Q$ and $\omega$ dependences of the transport coefficents, namely a heat diffusion $D_T=D_T^0{(1+Q^2{r}_0^2)}^{-1\mathrm{}}$ and a viscosity $\phi ={\phi }^0{\tau }_0^{-1\mathrm{}}{[-i\omega +{\tau }^{-1\mathrm{}}\mathrm{}(Q\left)\right]}^{-1\mathrm{}}$ with $\tau \mathrm{}\left(Q\right)={\tau }_0{(1+Q^2{R}_0^2)}^{-1\mathrm{}}$. The relaxation lengths and times for the establishment of local equilibrium are found to be on the order of a few Angstroms and ${10}^{-13\mathrm{}}$ sec, respectively.

A renormalized kinetic theory is developed for the classical phase-space density correlation function by means of the projection-operator formalism. The technique consists of introducing a sequence of projection operators which project onto spaces involving successively larger numbers of particles. The first such operator is the Akcasu-Duderstadt projection operator, which yields a generalized Langevin equation (kinetic equation) for the correlation function. The structure of the memory function in this equation suggests a second projection operator, which is shown to lead to a two-body kinetic equation for one factor in the memory function. Further projection operators proceed similarly, and the result is a continued-fraction expansion of the correlation function. This expansion is renormalized in the sense that the interparticle potential always drops out in favor of static correlation functions. The expansion is shown to be equivalent to the result of the kinetic theory formulated by Gross. The analogous development for self-correlations is also given.

We solve the familiar Langevin equation with stochastic damping to represent the motion of a Brownian particle in a fluctuating medium. A connection between the damping and the random driving forces is proposed which preserves quite generally the Einstein relation between the diffusion and mobility coefficients. We present an application to the case of a Brownian particle in a critical binary mixture.

Extensions of the Case and Ornstein-Uhlenbeck treatments of rigid-body Brownian motion to an elastically deformable body in $d$ dimensions are given. The motion of Brownian deformations in a fluid is considered to be locally damped by a retarding friction. To describe the expected fluctuations, velocity and displacement space-time correlation functions of a body are obtained from the relaxationfunction theorem. A general equipartition theorem is obtained without postulating certain fluctuating sources. However, it is possible to exhibit those fluctuating sources which would yield our correlation functions, and thus a generalized Einstein relation between fluctuations and retarding dissipations is obtained, which is proved to be necessary and sufficient. Sum rules and both Green's and scattering functions are given for strings, elastically deformable rods, and viscoelastic gels. Curves for the ensemble-average-square displacements and their integrations over the entire length are given.

Starting from interatomic potentials and static radial distribution functions, a self-consistent iteration scheme has been used to calculate velocity autocorrelation functions in liquid metals. The interatomic forces are treated directly. The calculation bypasses the details of the many-body dynamics and it is not necessary to introduce any additional parameters. Several simplifications may be used without introducing appreciable deviations. The results are in good agreement with computer experiments on liquid sodium at 383 °K, suggesting that the velocity autocorrelation function may be a simpler quantity than previously supposed.

A steric model of the smectic-$C$ phase is presented, with molecules assumed to have a symmetric zig-zag shape (this kind of molecular gross shape may arise from obliquely placed end chains). The interaction between such molecules depends on mixed tensors ${\overrightarrow{\nu }}^3{\overrightarrow{\nu }}^2$, etc., as well as on the usual tensors ${\overrightarrow{\nu }}^3{\overrightarrow{\nu }}^3$, ${\overrightarrow{\nu }}^2{\overrightarrow{\nu }}^2$, and similar higher-order tensors, where ${\overrightarrow{\nu }}^3$ and ${\overrightarrow{\nu }}^2$ are unit vectors denoting the directions of the long molecular axis and a transverse axis, respectively. A simple interaction, which includes a term that mimics the effect of the zig-zag shape, is constructed in terms of these tensors. Using quite plausible values for the magnitude of the zig-zag part of the interaction, a second-order phase transition to a smectic-$C$ phase is found, characterized by nonvanishing values of biaxial order parameters $〈{\overrightarrow{\nu }}^3{\overrightarrow{\nu }}^2〉$, etc. In the limit of perfect nematic order, the biaxial order parameters of the model are essentially equivalent to the vector order parameters used by de Gennes and by McMillan. The smectic planar structure is accounted for in the simple density-wave approximation of Kobayashi and McMillan. Only one phase with more orientational order than the smectic-$A$ phase is obtained; this is in contrast to McMillan's dipole model, which shows three different ordered phases (one of which corresponds to the smectic-$C$ phase). The present model predicts that the characteristic biaxialities in the smectic-$C$ phase may easily grow up to values of $O\left({10}^{-1\mathrm{}}\right)$.

Comparison of muonic- and kaonic-atom x-ray data with recent calculations on the formation and deexcitation of mesonic atoms indicates that relative to muons, kaons preferentially populate states of lower orbital angular momentum when initially forming a mesonic atom.

The temporal growth and spatial dependence of a three-wave backscatter parametric instability are obtained for a weakly inhomogeneous but finite plasma. In contrast to the case of an infinite plasma, a slowly varying phase mismatch does not lead to the saturation of the temporal instability.

Sum rules for the forward elastic scattering of photons from bound atomic systems are obtained from the appropriate dispersion relations and the nontrivial zeros of the scattering amplitude. The significance of these sum rules for photon scattering from the hydrogenic atoms is outlined.