A classical optical theory is given for the phenomenon of $\gamma$-ray quantum beats observed by Perlow in a study of the Mössbauer effect of a frequency-modulated source. The intensity $I({\omega }_0-{\omega }_0^{\prime },t)$ of the radiation from such a source transmitted through a resonant absorber is obtained as a function of ${\omega }_0-{\omega }_0^{\prime }$ and $t$, where ${\omega }_0^{\prime }$ is the frequency of an absorber resonance, ${\omega }_0$ is the central frequency of the frequency-modulated source, and $t$ is the laboratory time. An average is taken over the unobserved initial formation time of the excited nuclear state in the source. When viewed at fixed ${\omega }_0-{\omega }_0^{\prime }$, the calculated intensity displays beats in the time spectrum, and when viewed at fixed $t$, the intensity shows dispersion at appropriate values of ${\omega }_0-{\omega }_0^{\prime }$, responsible for the observed enhancement of intensity above background. The harmonic content of the quantum beats is calculated explicitly in the thin-absorber limit, and the observed linear variation about ${\omega }_0-{\omega }_0^{\prime }=0\mathrm{}$ of the ratio of Fourier components $\frac{D_1}{D_2}$ is explained. The use of $\frac{D_1}{D_2}$ to measure small frequency shifts is analyzed by a statistical comparison with the method of switching between steepest points of the line, as used in gravitational-red-shift measurements. The variances are comparable. The effect on $I({\omega }_0-{\omega }_0^{\prime },t)$ of line broadening due to sample inhomogeneities is calculated for a Lorentz distribution of center frequencies in source and absorber, and a prescription is given for modifying the various terms in $I({\omega }_0-{\omega }_0^{\prime },t)$ accordingly. Finally, the effect of a distribution of phase and amplitude of the motion of the vibrating source is discussed.

A laser perturbation method is used to determine the relaxation rate of the $3p{}_{}{}^4{}_{}{}^{}S_{}^o{}_{}{}^{}$ state of atomic nitrogen as function of pressure and current intensity in a glow discharge. Quenching is due to spontaneous radiative transitions towards lower levels and to inelastic collisions with ${\mathrm{N}}_2$ in the vibrationally excited ground state with a thermally averaged cross section of about 7.5×${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$. Measurements allow the determination of the dissociation rate as a function of electronic temperature in the range 1-3 eV.

Various aspects of the laser cooling of atoms are investigated theoretically. More generally, the authors investigate a process through which the kinetic energy of a collection of resonant absorbers can be reduced by irradiating these absorbers with near-resonant electromagnetic radiation. The process is described here as anti-Stokes spontaneous Raman scattering. Cooling mechanisms, rates, and limits are discussed for both free and bound atoms.

The effect of transformations carried out on the Hamiltonian for the Schrödinger electron-photon system is studied. These transformations include gauge transformations and certain similarity and "hybrid" transformations. The last named involve unitary transformations of either operators or states, but not both. Unitary and hybrid transformation are discussed, which affect the transverse components of the electromagnetic vector potentials and therefore are distinct from gauge transformations. A hybrid transformation is identified which leads to a form of the Hamiltonian that contains no reference to the transverse vector potential and includes electric and magnetic fields as well as nonlocal interactions of charges and currents. The behavior of the scattering matrix under the influence of these hybrid transformations is discussed. Comments are made on two-photon absorption calculations.

We define pseudoperturbations as the difference between two Hamiltonians that are related by a generalized gauge transformation. We state and prove the theorem that such pseudoperturbations cannot cause any real physical transitions. We also rigorously establish the generalized gauge invariance of physical transition-matrix elements in real processes. Our theorem also generates some interesting sum rules and onshell identities which can serve as useful constraints in variational calculations.

Relative transition probabilities for spectral lines arising from the $\mathrm{ns}{\left(\frac{3}{2}\right)}_2$ ($n=7,8\mathrm{}$) and $\mathrm{ns}{\left(\frac{3}{2}\right)}_1$ ($n=7,8\mathrm{}$) levels of Kri have been determined by means of emission line-intensity measurements. The lifetime values of the $\mathrm{ns}{\left(\frac{3}{2}\right)}_2$ ($n=7,8\mathrm{}$) levels have been measured by the delayed-coincidence method. With these lifetime values and taking into account the theoretical calculations in $\mathrm{jK}$ coupling and intermediate coupling for the lines beyond the experimental range, the relative transition probabilities were put on an absolute scale. The experimental values of the present work are compared with theoretical calculations.

The leading radiative corrections to the behavior of atoms in time-dependent electromagnetic fields are considered. The results are expressed in closed form for the resonant measurement of the Lamb shift and fine structure of the $n=2\mathrm{}$ levels of hydrogen.

The broadening parameters of five Ci singlets and two multiplets in vacuum-ultraviolet region were determined by measurement of total line intensities and use of experimentally obtained growth curves. The source was a high-current arc with an axial temperature of 12 500 K and electron density of ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Ratios of the theoretical and experimental Stark half-widths of the singlets range from 0.9 to 2.

The inverse scattering technique is used to show that the phase term in the Maxwell-Bloch equations should be set to zero when the slowly varying envelope approximation is assumed for self-induced transparency. A solvable model of two square pulses shifted and inverted with respect to each other is considered, and the threshold for "breather" generation for this profile is shown to correspond to an initial absolute area of $\surd 2\pi$ when the separation between the two pulses is zero, and approaches $\pi$ as the separation is increased. When the two pulses are identical, only breathers are found. Upper bounds on the energy of the $0\pi$ pulses are derived, along with threshold conditions for soliton generation. For an absolute area less than $\pi$ there are no bound solutions.

It is shown that the theoretically derived and experimentally observed differential sum rule for free-free transitions, induced by a long-wavelength laser, is an exact analog to the mutual cancellation of the infrared contributions of spontaneous bremsstrahlung and radiative corrections.

It is pointed out that the electromagnetic interaction $-\hat{\mu }·\hat{E}$ between an atom and a field, in which the atom is modelled as a point dipole of moment $\hat{\mu }$ interacting with the electric field $\hat{E}$, is not strictly consistent with both quantum mechanics and Maxwell's equations. Quantum mechanics allows magnetic point dipoles but not electric point dipoles.

Statistical properties of partially polarized Gaussian light were studied experimentally for degrees of polarization $P$ from 0.03 to 1 by a standard technique of photon counting. The Gaussian light with an arbitrary degree of polarization was obtained from Rayleigh scattering of orthogonally polarized laser beams. The factorial moments up to sixth order of the photoelectron distribution were measured with an arbitrary temporal and spatial coherence. After corrections were taken for the experimental conditions, the theoretical values of these factorial moments were compared with the experimental results. It is shown that the theoretical predictions were quantitatively well verified by the present measurements. The microscopic process is discussed from the standpoint of the light scattering system used in the present measurements, and it is shown that the orthogonally polarized components of the scattered light observed are statistically independent.

A set of adsorption isotherms of Ar on the basal face of graphite gives for the critical temperature of two-dimensional condensation in the first adlayer a value of 59±1 K, significantly different from that previously accepted. This value, together with those obtained for Kr and Xe, agrees well with the prediction of a virial expansion truncated after the fourth coefficient, suggesting that the liquid phases of the first monolayers of noble gases adsorbed on graphite are not significantly perturbed by the surface structure.

The spectrum of the velocity-autocorrelation function at small frequencies is evaluated within mode-coupling theory for liquid argon at the triple point and for liquid rubidium. We investigate the dynamical processes limiting the asymptotic range over which the low-frequency square-root cusp of the spectrum can be observed. The frequency dependence of the shear viscosity is shown to have the largest effect upon the suppression of the anomalous long-time decay of velocity correlations. Our results indicate that in the high-density fluids considered the above anomaly shows up only as a percent contribution to the spectrum below some ${10}^{11}$ ${\sec }^{-1\mathrm{}}$.

By including the theory of fluctuations in the axioms of thermodynamics it is shown that thermodynamic systems can be represented by Riemannian manifolds. Of special interest is the curvature of these manifolds which, for pure fluids, is associated with effective interparticle interaction strength by means of a general thermodynamic "interaction hypothesis." This interpretation of curvature appears to be consistent with hyperscaling and two-scale-factor universality. The Riemannian geometric model is a new attempt to extract information from the axioms of thermodynamics.

The relation of the second law of thermodynamics to the power conversion of fluctuation energy is analyzed using the master equation of the model for the conversion circuit. The performance equation for independent particles shows that the power-conversion performance is given by the second law both for classical and quantum-effect diodes. The relation of the second law to power-conversion models based on the theoretical and experimental results for diode performance for interacting particles exhibiting manybody, multiparticle, or other anomalous and excess-current effects is examined. The performance equations are derived from the master equation for models for interacting particles to determine the conditions required by the second law for power conversion. These conditions are given in terms of the distribution throughout the power-conversion circuit for all the parameters that determine the particle and multiparticle barrier-crossing probability such as the effective mass and spectral density functions. Circuits for spectroscopic measurements for power-conversion circuits with interacting particles are noted. Using selected experimental values for the diode nonlinearity factors in these circuits, open circuit voltages are computed that are not predicted by the second law of thermodynamics.

Magnetic-field-induced bend-splay deformation experiments are presented which show that the linear Frank-Oseen theory of nematic curvature elasticity is valid near a continuous nematic-smectic-$A$ transition where smectic fluctuations dominate the bend elasticity. The results are compared with the Chu-McMillan criterion for the limit of linear response based on the smectic-$A$ superconductivity analogy. It is shown that the success of the linear theory may be due to the unexpectedly small values of the longitudinal and transverse correlation lengths found in recent x-ray experiments.

For a large class of nonlinear stochastic processes with pure multiplicative fluctuations the corresponding time-dependent Fokker-Planck-equation is solved exactly by analytic methods. A universal eigenvalue spectrum and the corresponding set of eigenfunctions are obtained in closed form. The eigenvalue spectrum consists of a discrete as well as a continuous part. To emphasize the significance of the model proposed for the description of more-general stochastic processes the authors investigate its stability with respect to the inclusion of weak additive fluctuations. A discussion of the differences in the static as well as the dynamic behavior of multiplicative and additive stochastic processes is given in detail. It is shown explicitly how internal as well as externally imposed fluctuations can lead to multiplicative stochastic processes. The applications of the results to various fields such as nonlinear optics—subharmonic generation, parametric three-wave mixing, Raman scattering—electronic devices, autocatalytic chemical reactions, and population dynamics are given. In particular, a comparison with recent experiments by S. Kabashima et al., who investigated the statistical properties of electronic parametric oscillators driven by external noise, is carried out.

The viscosity of a 50% mixture of soft spheres (i.e., particles which interact according to the force law $\phi =\frac{d}{r^{12}}$) has been simulated by applying nonequilibrium molecular dynamics to a system of 108 particles. Results for several size (actually $d$) and mass differences are given and compared with the predictions of a conformal-solution Van der Waals 1 theory. To construct this theory, it was necessary to derive a mixing rule for the mass. Overall, agreement between theory and simulation is satisfactory to size differences of about 14% and to mass differences of about 5%. It is pointed out that nonequilibrium molecular dynamics is a powerful technique and appears well suited to this particular application: The simulated viscosity of the mixture can be obtained to within about 5% accuracy for the 108-particle system by applying a shear to the system and following its behavior for about 7000 time steps.

The results of direct measurements of the principal indices of refraction in the smectic-$A$ and smectic-$C$ phases of two homologous liquid crystals are reported. These results are compared qualitatively with the orientational model of Straley and with a model based on anisotropic nematic fluctuations due to coupling between orientational and translational order.