The authors have measured cross sections for the capture of $K$-shell electrons from Ne and C (in C${\mathrm{H}}_4$) by ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{2+}$, and ${\mathrm{Li}}^{3+}$ projectiles, and of $L$-shell electrons from Ar by ${\mathrm{H}}^{+}$ in an energy range from 0.4 to 3 MeV/amu. Detection of $K$- or $L$-Auger electrons from the target in coincidence with charge-changing projectiles was used to obtain the ratio of capture to total vacancy-production cross sections from the inner shell of interest. This ratio was found to become as high as 43% for the case of ${\mathrm{He}}^{2+}$ on C${\mathrm{H}}_4$, giving direct evidence that inner-shell capture becomes an important inner-shell vacancy-production mechanism as one approaches symmetric collisions. Independent measurements of total inner-shell vacancy production were performed, allowing the capture cross sections to be deduced. The capture cross sections increase slightly less rapidly with projectile charge than would be expected on the basis of first-order perturbation-theory Oppenheimer-Brinkman-Kramers (OBK) scaling rules, while scaling from one target shell or nuclear charge to another shell seems better described by these rules at high velocity. Breakdown of the OBK scaling rules occurs at low velocities. A comparison of experimental cross sections with various theoretical results is presented and discussed.

The authors have measured the two-photon correlation function in 632.8-nm single-mode He-Ne laser light which had been amplified by stimulated emission in a long He-Ne discharge tube. For laser light intensities which were comparable with the discharge-tube spontaneous-emission intensity into a single mode, the measured correlations agree well with those predicted for a simple mixture of laser and chaotic light. The results are consistent with the assumption that laser light linearly amplified by stimulated emission has the same statistical properties as unamplified laser light.

Orientation and alignment relaxation cross sections have been obtained for the $3{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and $3{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states of sodium by measuring resonance broadening of Hanle-effect signals at vapor densities up to about ${10}^{15}$ atoms/${\mathrm{cm}}^3$. In order to avoid reabsorption of the resonantly scattered light, the Hanle effect is measured in a region close to the wall of a specially constructed vapor cell. The width of the Hanle-effect signals is found to vary linearly with vapor density. The resulting cross sections for orientation and alignment relaxation are compared with theory.

$K$ x-ray transitions resulting from collisions between F projectiles, with charge states ranging from $1^{+}$ to $9^{+}$, and He atoms have been observed. Production mechanisms leading to projectile $K$ x rays include $K$-shell electron excitation, single $K$-shell multiple $L$-shell vacancy production, and electron capture. The measured F $K$ x-ray production cross sections range from ${10}^{-22\mathrm{}}$ ${\mathrm{cm}}^2$ for low charge states to ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for incident bare ions. Using calculated average fluorescence yields, the $K$-shell electron excitation, single $K$-shell, single $K$-shell + single $L$-shell, single $K$-shell + double $L$-shell ionization, and electron-capture cross sections have been determined. The measured ionization cross sections are found to decrease with the increase in projectile charge state, whereas single-$K$-shell electron-excitation cross sections increase with the increase in projectile charge state.

A cw dye-laser beam tuned to the high-frequency wing of the Na $D_2$ line (at 2-6 GHz from the center of the $D_2$ line) is focused into a Na vapor, forming a self-focused laser filament. The incident laser beam, which is mainly single frequency, contains very weak sidebands at about ± 1 GHz from the main frequency and of intensity ∼ ${10}^{-3\mathrm{}}$ of the main frequency. Such sidebands are found to be strongly amplified by the vapor. Amplification factors in excess of 100 have been observed at suitable Na density, laser power, and detuning. Such strong sideband amplification, previously unknown, is explained as an off-resonant stimulated Raman scattering process.

Calculations are presented for the effective photoionization cross section of the ${\mathrm{}\left(\mathrm{ns}\right)\mathrm{}}^2{\mathrm{}\left(\mathrm{np}\right)\mathrm{}}^4{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ level in O, S, Se, and Te, via excitation to autoionizing levels. The eigenvalues and eigenfunctions of 67 odd-parity levels with $J=1\mathrm{}$, both bound and autoionizing, are obtained via the diagonalization of a matrix including both configuration and spin-orbit interaction. The diagonal entries in the matrix are experimental values, where possible, as a constraint on the calculations was agreement between calculated and experimental energy levels to better than 200 ${\mathrm{cm}}^{-1\mathrm{}}$. The ${\mathrm{}\left(\mathrm{ns}\right)\mathrm{}}^1{\mathrm{}\left(\mathrm{np}\right)\mathrm{}}^5{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ levels are included, but do not satisfy the constraint for S, Se, and Te. The calculations on Te support the tentative level identifications of Bartelt, and suggest that the Te ionization potential in Moore's Tables in 800 ${\mathrm{cm}}^{-1\mathrm{}}$ too low. The calculations indicate that while the effective photoionization cross section for ${\mathrm{}\left(\mathrm{np}\right)\mathrm{}}^4{}_{}{}^1{}_{}{}^{}S$ is surprisingly large and broad for S, Se, and Te, there are windows in the spectrum for S and Se. These windows would permit efficient production of large ${}_{}{}^1{}_{}{}^{}S$ population densities via photodissociation of OCS or OCSe without substantial quenching of the ${}_{}{}^1{}_{}{}^{}S$ population via photoionization and secondary-electron superelastic scattering, e.g., Se at 1720 Å.

Using a heat-pipe furnace as an absorption cell to contain the sodium vapor, the author measured the sodium $K$ absorption-edge spectrum on a double-crystal monochromator. The primary features were a prominent resonance line at 1073.2 eV, a shoulder at 1074.3 eV, a weak peak at 1076.5 eV, and broad lesser features above the threshold. From an identification of the strong and weak peaks as $1s^{2}2s^{2}2p^{6}3s{}_{}{}^2{}_{}{}^{}S\to 1s2s^{2}2p^{6}3s\left({}_{}{}^3{}_{}{}^{}S\right)np{}_{}{}^2{}_{}{}^{}P$ ($n=3,4\mathrm{}$), the series limit of $1s2s^{2}2p^{6}3s{}_{}{}^3{}_{}{}^{}S$ at 1078.5±0.5 eV is obtained in good agreement with the experimental value from the $K-LL$ Auger spectrum and calculated relaxed-orbital $K$-electron binding energy. The lesser features above threshold are interpreted as transitions to autoionizing states in correspondence with the MgI optical spectrum.

A theory of Stark broadening of hydrogenic radiators which adds ion dynamic corrections to the unified theory of Smith, Cooper, and Vidal is presented. The dynamic parts of the ion collisions are treated in an impactlike approximation, which is justified for certain plasma conditions by the static-ion field cutoff in the ion interaction integrals. Approximate results are presented for the Lyman-$\alpha$, Lyman-$\beta$, and H-$\alpha$ lines of hydrogen, and comparison is made to experiment and to other theories.

The bremsstrahlung spectrum due to complete absorption of ${}_{}{}^{32}{}_{}{}^{}\mathrm{P}$ $\beta$ rays in thick aluminum absorbers in a sandwich geometry is measured in an energy range of 30-1300 keV. The spectral distribution after correction for detector response and target self-absorption is compared with various theoretical calculations. It is found to agree with the Bethe and Heitler theory corrected for Coulomb effects within 15%, but disagrees with calculations of Wyard and Rezanka et al.

This paper presents a fully classical theory of the free-electron laser. The theory is formulated in a moving frame where the pseudoradiation field due to static wiggler magnet is in resonance with the laser field imposed by an optical cavity. The basic amplification process is then one of elastic scattering. In this frame both fields are treated classically, as is the electron motion. When the laser and wiggler fields are taken to be constant during the interaction period, it is shown that the laser operation can be described by the classical pendulum equation. This is used to evaluate the unsaturated gain and momentum distribution. For the saturated situation numerical results are given, which have been obtained by the use of the Jacobi elliptic functions. The new features found are singularities in the momentum distribution and their evolution with intensity, saturation enhancement of the gain and the possibilities of bistability and hysteresis entailed by it, and the possibility of discussing and interpreting the various features in a unified way. Finally, a detailed discussion of the approximations and their validity is given.

A gaseous atomic or molecular system with four energy levels $E_a<E_b<E_c<E_d$ which is stimulated by resonant laser pulses at frequencies ${\omega }_1\simeq {\omega }_{\mathrm{ba}}$, ${\omega }_2\simeq {\omega }_{\mathrm{cb}}$, ${\omega }_3\simeq {\omega }_{\mathrm{dc}}$ is considered. The six photon echoes which are stimulated by first and second pulses at frequencies ${\omega }_1$, ${\omega }_2$, ${\omega }_3$ are discussed. For wave fronts which are described by $e^{i(\varphi -\omega t)}$ the echo phase is described by ${\varphi }_E=\Sigma (2\mathrm{}{\varphi }_m^{\mathrm{II}}-{\varphi }_m^{\mathrm{I}})$ at the sum frequency ${\omega }_1+{\omega }_2+{\omega }_3$ with $m=1,2,3\mathrm{}$, at ${\omega }_1+{\omega }_2$ with $m=1,2\mathrm{}$, at ${\omega }_1$ with $m=1\mathrm{}$, etc. For waves in the $z$ direction where $\varphi =\kappa \mathrm{}(x,y,z)+kz$ the gradient of the phase yields the wave-vector direction ${\overrightarrow{\mathrm{k}}}_E=\Sigma (2\mathrm{}{\overrightarrow{\mathrm{k}}}_m^{\mathrm{II}}-{\overrightarrow{\mathrm{k}}}_m^{\mathrm{I}})$ in a physically thin sample. A probe pulse at ${\omega }_2$ and ${\omega }_3$ after the second pulse can generate a probe-pulse echo at ${\omega }_1$ with phase ${\varphi }_1=\Sigma (2\mathrm{}{\varphi }_m^{\mathrm{II}}-{\varphi }_m^{\mathrm{I}})-{\varphi }_2^S-{\varphi }_3^S$, etc., for other frequency arrangements. Transverse phases ${\kappa }_m\mathrm{}\left(\mathrm{xy}\right)\mathrm{}$ can be added and subtracted, but no application is suggested for this novel feature. When all ${\kappa }_m$ except one are zero, phase conjugation or phase-adaptive optics can occur.

The intensity and amplitude correlation functions of the optical field of a ring laser at line center are calculated, under conditions when the two pump parameters corresponding to the counter-rotating traveling wave modes are not necessarily equal. This represents a generalization of earlier treatments by M-Tehrani and Mandel (1978) and Hioe (1978). The laser is assumed to be at rest. A perturbative technique is used to express the correlation functions for a small difference $\epsilon$ of pump parameters in terms of the solutions for $\epsilon =0\mathrm{}$. It is found that the cross correlations are unchanged to the first order in $\epsilon$, whereas the autocorrelations both of the light amplitude and of the light intensity are modified. Curves are presented to illustrate the behavior.

We consider the problem of two-photon transitions between atomic levels having the same parity. The semiclassical theory is developed from Maxwell's equations and the resulting transcendental equations for the pulse envelope solved exactly. They lead to an unstable pulse envelope if the higher-order processes are included. We then treat the laser as a birth/death process, deriving a Markovian (macroscopic) master equation for the probability function, which may be solved exactly in the steady state. By a suitable truncation procedure, this equation predicts a stable steady-state envelope, and is consistent with the microscopic quantum theory when virtual processes are neglected. A comparison is made between the macroscopic (master equation) approach and the microscopic quantum theory at the level of the moment equations. We find that, in the high-gain limit, the fluctuations predicted by the two theories are the same.

We consider a gas of homogeneously broadened two-level atoms in a Fabry-Perot cavity injected with a coherent resonant electric field. Adopting a macroscopic birth-death description, we construct a stochastic master equation for the output intensity distribution. From this starting point we find the steady-state distribution and show it to be bimodal in the region of the optical bistability. We compare our results for the mean and variance with the microscopic results of Bonifacio, Gronchi, and Lugiato as a test of the stochastic-master-equation approach.

The resonant response of a multilevel atomic system to strong coherent radiation is analyzed using an extension of the methods of time-independent scattering theory, adapted to the density-matrix formalism in order to include thermal bath effects. General steady-state expressions are derived for self-attenuation and resonance scattering rates in strong saturating fields, as functions of the coupling strengths, relaxation parameters, and frequency detunings. Formal expressions are given for radiative-damping and collision-broadening relaxation parameters, relating the latter to scattering amplitudes. Modifications of collision-broadening parameters by the presence of very strong fields are discussed. The Bloch equations are derived by transformation to the time domain, under specified conditions.

A general theory of optical bistability for a homogeneously broadened two-level system in a Fabry-Perot interferometer is presented. Both absorptive and dispersive mechanisms are included, and in the mean-field approximation a cubic state equation is derived relating transmitted intensity to all physical parameters. From the perspective of catastrophe theory, this equation describes an elementary cusp catastrophe. We show that bistable switching may follow not only from sweeping the incident laser intensity, but also with continuous variation of atomic or cavity detuning, or atomic density, with the laser intensity fixed. For the case having incident intensity as the variable control, the domain of bistability is studied in some detail as a function of the remaining fixed parameters. Stability criteria are considered for the general case including both absorption and dispersion.

An ensemble is developed which allows not only for variable numbers of particles, as in the grand ensemble, but also for variable numbers and kinds of particle species. In this "great ensemble" a new "speciation" modulus enters besides temperature and chemical potential. In situations of appreciable speciation, such as in chemical or nuclear reaction networks, it is shown how all questions of equilibrium composition may be approached.

The hydrodynamic theory of the smectic and the nematic phase is generalized to the vicinity of the nematic-smectic-$A$ phase transition by including the motion of the three slowly relaxing quantities. The sound spectrum is recalculated and found to be in agreement with recent experimental data on the dispersion and damping of first sound. In addition, the theory predicts two interesting effects for the nematic phase: (i) a smectic layer ordering induced by a stationary shear flow, and (ii) the existence of high-frequency shear waves.

Studies of the time dependencies of the Csii spectral emission and ${\mathrm{He}}^m\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ number density were made during the decay period of plasmas produced in helium-cesium gas mixtures. Transitions originating from 15 Csii energy levels (in the spectral range from 380 to 750 nm) were observed in the afterglow. One Csii energy level is produced by the Penning ionization of Cs by ${\mathrm{He}}^m\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$. Six Csii excited states are populated by charge exchange between ${\mathrm{He}}_2^{+}$ and Cs, and the remaining Csii energy levels are formed by an excitationtransfer process between ${\mathrm{He}}^m\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ and ${\mathrm{Cs}}^{+}$. No evidence was found for the production of excited cesium ions by charge transfer between ${\mathrm{He}}^{+}$ and Cs. A value of 7×${10}^{-10\mathrm{}}$ ${\mathrm{cm}}^3$${\sec }^{-1\mathrm{}}$ was measured for the reaction-rate constant for energy exchange between ${\mathrm{He}}^m\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ and Cs.

The Onsager-Machlup Lagrangian defined by the functional-integral representation of general continuous Markov processes is derived explicitly and concisely. Attention is given both to the mathematics and its physical interpretation. The method is based on (i) the consideration of continuous and differentiable paths connecting fixed end points in the convariant propagator, (ii) the application of a recently developed Fourier-series analysis of these trajectories in locally flat spaces, and (iii) the use of the proper transformations between locally Euclidean and globally Riemannian geometries. The spectral analysis allows for arbitrary paths rather than an a priori straight line even in the short-time propagator and avoids any ad hoc discretization rule. Specialized to globally flat spaces the result agrees with formulas given by Stratonovich, Horsthemke and Bach, Graham, and Dekker. It is demonstrated that a unique covariant path integral is equivalent to a whole class of stochastically equivalent lattice expressions.