Power per unit solid angle, spectrum and polarization as a function of angle, and integrated spectrum are calculated for the radiation from a beam of ultrarelativistic ($\gamma \gg 1$) charged particles in a magnet causing a deflection much smaller than $\frac{\mathrm{I}}{\gamma }$, with an arbitrary form of the magnetic field $B\left(z\right)\mathrm{}$. Some examples are given, and the connection with the "edge effect" is shown.

A semiclassical treatment is given for the serial, near-resonant interaction of three waves in seven equivalent four-level atomic or molecular systems. Explicit equations are presented for the complex susceptibilties for the three waves, valid for $t\gg T_2$, which contain implicit ac Stark-shift and -splitting information, and can be separated into one-, two-, and three-photon contributions. For the case of a weak third or terminal wave, equations for the degree of ac Stark shifting and splitting are found and indicate that the three-photon or triple-resonance contribution is immune to the optical Stark effect if the remaining two waves are tuned to at least two-photon resonance conditions. The conditions for Doppler-free triple resonance are outlined, and it is shown that an equivalent ac Stark broadening may exist but may also be minimized by an appropriate choice of field intensities.

By employing an analogy with a spin-$J$ system in a constant magnetic field the authors obtain a simple soluble model for stepwise laser excitation of an $N$-level system ($N=2J+1\mathrm{}$), including analytic treatment of Doppler detuning and of ionization loss. The solutions are periodic and hence permit complete population inversion. A simple graphical realization of the population dynamics, a generalization of the Feynman, Vernon, and Hellwarth vector model of the two-level Bloch equation, is then described.

The quantum-mechanical theory of optical bistability developed in an earlier paper is generalized to calculate the absorption spectrum (gain coefficient) of an optically bistable system in the presence of a weak probe field. The behavior of the gain coefficient on the cooperative branch and the single-atom branch is analyzed in detail.

A quantum-mechanical model of a damped harmonic oscillator (both with time-independent and time-dependent parameters) is studied in the framework of the linear Schrödinger equation with a Hermitian nonstationary Hamiltonian. Integrals of the motion of this equation and their eigenstates, including coherent states, are constructed. The influence of an external harmonic force to the time evolution of various average values calculated over coherent states is considered, including the resonance case. The specific symmetry of the Hamiltonian leading to the new concept of loss-energy states is discussed.

By a solution of the dynamical inverse problem of the classical Liouville equation is meant finding in general the time-dependent Hamiltonian function $H$ which gives rise to a given phase-space density $\rho$. Both $H$ and $\rho$ satisfy the same Liouville equation. The authors find some simple properties of such solutions and show that explicit, unique solutions exist, subject to some physically well-defined subsidiary conditions, when $\rho$ is chosen to be the solution of the usual Fokker-Planck equation for one or $N$ one-dimensional free particles, particles in a constant external potential, or harmonically bound particles. We speculate on the possibility of a relationship between the Brownian motion giving rise to the Fokker-Planck equation and the solutions of Hamilton's equations generated from the Hamiltonian obtained from the solution of the dynamical inverse problem for these cases.

Enhanced electron-density fluctuations in a plasma jet are produced by the nonlinear interaction of the plasma with two pulsed dye-laser beams, one of which is of variable frequency. The properties of the enhanced fluctuations are studied as a function of the laser intensities and frequencies by observing the spectra of ruby-laser radiation scattered by the density fluctuations. The ruby laser also pumps the dye lasers. The dependence of the scattered signals on the laser intensities is well described by theory, but the response of the plasma to mixing forces of variable frequency is anomalous.

Several spectrum lines from forbidden transitions in the ground configurations of highly ionized atoms have been observed in the discharges of Princeton Large Torus tokamak. Such lines allow localized observations, in the high-temperature regions of the plasma, of ion-temperatures, plasma motions, and spatial distributions of ions. Measured absolute intensities of the forbidden lines have been compared with simultaneous observations of the ion resonance lines. Model calculations have been carried out in order to deduce the relative importance of electron collisions and radiative decays in establishing excited-state populations.

The gradient correction to statistical kinetic free energy, well known at zero temperature, is generalized to finite temperatures, following the prescriptions of the density-functional formalism. The coefficient of the gradient term, a function of electron density, is explicitly determined, and an accurate approximation, suitable for numerical computation, is given. The corrected kinetic free energy, with a phenomenological extrapolation to all temperatures of the exchange and correlation contribution, is applied to equation-of-state calculations. Results are presented in the case of Be, Al, and Cu, for temperatures up to 50 eV and compressions 0.1, 1, and 10, and the influence of the gradient correction is discussed.

The influence of hydrodynamic interactions on the coarsening rate $r$ of a mist of droplets combining through diffusive coalescence is examined in detail. For a sufficiently rarified mist, the competing Lifshitz-Slyozov or evaporation-condensation mechanism is dominant, but the volume fraction of precipitate actually produced in most off-critical quench experiments probably favors direct coalescence. When the minority phase is continuous, as in a quench at the critical concentration, surface-tension effects lead to a crossover from $r\sim t^{\frac{1}{3}}$ to $r\sim t$, where $t$ is the time.

Using the quasistatic approximation as basis for the description of broadening by ion-produced fields and the impact approximation for electron-produced high-frequency fields, an analytic approximation procedure is developed and applied which allows for slow variations of the total field acting on a radiating atom. This low-frequency Stark broadening depends on the radiator velocity and is therefore correlated with the thermal Doppler broadening. The theory is extended to Lyman-$\alpha$ lines of hydrogenic ions.

The dispersion relation for capillary waves on isotropic fluids is written in a dimensionless form appropriate for propagation experiments and solved numerically. Using a recently developed technique to generate and detect capillary waves, the authors have observed a second mode on a highly viscous fluid whose characteristics are in good agreement with theory.

Accurate calculations by Shih and Uang of the surface tension and surface energy of argon at 85 K are used to extract the interfacial thickness. The data indicate that 80% of the transition from liquid to vapor takes place in about 4.5 Å.

The conclusion predicting no practical power output from the power conversion of energy fluctuations is shown to be the result of fundamental errors in physics and in the theory of the master equation. One decisive error was to compute the output voltage by assuming that no energy for the electron barrier crossings of the cold diodes is supplied by the fluctuation energy of the heated diode. Another fundamental error in the physics was to assume that the total available fluctuation power is small, whereas it is orders of magnitude larger than the radiated power alone. Computations using the master equation corrected for errors in physics give a maximum output power that is within (91-99)% of the Carnot-cycle efficiency for this reversible cycle. Physically realizable diode design options are noted (thin film, quantum effect, thermionic) that can enable the high power output and high-efficiency potential of this approach to be achieved with small material cost.

The orthogonally-spin-adapted form of the nonlinear system of equations for the extended coupled-pair many-electron theory, which involves the monoexcited, biexcited, and triexcited states and cluster components, is derived. A diagrammatic approach, based on second quantization, the time-independent Wick theorem, and the graphical methods of spin algebras, is employed. The advantages of using the orthogonally-spin-adapted states and cluster components, rather than the nonorthogonally-spin-adapted ones which have been previously employed, particularly in the triexcited case, are also discussed. It is also shown that the formulas for the direct configuration-interaction method can easily be obtained in compact form from the linear part of the system of extended coupled-pair equations.

An approach for treating electron capture into arbitrary principal shells or into continuum states of energetic projectiles is developed. The approach is based on the momentum-density matrix of the captured electron summed over all substates $l$, $m$ or integrated over all emission angles, respectively. In conjunction with the kinematics of energetic capture reactions it leads to drastic simplifications in capture theories. Within the eikonal approximation, the present approach yields an exact result for the cross section describing capture of hydrogenic $1s$ electrons into hydrogenic bound or continuum states of the projectile. The final result is a simple analytical expression factorizing into the Oppenheimer-Brinkman-Kramers cross section times a scaling factor between 0.1 and 0.4. The theoretical scaling factor for the total cross section turns out to be a function of $\frac{v}{v_K}$ (the ratio of projectile velocity to target $K$-shell velocity) which is approximately independent of the target and projectile charges. For hydrogen and helium targets surprisingly good agreement is obtained with a large body of experimental data.

The semiclassical scattering theory of Mott and Massey and Ford and Wheeler is here extended to multichannel scattering as occurs at a crossing or pseudocrossing of the transient molecule formed by the colliding atoms. The generalized theory incorporates both interference and diffraction phenomena, but the emphasis in this work is on diffraction. For small-angle scattering, diffraction effects become broader, not narrower, as the collision energy increases: $\Delta b\Delta \tau \ge \hslash {\left[\frac{E_{\mathrm{inc}}}{\mathrm{}\left(2m\right)\mathrm{}}\right]}^{\frac{1}{2}}$ relates the uncertainties in impact parameter $b$ and reduced scattering angle $\tau =E_{\mathrm{inc}}\theta$, and determines the range in $b$ required to resolve a structure in the deflection function of height $\Delta \tau$. In the kilovolt range of collision energies, the effects of local maxima and minima in the deflection function are washed out, and the Airy-function approximation of Ford and Wheeler is inappropriate to describe the differential cross section. More generally, it is shown that at keV collision energies the stationary-phase approximation, heretofore essential in the reduction to the semiclassical limit, breaks down in the vicinity of a level crossing. An approximate theorem is proposed which remains valid in this region and elsewhere reduces to the standard stationary-phase approximation. Several illustrative examples are considered. A separate development treats the effect on the differential scattering cross section of a change in electronic angular momentum when electronic excitation occurs.

A method used previously for inner-shell ionization in asymmetric ion-atom collisions is extended to include charge transfer between the target inner shells and projectile $K$ shell. We work in the energy range ${\eta }^{\frac{1}{2}}=\frac{\hslash v}{Z_N{e}^2}\lesssim 1$ and use an independent-electron model (Hartree-Fock) for the target. We treat the interaction with the projectile as a time-dependent perturbation due to a bare charge moving on a straight-line path. Our method, as for ionization, is very efficient in that with our target-centered expansion of the system wave function, all requisite matrix elements needed at a particular projectile energy are pretabulated and used at all impact parameters. A critical feature of our results is the recognition of the importance of target continuum states of energy approximately equal to the kinetic energy (in the target frame) of the electron on the projectile, and the development of a method to properly include such resonance states in our pseudostate calculation. We present selected numerical results to illustrate our method and to demonstrate the projectile energy and nuclear charge dependence of the cross sections. A general feature of the results presented is that the computed cross sections are of the order of 0.3-0.5 times the Brinkman-Kramers estimate. Simultaneously, we also compute cross sections for electron stripping of the projectile, and find them to be dominated by transitions to the above-described resonant continuum state of the target.

Total cross sections for the scattering of 2-50 eV positrons by helium and neon atoms have been measured using the time-of-flight technique, and are compared with recent experimental and theoretical results. The measurement of positron energies and the flight path length is described and possible sources of systematic errors, including the effects of small-angle forward scattering, are fully discussed.