High-resolution x-ray spectroscopy has been used to measure the cross sections for forming doubly excited ${\mathrm{F}}^{7+}$ ions in the 2s2p and 2$p^2$ configurations following ${\mathrm{F}}^{8+}$+He, ${\mathrm{F}}^{8+}$+Ne, and ${\mathrm{F}}^{8+}$+Ar collisions over a projectile-energy range of 13–31 MeV. The intermediate states are found to be formed predominantly by projectile-electron excitation coupled with target-to-projectile electron transfer to an excited state during a single ion-atom collision. This process is termed nonresonant transfer and excitation (NTE) [P. L. Pepmiller et al., IEEE Trans. Nucl. Sci. NS-30, 1002 (1983)]. A competing process for formation of the doubly excited states is resonant transfer and excitation (RTE) [D. Brandt, Phys. Rev. A 27, 1314 (1983)], a process analogous to dielectronic recombination. Although the projectile energies spanned the region where resonant transfer and excitation are expected to maximize, no resonant contribution to the measured cross sections could be positively identified for the collision systems studied here. This result is consistent with the relative magnitudes of the theoretical cross sections for resonant and nonresonant transfer and excitation presented in the present work.

The radiative lifetime of 14 levels in the $z^5$F, $z^5$D, and $z^5$G terms of Co ii have been measured with use of time-resolved laser fluorescence spectroscopy with a ${\mathrm{Co}}^{+}$-ion beam. Our lifetime values are shorter by 15–50 % than earlier results from beam-foil time-of-flight measurements. The lifetimes were converted to 41 individual transition probabilities with use of branching ratios measured on spectra recorded with the 1-m Fourier-transform spectrometer at the Kitt Peak National Observatory. On average our transition probabilities agree with those of Kurucz and Peytremann; for ΔS=1 transitions their calculated values are lower than our experimental results by a factor of ∼(1/4).

Target K x-ray production cross sections have been determined for 20–80-MeV ${}_{17}{}^{}{}_{}{}^{}\mathrm{Cl}_{}^{\mathrm{q}+}{}_{}{}^{}$ (q=3–10) ions incident on vanishingly thin (∼10 μg/${\mathrm{cm}}^2$) targets of ${}_{19}{}^{}{}_{}{}^{}\mathrm{K}$, ${}_{22}{}^{}{}_{}{}^{}\mathrm{Ti}$, ${}_{25}{}^{}{}_{}{}^{}\mathrm{Mn}$, and ${}_{35}{}^{}{}_{}{}^{}\mathrm{Br}$. In addition, intensity ratios $I_{K\beta }$/$I_{K\alpha }$ and Kα,Kβ x-ray energy shifts were measured. Using Hartree-Fock-Slater calculations and statistical scaling methods for multiple ionization, the number of 2p and 3p vacancies at x-ray emission is deduced from the Kα energy shifts and $I_{K\beta }$/$I_{K\alpha }$, respectively. From the number of 2p and 3p vacancies at x-ray emission the fluorescence yield ${\omega }_K$ in the presence of this multiple ionization is then determined. The modified values of ${\omega }_K$, which are as much as 40% larger than the single-vacancy fluorescence yields, were used to compare the measured x-ray cross sections with theoretical predictions of ionization from the perturbed-stationary-state (PSS) theory with energy loss (E), Coulomb deflection (C), and relativistic (R) corrections, i.e., the ECPSSR theory of Brandt and Lapicki. Reasonable agreement with theory is obtained for ${}_{17}{}^{}{}_{}{}^{}\mathrm{Cl}$${+}_{35}$Br ($Z_1$/$Z_2$∼1/2) with the agreement becoming progressively worse, as expected, for $Z_1$/$Z_2$→1. The results provide evidence for the validity of the ECPSSR theory for collision systems with $Z_1$/$Z_2$≃1/2 even when $v_1$/$v_{2K}$≃0.3.

The polarized-orbital method [originally developed by A. Temkin, Phys. Rev. 107, 1004 (1957)] is used to calculate the photoionization cross sections of sodium atoms, from threshold to about 60 eV. The polarized orbitals are calculated from Sternheimer’s equation. The polarizability of ${\mathrm{Na}}^{+}$ is found to be 1.0914$a_0^3$, which is very close to the experimental value. The scattering equation is solved in the exchange, the exchange-adiabatic, and the polarized-orbital approximations. For consistency, both the bound-state and the continuum-state wave functions are obtained in the same approximation. In the calculation of these wave functions, all perturbed orbitals are taken into account in the direct polarization potential and only the perturbation of the very tightly bound 1s orbital is neglected in the exchange-polarization terms. The length form for the photoionization-cross-section formula is used and all terms are included in the photoionization matrix element. Our results are in good agreement with the many-body calculations of Chang and Kelly. However, no calculation to date, including this one, agrees well with experiment except at low energies. The phase shifts thus obtained for s, p, and d waves for the e+${\mathrm{Na}}^{+}$ system are used to calculate the differential cross sections; the phase shifts, as well as these cross sections, agree very well with other available results.

The time-dependent difference-potential matrix generated by molecular-dynamics simulation in a system of one sodium atom in a bath of 255 argon atoms is used in a classical-path coupled states formalism to generate a resonance atomic line shape which incorporates the effects of relaxation of polarization. A comparable technique is used to generate the one-perturber spectrum, which is then used in the unified theories of Jablonski, Anderson, and Baranger, of Fano, and of Szudy and Baylis to predict the density-dependent line shape. At the high density used (2×${10}^{21}$ ${\mathrm{cm}}^{\mathrm{-}3}$), the Jablonski-Anderson-Baranger line shape is in excellent agreement with the simulated line shape, but the other unified theories show significant discrepancies. The effects of relaxation of polarization (‘‘m-changing effects’’ in quantum theory) on the line shape were found to be small.

$M_4$,5${\mathrm{N}}_4$,5${\mathrm{N}}_4$,5 Auger-electron spectrum of barium (Z=56) has been measured in the vapor phase with use of electron-beam excitation. The spectrum is characterized by strong anomalous peak structure which cannot be interpreted by the independent-particle description.

The classical theory of oblique-angle-stimulated Čerenkov radiation is developed. It is based on exact solutions for the electron trajectories in the presence of the medium and the stimulating laser pulse. The boundary conditions which are necessary in order to obtain gain are discussed. The gain for weak fields is obtained as a power series with respect to the intensity of the stimulating field, which displays the small-signal gain and saturation corrections. For strong fields numerical solutions are obtained and compared with an approximate analytical expression. The close analogy with the helical wiggler free-electron laser, which is based on a common pendulum equation, is emphasized.

Resonant transition radiation generated by high-energy electron beams traversing a periodic medium has been considered by many researchers as a potential source of both spontaneous and stimulated emission at short wavelengths. To our knowledge, this problem has only been treated classically. This paper presents a quantum-mechanical theory that leads to a unified description of both spontaneous and stimulated emission and agrees closely with the classical results.

We employ a Holstein-Primakoff expansion to derive a collective-mode macroscopic effective Hamiltonian from a microscopic model of a nonlinear optical medium where the atoms are treated as two-level systems.

We derive and discuss the behavior of several multilevel models relevant to the problem of molecular multiphoton excitation under the action of a quasimonochromatic laser field, the amplitude of which rises slowly and falls rapidly on a certain internal time scale. Our method is suitable for the numerical solution of problems involving the adiabatic excitation of large multilevel systems. We find adiabatic inversion to be a general characteristic of the models considered. The fact that adiabatic inversion is accompanied by marked qualitative and quantitative changes in the expectation value of the dipole operator makes our results useful for understanding the propagation of laser pulses. An explicit expression that is especially convenient for numerical evaluation is presented for determining the limiting internal time scale, which is determined by the energy levels and transition moments of the system and the laser frequency. We illustrate the criterion for adiabatic inversion by applying it to a particular multilevel model. From a density-matrix treatment we conclude that collisional damping destroys the coherence required for adiabatic inversion. On the basis of our results we believe that the adiabatic approximation may be appropriate for some experiments of current interest.

A nonperturbative theory is presented for the gas polarization induced by two lasers. The first laser ionizes Li(2s) by three-photon absorption, with the first two photons in resonance with the 3d level. A second laser stimulates recombination into the 3s level, thereby inducing an autoionizing-like structure in the continuum. It is found that the polarization (and hence possibly third-harmonic generation) is enhanced near the induced resonance.

The theory of free-electron lasers is extended to include the new coupling between an electron beam and optical wave propagating at an angle ϑ in an arbitrary harmonic. The coupling allows the laser to be tuned to a wider range of wavelengths and to include the effects of emittance in the electron beam. The formulation of the results in terms of coupling constants means that the existing knowledge of high gain, low gain, weak optical fields, strong optical fields, and short pulses in free-electron lasers can be immediately generalized to off-axis propagation in an arbitrary harmonic.

Starting from basic principles, we develop a description of the electromagnetic interactions of a molecular gas in terms of a set of correlation functions which we call the molecular-electromagnetic correlation functions (MECF’s). First we use the energy eigenfunctions for an isolated molecule of the species of interest to define a set of molecular creation and annihilation operators. We then derive a closed set of operator equations for these molecular creation and annihilation operators and the electromagnetic vector potential. Explicit definitions of the lowest-order MECF’s are given in terms of these operators, and it is shown how the operator equations which have been obtained can be used to derive equations of motion for the MECF’s. Finally, we illustrate the use of the MECF’s in describing physical properties of the molecular gas and the electromagnetic field. Brief indications are given of the application of the MECF formulation to the semiclassical approximation and to the description of quantum emission of radiation, topics which are treated in greater detail in subsequent papers. The basic MECF formulation described here contains three rather mild approximations: (1) Atomic nuclei are treated as elementary particles; (2) nuclei and electrons are treated nonrelativistically; and (3) the effect of molecular collisions with the container walls on the internal molecular state is neglected. Consequently, the physical description contained in the formulation is rather complete; and the MECF results can be used both to provide a sound basis for some aspects of the usual heuristic models, and to ascertain the ways in which those models are incomplete.

A mode-expansion method [R. Asby, Phys. Rev. 187, 1062 (1969)] is used to obtain an explicit expression for the conversion efficiency in the second-harmonic-generation process when the pump-depletion and the diffraction effects are included.

A detailed and systematic investigation of the Painlevé (P) properties of coupled quartic anharmonic oscillators is presented. Considering the two coupled oscillators we show that there exist four different parametric cases possessing P properties, two are identified with strong P property and the other two with weak P property. For each of these four cases explicit second integrals of motion can also be constructed directly. We then consider the three-coupled-oscillator system and identify three cases, one with strong P and the other two with weak P nature. We have explicitly derived the second and third integrals of motion for a special case of the strong P case, but for the remaining cases they have not yet been found. Finally, we extend the procedure to the N coupled oscillators and succeed to show that there exist three cases possessing P properties, which are the natural generalizations of the three-coupled-oscillator system.

Nondegenerate four-wave mixing on the j=0→j=1 transition, in a ‘‘V ’’ system, using orthogonal, circularly polarized pump beams is used to study theoretically the generation of the phase-conjugate signals. The efficiency of generation of the conjugate wave is studied as a function of the various system parameters such as pump-probe detuning, Zeeman splitting, pump-atom detuning, collisional parameters, and the intensities of the pump beams. The origin of the various resonances in the reflectivity is explained. For weak pump fields, some resonances are shown to have subnatural linewidths. In the degenerate case, the reflectivity as a function of pump-atom detuning has, in contrast to a two-level system, a doublet structure for moderate absorption-length parameters and field strengths. The reflectivity is shown to have additional resonances due to pump imbalance. The phase-conjugate signal is also shown to exhibit the pressure-induced extra resonances.

The first-passage-time problem associated with the decay of an unstable state is considered and analytic expressions for the first-passage-time distributions are derived. These expressions are quite general and are applicable to a large class of stochastic processes.

We report a numerical study of the self-diffusion of a single-point particle in a two-dimensional periodic potential of triangular symmetry. The self-diffusion coefficient is obtained via computer simulations for several values of the particle energy. We find that the self-diffusion process is complicated due to the existence of correlated motions involving two or more cells. A random-walk model which takes into account the effects of correlated motions involving only the nearest-neighbor cells is constructed, and compared with the experimental results.

The three-dimensional inverse problem for the scalar time-domain plasma wave equation is discussed using causality and time-reversal invariance. As shown by Balanis in one dimension and by Morawetz and others in three dimensions, the reconstruction of the potential requires only the discontinuity of the wave front at the characteristic surface. A complete solution that can be made rigorous is given for near-field inverse scattering for smooth compact potentials. Two formal methods for far-field inverse scattering from non-spherically-symmetric potentials are presented.

Viscous incompressible fluid flow along a flat plate is modeled by the Navier-Stokes equations with appropriate boundary conditions. A series solution is assumed and a set of three nonlinear ordinary differential equations is derived by truncating the series. The Reynolds number appears in these three equations as a parameter. These equations are solved by numerical integration. We show that these solutions exhibit qualitatively different behavior for different values of the Reynolds number of the fluid. The various modes include an asymptotic approach to a time-independent state, laminar (periodic) flow, and turbulence. We give several computer-generated pictures of the various modes.