A recent experiment in which an electron scattering off an atom at a resonance energy is excited to a higher resonance energy by absorption of a laser photon is analyzed. There is more than one mechanism for the reaction, but the cross section, as a function of the laser frequency, is shown to have only one peak for each pair of electron-atom resonance states which can be connected by absorption of a photon. The width of the peak is the width of the upper resonance state.

A generalized master equation previously proposed to describe oscillatory superfluorescence is numerically solved in the case of strong ringing. When the atomic system is fully excited, anomalous fluctuations and large atom-field correlations make the time evolution of the mean quantities (e.g., number of photons, total population inversion) quantitatively different from those found in the semiclassical treatment. In particular, because of fluctuations, the minima of the radiation output are notably larger than zero. On the contrary, when the atomic system exhibits a sizable initial macroscopic polarization (superradiance), we find a remarkable non-Markoffian effect consisting of a sizable delay in the radiation emission. However, in such conditions all quantum effects disappear, as in the case of pure superradiance.

A generalization of previously reported statistical theories is developed for determining the excited-level populations and the ionization-recombination balance of multiply charged atomic ions in an optically thin high-temperature plasma. Account is taken of the most important collisional and radiative processes involving bound and autoionizing levels in three consecutive ionization stages. We obtain a set of rate equations for the population densities of the low-lying levels which contains effective excítation, ionization, and recombination rates describing indirect transitions through the more highly excited bound and autoionizing levels. The familiar corona-model equations for the ground-state populations are recovered by making the assumption that all excited states decay by only spontaneous radiative or autoionization processes. When collisional processes become efficient in depopulating the highly excited levels important in dielectronic recombination, the effective rate of recombination must be described by a collisional-dielectronic recombination coefficient. Results of calculations are presented for the collisional-dielectronic recombination rate coefficients for recombination of ${\mathrm{Fe}}^{+8\mathrm{}}$-${\mathrm{Fe}}^{+13\mathrm{}}$ ions. At an electron density of ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$, dielectronic recombination is still the dominant recombination process. However, the collisional-dielectronic recombination rate coefficients are found to be reduced by about an order of magnitude from their corona-model values due to the effects of multiple-collisional excitations on the populations of the highly excited bound levels of the recombined ion. The dielectronic recombination rates into these highly excited levels are found to be enhanced by the effects of collisionally induced angular momentum redistribution on the populations of the autoionizing levels.

We present a quantum-mechanical theory of the electron drift speed $W$ in a gas in a field at low $\frac{E}{N}$ and relatively high pressures. It is able to give a quantitative interpretation of the experimental results, as regards the dependence of $W$ on both the gas number density and the gas temperature. As an application, we make a comparison between theory and experiment in He, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and Ar.

The ionization stages in x-ray spectral data (3-5.5 Å) from single- and multiple-exploded-Mo-wire experiments were interpreted with atomic-structure calculations. Both exploded-wire experiments produced spectra in which Ne-like Moxxxiii was the most abundant ionization stage. Experimental wavelengths from higher Rydberg transitions in Moxxxiii were obtained. Except for the Ne-like lines, the Mo spectra are characterized by complex, overlapping line structure due to the F- and Na-like ionization stages.

Expressions appropriate for the evaluation of the hyperfine splitting in ferric-hemoglobin hydroxide have been derived in the Hartree-Fock approximation using "giant" multielectron molecular-orbital wave functions formed as linear combinations of atomic orbitals of the constituent atoms and the molecular orbitals of the O${\mathrm{H}}^{-}$ complex incorporating overlap effects. Core orbitals as well as valence orbitals have been considered. The relevant multicenter matrix elements have been evaluated accurately by means of the analytical expressions which we have derived by employing a general closed-form expression developed previously for the coefficients of the expansion of a Slater orbital from one center onto the other. Various calculated electric field gradient components have been analyzed separately in terms of the valence and the core orbitals of the central ion (iron) interacting with the orbitals of the other constituent atoms and the complex O${\mathrm{H}}^{-}$. One finds that the "local" and "distant" parts of the field gradient due to O${\mathrm{H}}^{-}$ nearly cancel one another and, consequently, produce negligible effect on the hyperfine splitting of iron. The nitrogens of the porphyrin plane contribute dominantly to the splitting. Other surrounding atoms contribute less and their influence decreases rapidly as their distance from the central ion increases. On combining various contributions, the calculated hyperfine splitting comes out to be 1.44±0.16 mm/sec, which agrees excellently with the experimental splitting 1.57 mm/sec observed by Lang and Marshall. The results from the present calculations have been compared with those obtained by Weissbluth and Maling employing semiempirical treatment on a porphyrin-hydroxide model compound. Their estimate is found to give negative sign to the splitting in contrast with our result. Sources of disagreement have been pointed out. Comparison has also been made with the previous calculations on hemin and the observed differences in the splittings in relation to the present system have been clarified. Arguments have been presented, which lead to the prediction of positive hyperfine splitting in ferric-hemoglobin compounds.

The order-parameter fluctuation spectrum of a chiral system undergoing a helicoidal ferroelectric $\mathrm{s}\mathrm{m}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{c}-A\to \mathrm{s}\mathrm{m}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{c}-\tilde{C}$ phase transition is evaluated both above and below $T_c$. The transition is produced by a condensation of a coupled tilt-polarization soft mode. The "in-phase" amplitude fluctuations in the tilt and the polarization represent the soft mode of the low-temperature phase, whereas "in-phase" orientational fluctuations represent the Goldstone mode which is recovering the continuous symmetry group broken at $T_c$.

Two-plasmon decay has been observed in a C${\mathrm{O}}_2$-laser-gas-target-plasma interaction experiment. The spectrum of $\frac{3}{2}$-harmonic radiation has been measured and the threshold intensity for decay determined. An experimental value of ∼ 2 × ${10}^{11}$ W/${\mathrm{cm}}^2$ is in reasonable agreement with theoretical predictions for an inhomogeneous plasma.

Topological-degree and Lyapunov-potential techniques are used to study the stability of nonlinear dissipative structures found in a problem involving autocatalysis and the Langmuir-Hinshelwood adsorption law.

We have studied a model of tangential viscosity of a fluid in which high-order spatial derivatives of the velocity are taken into account. The model indicates that for a gas in the transition regime, and within a range of boundary conditions, the tangential stress presents an oscillatory dependence on the density. An experiment designed to detect these oscillations was done with helium at constant temperature $T=294\mathrm{}°$K and varying the pressure within the range 0.5-50 mTorr. The results were found to be in good agreement with the oscillations predicted by our model when the spatial derivative of the fluid velocity near the boundaries was close to zero. From the separation in density between these oscillations, it is possible to obtain an independent measurement of the atomic mean cross section for helium. This method makes specific use of the way the viscosity oscillates with the density in the transition regime instead of using the value that the viscosity takes in the continuous regime. The good agreement between our measurements of the cross section and the values that have been obtained by other methods gives an indication of the validity of the proposed model.

The equations used by Yater to calculate dc power conversion of energy fluctuations are shown to contain mistakes which prohibit their use in general calculations. Corrected equations are presented which converge to known results in the limit of large capacitances: Yater's conversion-efficiency equations do not. Calculations with the present equations are used to demonstrate that the high conversion efficiencies approaching the Carnot cycle do occur, but only for circuit situations where the power output is considerably below the maximum obtainable fluctuation power and where the circuit capacitances are impractically small (≈3×${10}^{-19\mathrm{}}$ F). Conversion efficiencies at the maximum output power are considerably smaller than the Carnot-cycle limit. No net power conversion is predicted for practical circuit capacitances.

A new-type Bohm-Aharonov experiment is proposed. The experiment can be carried out in a large scale without the help of an electron microscope.

The inelastic energy losses for single collisions of ${\mathrm{Xe}}^{+}$ ions with Xe targets have been measured for incident ion energies from 0.3 to 1.2 MeV and for scattering angles from 3° to 20°. The energy losses were found to range from 1 to 11 keV with distinct steps at distances of closest approach of 0.22 and 0.12 Å. By comparing these data with earlier ionization data by the same authors these steps are shown to be caused by $M$-shell excitation. Other excitations observed in the ionization data may be attributed to $N$-shell excitation. The distances of closest approach at which these excitations occur agree well with calculations by Eichler and Wille and co-workers, giving further evidence of the usefulness of Fano and Lichten's one-electron molecular model and these calculations.

We show that the lowest order of relativistic corrections to the excitation and ionization cross sections of atoms by electron impact is quadratic in $Z\alpha$ and $\frac{v}{c}$.

Extremely compact analytical formulas are derived for molecular two-center one-electron integrals and Coulomb integrals, which occur in linear-combination-of-atomic-orbitals calculations with Slater-type orbitals (STO's). The derivation is based on the connection of the STO's with the reduced Bessel functions (RBF's) and makes use of the convolution theorems of RBF's. The final results are of a surprisingly simple structure and are, therefore, especially useful for practical applications.

The theory of near-adiabatic collisions is formulated in a fully quantum-mechanical form, correctly taking into account the role of electron translation factors (ETF's). A general form for the ETF, using switching functions, is given for systems which are electrically either asymmetric or symmetric (with or without mass asymmetry). The main result is that the close-coupled scattering equations obtained in the perturbed-stationary-states theory must be replaced by equations of identical form, but having modified nonadiabatic coupling matrices. In general, the corrections involved are substantial; their nature, and effect on coupling matrices, is discussed, and conditions when they are likely to be important are described. The remaining problem of determining the switching function is discussed briefly. The correct form for ETF's, their quantum-mechanical formulation, and the resulting correct form for the coupled equations, have not been given previously.

We have studied the ground state of the ${\mathrm{H}}_2^{+}$ molecular ion in the presence of a homogeneous magnetic field, basing this study on a linear combination of atomic orbitals obtained from the hydrogen atom in a magnetic field. The calculations have shown that this scheme is adequate to describe the binding energy of the molecule at field strengths up to approximately ${10}^{10}$ G.

A rigorously correct and fully quantum-mechanical theory of slow atomic collisions is presented, which removes the formal defects and spurious nonadiabatic couplings of perturbed-stationary-states theory, and arrives at coupled equations for the heavy-particle motion which are the same as those obtained in the preceding paper by the electron translation factor formulation. Here, however, the theory is formulated in terms of suitably defined scattering coordinates, and electron translation factors do not appear. A unified physical interpretation of both approaches can thereby be made, and smaller terms in the coupled equations, describing corrections of order $\frac{m}{\mu }$ to electronic binding energies and to the collision kinetic energy, are placed on a firmer footing. Particular attention is paid to the critical test case of isotopic systems such as H${\mathrm{D}}^{+}$ and it is shown how a correct theory of isotopic charge exchange can be formulated.

The finiteness of the speed of light is known to change the long-range interaction of atomic systems. Stimulated by recent advances in precision measurements of high Rydberg states, we consider these "retardation effects," not on the interaction of two separate systems, but on the energy eigenvalues of the high Rydberg states of an isolated heliumlike ion, where the outer electron has quantum numbers $n>l\gg 1$, and where the core—the nucleus and the inner electron—is in its (spherically symmetric) ground state. We analyze the time-ordered Feynman-like graphs that contain one or two instantaneous or transverse photons, and find a retardation correction, $\frac{11e^2\hslash {\alpha }_d}{\left(4\mathrm{}\pi \mathrm{mc}{R}^2\right)}$ to the leading ($-\frac{e^2{\alpha }_d}{2R^4}$) polarization potential; ${\alpha }_d$ is the static electric dipole polarizability of the ion core, and $R$ is the nuclear-outer-electron separation. The correction is also applicable to scattering problems, to high Rydberg states of atoms and ions with more than two electrons, and, with $m\to m_{\mu }$, to a muon bound to a nucleus. Very recently, Bernabéu and Tarrach used dispersion theory to obtain an identical term as the retardation correction for the interaction of a charged particle with a neutral polarizable system; their procedure is not applicable, as it stands, to the present situation.