In the semiclassical version of the Jaynes-Cummings model without the rotating-wave approximation, an exact periodic solution has been obtained and studied for some specific values of the coupling constant and the detuning.

Early-time dynamics of transient periodic structures in reorienting lyotropic nematics are analyzed via digital video microscopy. Measurements of the time dependence of the pattern power spectrum and critical wave number are presented. The data are compared to the results of a simple linear theory.

Using the SO(2,1) radial (or spectrum-generating) subgroup of the SO(4,2) dynamical group of the Coulomb problem, we construct the associated coherent states that follow the classical radial motion. These wave packets evolve in a fictitious time variable proportional to the eccentric anomaly. The packets consist of a superposition of Coulomb Sturmian functions and do not disperse as they evolve although the width of the packets changes periodically.

We establish a basis set of atomic orbitals suitable to describe molecular wave functions at arbitrary magnetic field strengths and for an arbitrary orientation of the molecule relative to the magnetic field. A simple calculation for the hydrogen atom demonstrates the superiority of such an orbital over common orbitals. All types of matrix elements of the Hamiltonian of a molecule in a strong magnetic field are evaluated within our basis set of atomic orbitals.

Based on the first-quantized wave-function formalism, the contribution of the radiative effects to the effective potential for relativistic, spinless particles is calculated. Basic properties of the self-radiation without quantization of the electromagnetic field are discussed.

Relative differential cross sections for He-He collisions in the keV-energy range are reported for laboratory scattering angles between 35° and 56°. The experiment utilizes two position-sensitive detectors to detect both collision products in coincidence following the collision. A strong periodic variation in the differential cross section with scattering angle is present whenever the collision partners have identical nuclei and is ascribable to well-known interference effects resulting from the indistinguishability of the collision products. Calculations of these differential cross sections considering only the Coulomb interaction between nuclei of the colliding atoms agree well with the experimental data.

We formulate a close-coupling theory of slow ion-atom collisions based on molecular (adiabatic) electronic states, and including the electronic continuum. The continuum is represented by packet states spanning it locally and constructed explicitly from exact continuum states. Particular attention is given to two fundamental questions: (1) Unbound electrons can escape from the local region spanned by the packet states. We derive close-coupled integral equations correctly including the escape effects; the ‘‘propagator’’ generated by these integral equations does not conserve probability within the close-coupled basis. Previous molecular-state formulations including the continuum give no account of escape effects. (2) Nonadiabatic couplings of adiabatic continuum states with the same energy are singular, reflecting the fact that an adiabatic description of continuum behavior is not valid outside a local region. We treat these singularities explicitly and show that an accurate representation of nonadiabatic couplings within the local region spanned by a set of packet states is well behaved. Hence an adiabatic basis-set description can be used to describe close coupling to the continuum in a local ‘‘interaction region,’’ provided the effects of escape are included. In principle, the formulation developed here can be extended to a large class of model problems involving many-electron systems and including models for Penning ionization and collisional detachment processes. However, we restrict specific attention here to the simpler problem of collisional (impact) ionization in one-electron systems (e.g., proton–hydrogen-atom collisions) and some results have been proved rigorously only for those systems.

The preceding paper (I) of this series develops a molecular-state close-coupling theory of ion-atom collisions including the electronic continuum, which is described by packet states spanning it locally. The present paper describes results of computations applying this formulation to the prototype problem of impact ionization in proton–hydrogen-atom collisions, in particular, studies of the properties of the basis states and the nonadiabatic couplings among them. (1) We construct continuum eigenfunctions using a ‘‘quantal momentum’’ or phase-amplitude representation and use this to study construction and properties of continuum packet states, and we show how localization of packet states within a specified interaction region leads to specification of packet widths and/or energies. (2) We verify assumptions made in the derivations given in paper I about nonadiabatic couplings of continuum states, and report computations of coupling matrix elements needed to implement the theory for this system. Subsequent work will present close-coupling calculations using this data.

We point out that the plane-wave Born approximation sometimes gives rise to a conspicuous minimum of the integral cross section for excitation in ion-atom collisions; for illustration we present results for a transition 1$s^2$2$s^2$ ${}_{}{}^1{}_{}{}^{}s_{}^2{}_{}{}^{}$2s3p ${}_{}{}^1{}_{}{}^{}P$ of berylliumlike ions calculated by using configuration-mixing wave functions. The minimum of the integral cross section arises from a zero of the generalized oscillator strength.

We report the measurements of the relative total cross sections of collisions between electrons and molecular nitrogen and between electrons and carbon monoxide for incident electron energies in the range 10–25 eV. Through the use of a crossed electron–supersonic-molecular-beam configuration and a phase-lock detection technique we obtain direct measurement of features in the relative total cross section that are approximately ${10}^{\mathrm{-}3}$ of the total cross section itself. Our measurements confirm that the $e^{\mathrm{-}}$-${\mathrm{N}}_2$ collisions exhibit a number of features that can be consistently interpreted with the grandparent model proposed by Sanche and Schultz [Phys. Rev. A 6, 69 (1972)], and further developed by Brunt, King, and Read [J. Phys. B 11, 173 (1978)]. The $e^{\mathrm{-}}$-CO collisions are also amenable to this interpretation. We find no evidence of a Feshbach resonance at 15.6 eV and suggest that the Feshbach resonances in the $e^{\mathrm{-}}$-CO system arise from only two grandparent states, as they do in the $e^{\mathrm{-}}$-${\mathrm{N}}_2$ system.

The diffusion constant of atomic hydrogen in helium gas, $D_0$(H-He), was measured with use of an optical-pumping–spin-exchange technique. Atomic hydrogen was produced by an inductive discharge in spherical Pyrex cells containing helium and small amounts of molecular hydrogen (<2%) and rubidium. The rubidium was optically pumped by a vapor lamp and the hydrogen was polarized by subsequent spin-exchange collisions. The decay rate of the hydrogen concentration was obtained from the observed time dependence of the hydrogen Zeeman signal and the diffusion constant was determined by measuring the decay rate in cells of different radius and helium pressure. $D_0$(H-He) was found to be 2.42(7) ${\mathrm{cm}}^2$ ${\sec }^{\mathrm{-}1}$ at 60 °C, which may be extrapolated to 1.70(5) ${\mathrm{cm}}^2$ ${\sec }^{\mathrm{-}1}$ at 0 °C. This result is significantly more accurate and more consistent with theoretical calculations than the results of previous experiments.

The absolute yield of multiply charged ions of the noble gases argon, krypton, and xenon as a function of laser intensity in the range of ${10}^{13}$≤I≤5×${10}^{14}$ W/${\mathrm{cm}}^2$ is reported. The actual numbers of ions produced using a well-characterized tunable picosecond dye laser were measured. These absolute measurements allow a direct, quantitative comparison of the data with theory. Both lowest-order perturbation theory and the ‘‘tunneling ionization’’ theory of Keldysh are used to model the experiment. Ionization rates obtained from the Keldysh theory are in quantitative agreement with the experimental results for production of the first charge state only. Reasons for the inability of the Keldysh theory to describe the production of multiply charged ions are discussed.

Optical properties of an atom in the vicinity of a metal or dielectric are different from those in free space. The spontaneous decay of an atom with two degenerate levels is studied, where the relaxation operator is obtained as a function of the atom-surface separation and the complex bulk dielectric & of an excited state ‖$j_e$$m_e$〉 appears to depend on the magnetic & is derived, and from the rotational symmetry with respect to the surface normal it is found &. A general expression for the fluorescent radiation field in the far zone is then derived, which incorporates the polarization properties of the fluorescence, as they are modified by the presence of the dielectric. It is shown that the angular distribution of the emitted intensity depends strongly on ε(ω), and it is pointed out how information about the substrate, e.g., ε(ω), can be extracted from the temporal statistical behavior of the emitted photons. It is emphasized that the major surface effects are purely geometrical, despite the essential quantum nature of the problem.

The photon correlations of resonance fluorescence emitted by a degenerate two-level atom near a metal surface are studied. An intense nonmonochromatic optical laser drives a low-lying atomic transition, and the emitted fluorescence is detected by a photon counter. An expression for the spontaneous-decay operator is derived, and it appears that the various substates of the upper level have a different lifetime due to the presence of the surface, or equivalently, due to the loss of spherical symmetry. The temporal photon correlation function is then evaluated in terms of a photon-emission operator and the time-evolution operator for the atomic density matrix. The general theory is exemplified with a detailed elaboration of the $j_g$=0→$j_e$=1 transition, for which the two-photon correlation is obtained explicitly as a function of the inverse lifetime A(h), depending on the atom-surface distance h, the laser linewidth, the detuning from resonance, and the dipole-coupling strength with the external field.

Transverse-optical-mode trapping (‘‘active guiding’’) in the free-electron laser (FEL) is discussed via a variational approach based on classical field theory. The variational principle for the field leads to a set of simple evolution equations for the mode parameters which generalizes the discussion in A. Amir and Y. Greenzweig, Phys. Rev. A 34, 4809 (1986), where a parabolic expansion of the interaction term was used. The method can be applied to calculate the evolution of the optical-beam parameters under the interaction with an arbitrary electron-beam profile. Electron-beam inhomogeneities are included by using a distribution function. In the linear regime, the stationary condition of these equations results in a simple algebraic equation for the trapped-mode parameters. The values obtained in this method are compared with the results of several numerical simulations. The equations of motion for the optical-beam parameters are also derived for the full nonlinear FEL problem using the same principles.

We have solved Maxwell’s equations for a source, consisting of an oscillating dipole, located in a plane-bounded dielectric half space. Formulas are given for the radiation yield from this source in the region outside the dielectric. The medium is characterized by a local, complex dielectric function ε(ω)=${\epsilon }_1$(ω)+i${\epsilon }_2$(ω). The application of these formulas to the analysis of experimental data on luminescence from solids is discussed, and calculations are presented for aluminum, carbon, silver, copper, and gold.

We compare the classical and quantum theories of a Morse oscillator driven by a sinusoidal field, focusing attention on multiple-photon excitation and dissociation. In both the classical and quantum theories the threshold field strength for dissociation may be estimated fairly accurately on the basis of classical resonance overlap, and the classical and quantum results for the threshold are in good agreement except near higher-order classical resonances and quantum multiphoton resonances. We discuss the possibility of ‘‘quantum chaos’’ in such driven molecular systems and use the Morse oscillator to test the manifestations of classical resonance overlap suggested semiclassically.

It is shown that classical linear canonical transformations are possible in the Wigner phase space. Coherent and squeezed states are shown to be linear canonical transforms of the ground-state harmonic oscillator. It is therefore possible to evaluate the Wigner functions for coherent and squeezed states from that for the harmonic oscillator. Since the group of linear canonical transformations has a subgroup whose algebraic property is the same as that of the (2+1)-dimensional Lorentz group, it may be possible to test certain properties of the Lorentz group using optical devices. A possible experiment to measure the Wigner rotation angle is discussed.

The cubic Schrödinger equation (CSE) (${\mathrm{iu}}_t$+$u_{\mathrm{xx}}$±2‖u${\Vert }^2$u=0) is a generic model equation used in the study of modulational problems in one spatial dimension. The CSE is exactly solvable using inverse-scattering techniques. Periodic solutions of the focusing CSE (‘‘+’’ sign in the above equation) are also well known to be subject to modulational instabilities. This unique mixture of solvability and instability allows the development of a complete and explicit analytical theory for the long-time behavior of the instabilities. Among the results to be discussed are (i) a method for calculating the growth rates of instabilities around (spatially nonuniform) initial states, (ii) a discussion of recurrence phenomena for systems with finite spatial period, and (iii) a method for calculating the recurrence time.

Effects of radiative cascades from higher-level satellite states on the intensities of dielectronic satellite lines of lower-lying states are investigated for selected hydrogenlike ions. The ratio of intensities of a particular satellite line from radiative cascades and from direct transitions is found to depend on the atomic number of the ion and the plasma temperature. For the most prominent satellite lines the increase in intensity is ≤6%. Results are reported for hydrogenlike Ne, Si, Ar, Ca, Ti, Cr, Fe, and Ni at various plasma temperatures.