Absolute rate constants for ionization of Rb(ns,nd) atoms in collisions with ${\mathrm{SF}}_6$ have been measured for values of n in the range 38–106. In addition, the kinematics of such reactions have been investigated using Xe(nf) atoms. The data confirm that collisions of Rydberg atoms with targets that attach free low-energy electrons are well described by the ‘‘essentially-free’’-electron model. Analysis of the data shows that the cross section σ(v) for electron attachment to ${\mathrm{SF}}_6$ at very low electron energies (≲10 meV) is inversely proportional to the electron velocity v and, if v is expressed in cm ${\sec }^{\mathrm{-}1}$, is given by σ(v)=(4.2±1.0)×${10}^{\mathrm{-}7}$/v ${\mathrm{cm}}^2$.

The scattering of electrons from argon atoms is studied by the method of polarized orbitals. The 3p→d perturbed orbital calculated using the Sternheimer approximation gives the polarizability 14.29$a_0^3$. The perturbation of the orbitals 1s, 2s, 2p, and 3s is taken into account by renormalizing the 3p→d orbitals to give the experimental value 11.06$a_0^3$. Using only the modified orbital in the total wave function, phase shifts for various partial waves have been calculated in the exchange, exchange-adiabatic, and polarized-orbital approximations. They are compared with the results of the previous calculations. The calculated total elastic, differential, and momentum-transfer cross sections are compared with the experimental results. The elastic total cross sections obtained in the polarized-orbital approximation agree very closely with the recently measured cross sections by Jost et al. and Nickel et al. The critical point (the value of $k^2$ and theta at which the differential cross section is minimum) is at 0.306 eV and 80°, in good agreement with the measurements of Weyhreter et al.

The cross sections for electron-impact excitation of Na(3S) and Na(3P) atoms to the 3D state have been measured from threshold to 1000 eV, with ∼0.3 eV resolution. The 3P-state atoms are produced in the $m_l$=1, $m_s$=(1/2) level by optical excitation, and 3D→3P fluorescence is detected at 90° to the quantization axis. The resulting polarization anisotropies are considered, and included along with cascade effects in the high-energy normalizations to the Born approximation. The 3S→3D and 3P→3D excitation cross sections both rise very abruptly at threshold, and are indistinguishable from a step function with our energy resolution.

The impact-parameter method for electron-impact excitation of diatomic molecules is reformulated to explicitly treat molecular vibration and rotation and to permit the study of molecular dissociation. Applications are made to optically allowed transitions involving the X ${}^1$${\Sigma }_g^{+}$, B ${}^1$${\Sigma }_u^{+}$, and B’ ${}^1$${\Sigma }_u^{+}$ states of ${\mathrm{H}}_2$. The resulting cross sections are compared to other theoretical calculations and to experimental data. This method is applicable to heavy diatomic molecules and is expected to be useful in studying trends in electronic excitation and dissociation cross sections associated with variations in internal energy.

The impact-parameter method is used to calculate integral cross sections for electronic excitation and dissociation of ${\mathrm{O}}_2$ and ${\mathrm{S}}_2$ by electron impact. For both molecules, excitations to bound and dissociative states are considered for transitions from the ground electronic state (X ${\mathrm{}}^3$${\Sigma }_g^{\mathrm{-}}$) to the two lowest states of ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{\mathrm{-}}{}_{}{}^{}$ symmetry (labeled B and E for ${\mathrm{O}}_2$ and B and 2 for ${\mathrm{S}}_2$) and the lowest state of ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{}{}_{}{}^{}$ symmetry. The dependence of the cross sections upon initial vibrational and rotational states is studied for low collision energies (threshold to 25 eV). For some transitions a change in initial vibrational state can have a significant effect upon the cross sections, but, in general, the effect of changing the initial rotational state is small.

In this paper we consider the quadratic Zeeman effect from the point of view of scaling variational method based on the SO(4,2) dynamical group of the point Coulomb problem. In this formulation, the tilting angle is treated as a variational parameter. We scale a linear combination of the SO(4,2) basis states, solving numerically for the eigenvalues by diagonalization of the resulting matrix representation of the effective Hamiltonian. The SO(4,2) formulation has the advantage that the basis states form a complete set without the inclusion of continuum states, and furthermore, all matrix elements are calculated algebraically. The method is shown to be valid for field strengths at least as high as ${10}^{10}$ G and possibly up to ${10}^{12}$ G.

The conventional low-density isolated-resonance theory for the intensities and widths of the 2l’2l’’→1s2l and the 1s2l’2l’’→1$s^2$2l dielectronic satellite lines has been generalized to take into account angular-momentum-changing electron collisions and the interaction between the atomic system and the quantized radiation field. The electron collisional transitions alter the population densities of the autoionizing levels, while the atom-field interaction modifies the relative probabilities for autoionization and radiative decay. The modifications to the conventional low-density expression for the satellite-line intensities may be interpreted as interference between the resonant and nonresonant electron continua together with radiative corrections. These modifications have been expressed in terms of the unperturbed decay rates, the photoionization cross sections, and the Fano line-profile parameters. Using the transition probabilities obtained from two different relativistic atomic structure codes, the K-shell satellite-line intensities and widths have been calculated for argon as functions of temperature and density, taking into account both dielectronic recombination and inner-shell-electron collisional excitation. The combined effects of relativity, radiative corrections, and angular-momentum-changing electron collisions are predicted to be most significant for radiative transitions from the 2$p^2$ ${}^3$P and 1s2$p^2$ ${}^2$P metastable autoionizing states, which give rise to satellite lines that are relatively weak at low densities but are among the most prominent spectral features in high-density plasmas.

The recursive-residue-generation method initially intended by Nauts and Wyatt to treat large quantum systems described by a time-independent Hamiltonian with a discrete and nondegenerate spectrum, is extended to the case of a degenerate spectrum.

Spectral, temporal, and density behavior of dye-laser-excited dense xenon below and above breakdown threshold has been studied. Observation of three-photon resonant excitation at 147 nm is limited to very low density (ρ<7×${10}^{16}$ atoms ${\mathrm{cm}}^{\mathrm{-}3}$), whereas four-photon enhanced photoionization plays a major role between 500 mbar and 15 bar of pressure (1.4×${10}^{19}$ to 40×${10}^{19}$ atoms ${\mathrm{cm}}^{\mathrm{-}3}$). Excitation and deexcitation schemes are discussed from existing data and our spectral and temporal results obtained from either excimer (172-nm continuum) or laser spark emission.

Asymptotic expansions for the wave functions and energy spectrum of the two-Coulomb-center system ($Z_1$,e,$Z_2$) are derived in the region R≫1 (R being the distance between Coulomb charges $Z_1$ and $Z_2$) for the strongly asymmetric case $Z_1$≪$Z_2$∼R, with use of the comparison-equation method. The energy splitting Δ(R) of adiabatic molecular states having the same symmetry is calculated asymptotically exactly. For the particular system (p,e,$Z_2$), Δ(R) is calculated at the potential-curve pseudocrossings for 5≤$Z_2$≤26, and the results are compared with those obtained with use of either other asymptotic expansions or numerical solution of the eigenvalue problem for this system.

We describe a class of continuously phase-modulated radiation pulses that result in coherent population inversion on resonance as well as over a large range of transition frequencies and radiation field strengths. This is a population-inversion analogy to self-induced transparency. Simulations of the inversion properties of the modulated inversion pulse (MIP) are presented. It is shown that the inversion behavior can be explained by treating the MIP as a highly efficient adiabatic sweep. Criteria for establishing adiabaticity are discussed in detail. Finally, a method is presented for generating a sequence of phase-shifted radio-frequency pulses, from the continuously modulated pulse, which can be implemented on modern NMR and coherent optical spectrometers; experimental confirmation is given.

Off-axis electron orbits in free-electron-laser beams of finite thickness, subjected to combined helical wiggler and axial guide fields, have been studied analytically. A semiempirical equation for the electron velocity components, averaged over the electron’s oscillatory (betatron) motion, has been derived as a function of the radial displacement of the electron guiding center. The predictions from the equation are compared with single-particle numerical simulations, and with free-electron-laser experiments. Good agreement is found.

We have accurately measured the dispersion properties of the nonlinear susceptibilities of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ over a sufficiently wide range to permit an extrapolation to the static limit, where a comparison is made with theory. The effect of the vibrational resonances is calculated and is shown to be sig- nificant.

Resonantly enhanced sum-frequency generation of pulsed laser radiation is treated theoretically for the case of a three-level system. The density-matrix equations of motion are solved using second-order, time-dependent perturbation theory with the inclusion of transient effects. The energy and spectrum of the generated radiation are calculated as functions of laser detunings, laser pulse lengths, and temporal overlap of the laser pulses. The tuning characteristics and output pulse characteristics are found to differ qualitatively depending on whether or not the excitation pulses satisfy the adiabatic following criteria generalized for the case of a three-level atom.

Time-delayed four-wave mixing (TDFWM) on the 3S-3P transition in Na vapor has been studied using intense 7-nsec pulses from a broadband laser. Large-scale 1.9-psec modulation associated with the fine structure of the 3P state is observed throughout. At low buffer-gas pressures and low Na-vapor temperatures, pulse-induced relaxation effects are observed while at higher Na-vapor temperatures an anomalous response develops. In the normal region the TDFWM signal is interpreted in terms of either accumulated free decays or photon echoes. We estimate the relaxation induced by the excitation pulses.

Atomic excitation by strong noisy lasers with Kubo-Anderson–type fluctuations (randomly-interrupted-jump-process noise) is examined. A unified exact approach (based on the Bourret theorem) to phase and amplitude fluctuations is presented. Comparison with the Burshtien method, which was extensively used in recent works, is given. An exact analytical formula for the resolvent of the master Bloch equation in the general case, not necessarily only in resonant excitation, with simultaneous amplitude and phase fluctuations is derived. Some examples are analyzed.

A two-mode laser operating in the bistable region switches spontaneously from one mode to the other under the influence of quantum fluctuations. We present here a Monte Carlo simulation of the coupled Langevin equations describing the dynamics of a two-mode laser. We present results on the variation of average switching time with pump parameter. We show that if fluctuations in the pump parameter are incorporated, the Monte Carlo estimates agree well with measured switching times. To further check this observation we reanalyze the results of a recent analytical study and show that by including the same pump parameter fluctuations, the agreement with measurements becomes much better.

We use a Markovian master equation to solve for the dynamics of a free particle damped by the coupling of its coordinate to a bath of harmonic oscillators. In the coordinate basis the reduced density matrix for the free particle tends to be diagonalized. Considering the evolution of an initial superposition of two plane waves, we find that the interference-pattern fringe contrast is decreased by the damping. However, for fixed times and sufficiently large damping, the fringe contrast increases with increasing damping. Considering an initial coordinate-space Gaussian wave function, we find that for sufficiently large damping the coupling to the environment models a quantum measurement of the particle’s coordinate.

Thermal convection between horizontal plates is considered for a situation in which the driving force varies periodically in time. This variation may come from changes in the temperature or the plates or from a vertical oscillation of the cell, causing variation of the gravitational force. Truncation of the Boussinesq equations leads to a three-mode model which is a generalization of the Lorenz model to the case of external modulation. Similar models have previously been introduced by Finucane and Kelly for stress-free horizontal boundaries and by Gresho and Sani for the rigid-boundary case. The threshold behavior is that of a parametrically driven damped oscillator, whose bifurcations are studied numerically, as well as analytically in certain limits. It is found that in general the modulation stabilizes the conducting state. For stress-free horizontal boundaries the threshold shifts predicted by the model coincide with the results of Rosenblat and Herbert in the limit of low frequency and agree well with Venezian’s results for small modulation amplitude, both obtained using the full Boussinesq equations. For rigid boundaries the results agree well with numerical calculations of Rosenblat and Tanaka. The nonlinear behavior of the model is also studied, and the convective contribution to the heat current evaluated. The Lorenz model is shown to reproduce, either exactly or to a good approximation, most previous theoretical results on modulated convection, and the model can be studied simply for a wide range of parameters. The above discussion refers to a laterally infinite system. For a real finite system, sidewall effects are shown to cause a rounding of the convective threshold in the presence of modulation, particularly at low frequencies. A calculation of these effects is carried out within the framework of the Lorenz truncation, and the resulting imperfect bifurcation of the model is studied numerically. In a companion paper (immediately following this one) quantitative experimental results are presented and compared to the predictions of the Lorenz model.

Experimental data are presented on the temperature response of a Rayleigh-Bénard system to sinusoidal modulation of the heat current supplied to the lower plate near the onset of convection. Quantitative results are obtained for the average convective current as a function of the average Rayleigh number and of the amplitude and frequency of the modulation. Results are also presented on the temporal behavior of the response, above the convective threshold. The data are interpreted in terms of a previously proposed model which is a generalization of the Lorenz equations to periodic external driving. An important effect included in the model is the dynamic thermal mismatch between the sidewalls and the fluid which leads to an imperfect bifurcation between the conductive and convective states. As a result, the upward shift of the convective threshold caused by modulation in the ideal system is masked by the presence of sidewalls. In our model, this effect is controlled by a single adjustable parameter which turns out to agree in order of magnitude with previous experimental and theoretical estimates pertaining to a lower frequency range. The detailed comparison between experiment and theory shows good qualitative agreement, and some quantitative discrepancies in the parameter range explored. Suggestions are made for additional experiments to test a larger parameter range and in particular to minimize the sidewall effect in order to approximate the ideal threshold behavior more closely.