Statistical regularization as applied to phase-shift analysis of elastic scattering data and to the construction of potentials from such data is discussed. A recent phase-shift analysis and determination of potentials from e-He scattering data below the first excitation threshold are substantially improved by these techniques. The extraction of total elastic and momentum transfer cross sections from the differential cross-section data with a rigorous error analysis is discussed.

Electron-hydrogen scattering is studied in the range of incident energies from 12 to 100 eV. The equations resulting from a six-state close-coupling expansion are supplemented by an optical potential to represent contributions from states not explicitly considered. The optical potential is evaluated through the use of a pseudostate expansion. Solutions are obtained by a linear algebraic integral equation method. Results are presented for elastic scattering and total cross sections for initial 1s, 2s, and 2p states. All 1s→n=2, 1s→n=3, and n=2→n=3 excitation cross sections are computed. Particular attention is given to obtaining convergence of sums with respect to the total angular momenta. Analytic formulas are given for the energy dependence of the cross sections from least-squares fits. Effective collision strengths are determined by averaging over a thermal distribution of incident electron energies.

New measurements of absolute cross sections for multiple ionization of helium, neon, argon, and krypton by 50–500-keV/amu ${\mathrm{He}}^{2+}$ impact are presented. By measuring projectile-ion–target-ion coincidences, these cross sections are obtained for the direct ionization as well as the single- and double-electron-capture channels. The present data are combined with previous measurements by the author that covered the energy range between 5 and 67 keV/amu in order to provide a broader description of ${\mathrm{He}}^{2+}$ impact ionization of atomic targets. The earlier measurements were found to require reevaluation in order to correct ion detection efficiencies used in that study. An analysis of the direct-multiple-ionization cross sections demonstrates that a simple impact-parameter, independent-electron model can be used to describe these cross sections over a broad range of low to intermediate impact energies. In particular, this analysis, when applied to fully stripped ion (1≤Z≤8) impact on helium, yields a single universal curve in the velocity range investigated here.

Energies of excited states of ${\mathrm{HCl}}^{2+}$ have been determined experimentally by the technique of double charge transfer and are compared with present results of a multireference single- and double-excitation configuration-interaction calculation. The calculation shows the existence of four bound states. The good agreement obtained permits a direct assignment of the four lowest-energy excited states with singlet symmetry. Comparison of our work with previous information obtained from photoion-photoion coincidence, electron impact, charge stripping, and also from HCl xuv Auger analysis is given. We report the double-ionization energies of stable states ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{}^{\mathrm{-}}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}\mathrm{\Delta }$, and ${\Sigma }^{+}$ ${\mathrm{HCl}}^{2+}$ as 35.9±0.2, 37.4±0.15, and 38.6±0.3 eV, respectively, while dissociative states ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }$ and 2 ${}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ are at 40.9±0.3 and 45.6±0.3 eV.

We have measured the impact-parameter dependence P(b) of Ne K-Auger- and δ-electron production for 0.23- and 0.13-MeV/u ${\mathrm{F}}^{8+}$+Ne collisions. For the higher energy an improved agreement with multiple-state atomic expansion theory has been found compared to previous data. A strong damping in the oscillatory structure of the P(b) which appears at the smaller collision energy shows a significant discrepancy of experiment and theory. For δ-electron production it is shown that dominant contributions arise from very distant collisions greater than or equal to 0.4 a.u.

Recent experience with semiclassical approximations with wave packets make possible a new intuitive basis and new computational tools for incoherent neutron scattering. We review our approach in the context of others which have been proposed for neutron scattering, and we find it advantageous to launch semiclassical approximations from the Schrödinger picture rather than the Heisenberg picture of quantum mechanics. An application to a model for crystalline HCN is given.

Contributions to the electron-impact ionization of Li-like ions due to resonant recombination followed by double Auger emission are calculated using first- and second-order perturbation theory. The double Auger rate is found to be quite sensitive to the choice of both continuum phase and excited orbital basis set. In particular we find that resonant recombination to the 1s2$s^2$2p ${\mathrm{}}^3$P term of ${\mathrm{O}}^{4+}$, followed by double Auger emission to the 1$s^2$ ${}_{}{}^1{}_{}{}^{}S$ term of ${\mathrm{O}}^{6+}$, has a cross section ranging from 6.4×${10}^{\mathrm{-}22}$ to 4.9×${10}^{\mathrm{-}21}$ ${\mathrm{cm}}^2$ depending on how the double Auger rate is calculated. The maximum represents 0.65% of the total ionization cross section for ${\mathrm{O}}^{5+}$ at the resonance energy of 436.3 eV. Thus a noise level of 1.0%, which is probably a lower limit of current crossed-beam experiments, will mask the contribution in ${\mathrm{O}}^{5+}$. Similar results are found for other Li-like ions in the first-row Periodic Table elements.

Cross sections have been calculated for the Penning ionization of ground-state potassium atoms in collisions with metastable He(2 ${}_{}{}^1{}_{}{}^{}$,3S) atoms for the range of center-of-mass-system energies 0.01 eV≤E≤1.0 eV. The cross sections were calculated using ab initio ptical potentials. The real part of the optical potential was obtained by adjusting the potential curve resulting from a configuration-interaction (CI) calculation performed on the HeK molecule so as to include the correct van der Waals asymptotic form. The imaginary part was obtained by performing a Stieltjes moment analysis of a discrete ($L^2$) representation of the ${\mathrm{HeK}}^{+}$+${\mathrm{e}}^{\mathrm{-}}$ continuum generated in a CI procedure. The calculated cross section for He(2 ${\mathrm{}}^3$S) scattered from K at E=0.032 eV is in good agreement with stationary afterglow measurements at room temperature. A nearly degenerate core-excited state of potassium [which has a curve crossing with the He(2 ${\mathrm{}}^3$S)K molecular state] is then explicitly included in a Landau-Zener formulation which further increases the calculated cross section, but it still agrees well with the room-temperature measurements. Elastic differential cross sections for He(2 ${\mathrm{}}^1$S) on K are also reported.

The interaction of ultrashort laser pulses and colliding atoms has been studied theoretically and experimentally. Solutions to the semiclassical Schrödinger equation in Bloch-equation form predict the effect of pulses whose duration is shorter than the collision duration. These results have been applied to the process Na(3S)+Ar+ħω→Na(3$P_{1/2}$)+Ar using intense, off-resonant laser pulses with variable temporal duration. It has been found that at a fixed laser intensity the efficiency of exciting the Na(3$P_{1/2}$) state is higher for ultrashort pulses than for pulses with duration longer than the collision duration. This effect is caused by a time-dependent modification of the collision potentials by the intense laser field. The theoretical calculation is in qualitative agreement with the experimental results, although a large discrepancy exists between the predicted and observed laser power needed to observe the increased efficiency with short pulses.

Distorted-wave theories satisfying Coulomb boundary conditions are classified with respect to the behavior of the distorting potentials around the origin R=0. The ‘‘soft’’-type distorting potentials that are regular at R=0 lose their effect on the capture cross sections at high energies, and their cross sections converge to the Oppenheimer-Brinkman-Kramers (OBK) limit. On the other hand, the ‘‘hard’’-type distorting potentials that are singular at the origin as $R^{\mathrm{-}1}$ continue to have an effect in the high-energy limit so that a finite difference remains between the distorted-wave and the OBK cross sections. This feature, peculiar to electron capture, is attributed to the rapid decrease of the interaction region with the projectile velocity. The eikonal approximation is also analyzed from this point of view. Comparison with experimental data indicates that the ‘‘hard’’-type distorting potential is preferable for a first-order description of electron capture.

The hyperspherical treatment of ${\mathrm{HD}}^{+}$ is extended to make it suitable for a multichannel approach including the rotational coupling. For this purpose, a new and symmetric set of coordinates is introduced. The approximate hyperspherical adiabatic potential curves are calculated. In contrast to the Born-Oppenheimer adiabatic potential curves, the hyperspherical ones exhibit the correct dissociation limits. The lowest-order vibrational spectrum obtained compares favorably with the conventional higher-order calculations. It is shown that this approach is better suited to describing the dynamics of three-body systems.

In this work we study the effect of thermal fluctuations in the resonance fluorescence of a two-level system. The damped two-level system is driven by a strong incident classical field near resonance frequency. To simulate the thermal bath we introduce a large system of harmonic oscillators that represent the normal modes of the thermal radiation field. To obtain the time development of the fluorescent light intensity we solve the Heisenberg equations of motion transformed in a system of coupled integral equations by an iterative method. The results show that the presence of the bath modifies dramatically the time development of the fluorescence light intensity when compared with the case T=0 K.

We report detailed studies of Ramsey-type resonances due to collisional velocity diffusion of Sm atoms within the Doppler-broadened ${}_{}{}^7{}_{}{}^{}\mathrm{F}_1^{}{}_{}{}^{}$→${\mathrm{}}^7$${\mathrm{F}}_0$ ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$ transition at λ=570.68 nm in the presence of rare-gas perturbers (He,Ne,Ar,Kr,Xe). The experimental technique uses counterpropagating laser fields and relies on coherent resonance Raman processes to excite and detect sublevel coherence optically. A modulated pump laser field is used for velocity-selective resonance Raman excitation of oscillating Zeeman coherence in the J=1 ground state of Sm; the sublevel coherence is monitored by Raman heterodyne detection using a counterpropagating, unmodulated probe laser field. If the pump and probe fields interact with different atomic velocity subgroups, a signal only occurs in the presence of velocity-changing collisions which provide a transport of the Sm atoms with sublevel coherence in velocity space. The sublevel resonance curves turn out to be sensitive to both depolarizing and velocity-changing collisions; the measured line shapes show the characteristic features of Ramsey-type resonances. Our theoretical treatment is based on a novel four-level density matrix calculation; the analysis reveals that the temporal evolution of the collisional velocity-diffusion processes can simply be obtained by means of a Fourier transformation of the measured sublevel resonance curves. In the case of He perturbers the diffusion in velocity space can be described by a Fokker-Planck equation; here, the theoretical fits of the measured sublevel resonance curves directly yield the time constant for collisional thermalization and the cross section for depolarizing collisions. In the case of the heavier rare gases, however, the Fokker-Planck model fails to describe the velocity thermalization; here, the Keilson-Storer kernel yields a better agreement with the experimental data. We derive cross sections for depolarizing and velocity-changing collisions and values for the collisional velocity changes associated with orientation-preserving collisions.

The pattern of electron correlations is examined for odd-parity L=1 states of calcium over a wide range of energies from far below the 4s threshold up to the 4p threshold of ${\mathrm{Ca}}^{+}$. By combining quantum-defect theory with a small-scale eigenchannel R-matrix calculation, good agreement with the observed photoabsorption spectrum is obtained. The two-electron probability densities and channel-interaction parameters are analyzed as functions of the total energy. A novel interference between direct (4sɛp-3dɛp) and indirect (4sɛp-4pɛs-3dɛp) channel-interaction amplitudes greatly reduces the width of the 3d6p autoionizing resonance compared to adjacent series members.

We consider near-threshold ionization of atomic hydrogen by strong laser light. Nonperturbative features of the photoelectron spectrum and double optical resonance spectrum (in the V configuration) are obtained and discussed. We show that in contrast to the usual sign of the ac Stark shift the ionization threshold is dynamically lowered due to ‘‘pulling’’ by the atoms near threshold Rydberg levels. Dynamical widths of the spectra are also found. Our results are obtained analytically by means of a variant of the single-pole approximation and are qualitatively consistent with experimental results.

The multiphoton ionization of helium has been determined for a number of laser wavelengths and intensities using the time-dependent Hartree-Fock model. Conclusions about the ionization dynamics for very-short-pulse, high-intensity lasers are discussed. The limits and characteristics of the time-dependent Hartree-Fock method for atomic physics processes are also evaluated.

Electromagnetic interactions of a single charged particle in the presence of damping are investigated theoretically in this work. Classically, by considering the explicit example of a particle in a constant magnetic field, it is shown that the minimal coupling prescription is inadequate for the infinitely large number of Hamiltonians from which the equations of motion in the presence of damping are derivable by Hamilton’s equations. The use of minimal coupling procedure to switch on electromagnetic interactions in phenomenological quantum equations of damped motion is shown to lead to incorrect equations in the classical limit. It is necessary to consider the microscopic models of damping to allow for electromagnetic interactions in these systems. Two microscopic models for damping involving a linear coupling with a heat bath of oscillators are considered in detail and it is shown that correct Heisenberg equations of motion follow upon elimination of bath degrees of motion so that damping and Lorentz force do not affect each other. However, the field couples to the mechanical momentum as mv-(e/c)A rather than to the canonical momentum. The linearly coupled quantal case is analogous to the classical situation. The Schrödinger-Langevin equation contains an extra term ${\mathcal{F}}^{\mathrm{r}}$ A⋅dr’; however, the gauge invariance character and the Aharonov-Bohm effect are unaffected. Two nonlinear models of damping are studied by considering the exchange of bosons in the different states of the central particle. In this situation the Lorentz force is not recovered in the classical limit.

We present a theoretical study of strong-field autoionization electron spectra, including laser dephasing with variable band shape. We show that in the weak-field limit the usual peak reversal is obtained when the spectrum changes from the Lorentzian limit to the Gaussian limit. When the laser field strength is increased, different peak reversal behaviors are predicted in the Lorentzian and Gaussian limits, which is quite different from that in the weak-field case. A comparison between the effect of Doppler and laser dephasing on the photoelectron spectrum of autoionization is also made in the static limit.

A single laser, which is used to induce and detect spontaneous Raman transitions, can be used to observe quantum jumps in a single atom. The population dynamics of a particular system, consisting of two ${}_{}{}^2{}_{}{}^{}\mathrm{S}_{1/2}^{}{}_{}{}^{}$ ground-state levels and four ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{3/2}^{}{}_{}{}^{}$ excited-state levels split by a magnetic field, is analyzed for a laser tuned near a particular transition. We find that the statistics of the fluorescence emitted by this system are described by the same formalism developed for the three-level V configuration irradiated by two light sources. Over a wide range of observation times, the fluorescence intensity will be two valued, either off or on, as has been verified for the V configuration. Some surprising and elegant features of this new system are described.

Almost forty years ago one of us (W.E.L.) noticed that within the analysis of experiments on the hydrogen fine structure the matter-field interaction was sensitive to the choice of gauge when decaying states were used. In the present paper this problem is resolved for the Bethe-Lamb equations in the context of the two-level model with Weisskopf-Wigner decay included.