We report numerical results for the triply differential cross sections (TDCS) for electron-impact ionization of helium in the Glauber approximation in the incident energy range 224.58-2824.58 eV. The present calculation is based upon the technique of Roy et al., which has an advantage over the conventional partial-wave method in calculating TDCS in that the latter requires substantial computer time where many partial waves are involved. A comparison is made of the present TDCS with the results of available theoretical calculations and absolute measurements.

It is pointed out that the usual Heisenberg equations-of-motion or Liouvillian superoperator perturbation-theory approaches to systems with arbitrary statistical ensembles can give spurious, nonconvergent results when attempts are made to calculate the expectation value for certain operators which commute with the zeroth-order Hamiltonian. The non-Markovian, long-time tail of the Weisskopf-Wigner spontaneous-emission decay of a two-level atom is presented as an example of this failure. The general reason for such failures is elucidated and a new method applicable to arbitrary equilibrium or nonequilibrium statistical ensembles is formulated. The new method is applied to the same example of spontaneous emission to derive the correct short- and long-time behavior. The physical model of a two-level atom is discussed and some mathematical techniques of general usefulness are presented. The present results are also briefly discussed in the context of previous work on nonexponential decay. A fully quantum-mechanical definition of time-dependent spectral line shape is given in terms of the response of a two-level—atom detector with variable frequency interacting with electromagnetic radiation. The non-Lorentzian line shape recorded by such a detector for the spontaneous emission of a source two-level atom is calculated as another example of a problem for which the usual methods give incorrect results. The extension of the present method to Liouvillian or master-equation approaches is discussed.

The formation of ${\mathrm{Na}}^{+}$ and ${\mathrm{Na}}_2^{+}$ in laser-irradiated sodium vapor has been studied using a nitrogen-laser-pumped dye laser. The effects of irradiation by this pulsed laser are substantially different from those reported previously using a cw device, but otherwise identical experimental conditions. In contrast to the earlier experiments, in which ions were observed only when the cw laser was tuned to a $D$ line, relatively large "background" ion signals are observed at all excitation wavelengths, a result of multiphoton processes involving the ${\mathrm{Na}}_2$ component of the vapor. It is shown that the laser bandwidth and pulse duration are extremely important parameters; a wide bandwidth effectively magnifying the importance of the dimer component of the vapor and a short pulse duration minimizing the effects of interactions between excited atoms and molecules.

A number of spectrum lines arising from magnetic dipole transitions in the $3s^{2}3p^5$, $3s^{2}3p^4$, $3s^{2}3p^3$, $3s^{2}3p^2$, $3s^{2}3p$, and $3s3p$ electron configurations in elements $29\le Z\le 42$ have been identified. The lines were observed in the Princeton Large Torus tokamak discharges into which the appropriate elements were introduced by means of laser blowoff. The identifications are based on time and space dependence of the observed emissivities, and the systematic consistency of the observed wavelengths with isoelectronic extrapolations based on known lower-$Z$ elements.

Theoretical values for atomic photoionization cross sections, angular distribution asymmetry parameters, and spin-polarization parameters for the $3s$, $2p$, and $2s$ shells of magnesium are reported. Effects of the relativistic spin-orbit interaction and the electron-electron correlations are included by the use of the relativistic random-phase approximation in this study. Several series of autoionization resonances have been analyzed by making use of the multichannel quantum-defect theory. Comparisons with previous theoretical and experimental results where available have been made.

Photoionization cross sections and photoelectron angular distributions (asymmetry parameters) are obtained for $3p$-subshell ionization of the Cl ground state. A substantial amount of bound-state electron correlation is taken into account through use of a multiconfiguration description of the ground state and residual ionic core. Both independent-channel and coupled-channel final states are used in evaluating the length and velocity forms of the dipole transition amplitudes. In the coupled-channel case, channel interaction is included via the reaction-matrix ($K$-matrix) method which diagonalizes the total $N$-electron atomic Hamiltonian in the manifold of single-channel basis states of the model Hamiltonian. In all of the ${}_{}{}^2{}_{}{}^{}D$ and ${}_{}{}^2{}_{}{}^{}P$ final-state channels, the photoabsorption transition probabilities exhibit significant contributions from interchannel interaction. In determining the cross sections for any of the ${}_{}{}^2{}_{}{}^{}S$ channels, it was necessary to include the low-lying $3s3p^6$; ${}_{}{}^2{}_{}{}^{}S$ bound state because of its large Coulomb interaction with the continuum of the $3p^4{}_{}{}^1{}_{}{}^{}D$, $\epsilon d$; ${}_{}{}^2{}_{}{}^{}S$ channel. The addition of the channels which originate from a $3s\to \epsilon p$ transition into the set of interacting ${}_{}{}^2{}_{}{}^{}S$ channels nearly cancels the effect of the $3s3p^6$; ${}_{}{}^2{}_{}{}^{}S$ discrete state on the cross sections of both the $3p^4{}_{}{}^1{}_{}{}^{}D$,$\epsilon d$; ${}_{}{}^2{}_{}{}^{}S$ and $3p^4{}_{}{}^1{}_{}{}^{}S$,$\epsilon s$; ${}_{}{}^2{}_{}{}^{}S$ channels. The asymmetry parameters for the three ionic multiplets ${}_{}{}^3{}_{}{}^{}P$, ${}_{}{}^1{}_{}{}^{}D$, and ${}_{}{}^1{}_{}{}^{}S$ all show strong channel-interaction effects. The effects of the $3s3p^6$; ${}_{}{}^2{}_{}{}^{}S$ bound state and the $3s3p^5$; ${}_{}{}^{3,1}{}_{}{}^{}P$,$\epsilon p$; ${}_{}{}^2{}_{}{}^{}S$ channels on the ${}_{}{}^1{}_{}{}^{}D$ and ${}_{}{}^1{}_{}{}^{}S$ $\beta$ parameters are discussed.

Results of a nonperturbative investigation of the global behavior of quantum systems with time-periodic Hamiltonians are presented. These include the proof of a theorem stating that such systems, if bounded and nonresonant, will reassemble themselves infinitely often in the course of time. In order to illustrate the applicability of this result, an analytic study of a driven harmonic oscillator is presented, together with computer simulations of quantum maps describing the dynamics of a pulsed electron in a well and a periodically kicked rotor. A quantitative study of resonance excitation also shows that in practical situations recurrence is pervasive. Several unique quantum effects are analyzed, and their relevance to the classical limit is discussed. A formula is derived for recurrence times, and computer experiments are performed to test its validity.

The modification of the photoionization cross section due to the presence of an intense lowfrequency laser is obtained for the hydrogen-atom target. Previous calculations of this effect have neglected the effects of the Coulomb potential in the final state. A sum rule was obtained which indicates that the photoelectric current is unaffected by the presence of the low-frequency laser to lowest order in the laser frequency. We find that the Coulomb potential changes this result and that the photoelectric current is changed by a factor which depends upon the laser parameters and the electron momentum. A simple experiment is suggested to confirm this prediction.

Stark widths of the Ca II 3933.7- and 3968.5-Å resonance lines are measured around a temperature of 13 000 K and an electron density of ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$ in a stationary wall-stabilized arc burning in argon with a small addition of Ca vapor. The electron density is measured using the Stark width of the hydrogen H $\beta$ line. Optical-depth measurements are performed at the peaks of the investigated lines and the calcium concentration is carefully controlled to minimize the reabsorption. A Fabry-Pérot interferometer, whose instrumental profile is measured, yields the required high spectral resolution. The experimental profiles are analyzed using a least-squares fit of the Voigt function to all profile intensity points. The width of the Ca II resonance doublet is found about a factor of 2 lower than both semiclassical and full quantum calculations, in agreement with the earlier experiments of Yamamoto and of Roberts and Eckerle.

We have measured the time-dependent fluorescence of the sodium $D$ lines following pulsed excitation of one $D$ line, in the presence of radiation trapping with optical depths $k_{0}L$ of ∼10 to 2000. When collisional coupling of the $3P_{\frac{1}{2}}$ and $3P_{\frac{3}{2}}$ levels and different radiative-escape probabilities for each $D$ line are taken into account, we obtain excellent agreement with Holstein's theory for the effective radiative decay rates in the Doppler region ($k_{0}L\sim 10-300$) and in the redistributed Lorentzian region ($k_{0}L>\mathrm{}1000\mathrm{}$). For $k_{0}L$ between these two regions, we observe an abrupt transition between the two limiting formulas. The buildup rate of the sensitized fluorescence signal also yields a $3P_{\frac{3}{2}}\to 3P_{\frac{1}{2}}$ excitation transfer cross section in agreement with our previously reported cw measurement. Additionally, we have measured the dependence of the $3P$ fluorescence on laser power and beam diameter, and we explain the observed approach to saturation. We suggest that the previously reported "anomalous" approaches to saturation may be explained in terms of the laser beam burning through the optically thick vapor. Laser-beam spatial intensity variations and self-focusing also contribute to fluorescence signals that deviate from the usual single-atom saturation behavior.

We report an electron spectroscopy study of continuum-continuum transitions that follow multiphoton ionization. Xenon was ionized by 10-ns multimode pulses at wavelengths of 1064, 532, and 355 nm, at intensities up to ${10}^{13}$ W/${\mathrm{cm}}^2$. The photoelectrons are confined by a diverging magnetic field and energy analyzed by means of the time-of-flight technique. Our setup allows an acceptance angle of $2\pi$ sr at an energy resolution of 15 meV. At a wavelength of 1064 nm, 11-photon ionization is energetically allowed but we report spectra in which the 12- and up to 19-photon ionization processes show higher relative probabilities. The intensity dependence of the separate processes gives a result that deviates strongly from lowest-order perturbation theory. An interpretation of the width of the peaks in the electron spectra based on the ponderomotive force is proposed.

The core-valence-valence Auger spectrum of the ${\mathrm{F}}_2$ molecule has been calculated by the particle-particle Green's-function method. Main emphasis has been laid on the intermediate-energy region. The pronounced gap at 621-626 eV has been explained as a consequence of the partial breakdown of the quasiparticle picture for the inner-valence electrons.

Electron spectroscopy, combined with synchrotron radiation in the photon-energy range $h\nu \simeq 60-190$ eV, was used to measure the angular distributions of Xe $5p$ and $5s$ photoelectrons and of $N_{4,5}\mathrm{OO}$ Auger electrons. The branching ratios and partial cross sections for photoionization and Auger processes were also measured in certain cases. The measured asymmetry parameter $\beta$ for $5p$ photoelectrons agrees well with many-electron calculations, which predict a pronounced oscillation in ${\beta }_{5p}$ above the $4d$ ionization threshold due to the $4d-5p$ intershell interaction. The $N_{4,5}\mathrm{OO}$ Auger electrons are produced with photon-energy-dependent anisotropic angular distributions, resulting from alignmentof ${\mathrm{Xe}}^{+}$ by photoionization. The theoretical analysis of Auger-electron angular distributions is described, and theoretical calculations are found to predict the measured asymmetries well. In addition, Auger-electron peaks were observed to broaden and shift at photon energies near the $4d$ ionization threshold because of postcollision interaction. The measured shifts of the $N_5{O}_1{O}_1$ ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ line agree with previous measurements and theory. Electron spectra recorded through the energy region of the $4d\to \mathrm{np}$ Rydberg states show that they decay primarily by the Auger process, while the $5p$ and $5s$ partial cross sections are relatively weakly affected by autoionization. However, distinct resonance structure was observed in the $\beta$ parameters for $5p_{\frac{3}{2}}$ and $5p_{\frac{1}{2}}$ photoelectrons. The measured results are compared with a theoretical calculation of resonant photoionization for the $4d\to 6p$ excitation.

Degenerate perturbation theory is applied to study the first 14 energy levels of the hydrogen atom in a uniform magnetic field up to the second order. The twofold degeneracy of all the levels among them in terms of the oscillator or parabolic states is completely removed. The results obtained with the use of the Padé approximant are compared with those found in the literature. Level crossings are discussed.

The high-resolution Auger electron spectrum of HCl has been measured in the gas phase with the use of electron-beam excitation. The fine structure of the spectrum has been interpreted and compared with the calculated line energies. The energies of the initial states in H${\mathrm{Cl}}^{+}$ and the final states in H${\mathrm{Cl}}^{2+}$ have been calculated in the molecular-orbital linear combination of atomic orbitals self-consistent-field approach, with the correlation effects being taken into account in the frame of the configuration-interaction technique. The relative line intensities have been discussed in the light of the analogy to the Auger spectrum of the next-neighbor and isoelectronic element argon.

Numerical results for the statistical properties, and time-intensity correlation function, of a multiphoton-laser amplifier operating at very low intensity level are obtained and analyzed. Comparison with the rotating van der Pol oscillator model is made. Time variation of the second-order cumulant of the photon number displays a maximum at a time which is approximately evaluated.

It is shown that intense collisionless Raman-type extraresonant signals in four-wave mixing can be obtained by exciting a strongly fluorescent atomic or molecular eigenstate which is not directly connected to the states coupled by the Raman transition. The process which triggers the extraresonant signal is associated with resonance-enhanced three-photon scattering or, equivalently, with excited-state Raman scattering.

We show that the optical dephasing time $T_2$ can be obtained from a measurement of the time delay $T_0$ between two shifts of $\pm \frac{\pi }{2}$ in the phase of the exciting laser for which a null occurs in the jump in the nonlinear transmission through a sample. The phase shift is imposed upon a single-mode cw laser by applying a rectangular voltage pulse to an electro-optic phase modulator placed in the laser beam. The time delay at which the null occurs is proportional to $T_2$, which is given by the expression $T_2=\left(\frac{2}{\ln 2}\right)T_0$. The method is demonstrated in atomic sodium and iodine vapor and the separation of third-order optical transients from linear transients induced by the phase shift is discussed. An analytic expression for the jump in the nonlinear transmission, induced by the second phase shift, as well as for the transient in transmission following a single phase shift of a laser which weakly saturates an optically thin sample is derived. It is also shown that optical dephasing rates may be inferred from the variation of the integral of the transmitted light in a double-phase-switching experiment.

Absorptive optical bistability with a Gaussian amplitude fluctuation of the injected signal is investigated. In the limit of large laser linewidth and good stabilization of the amplitude fluctuations, a Fokker-Planck equation for absorptive optical bistability is derived. The stationary probability distribution is derived and its properties are discussed.

The spectrum, angular distribution, polarization, and coherence properties of the radiation emitted by relativistic electrons undulating through a quasiperiodic tapered magnetic field are studied. Tapering the wavelength and/or field strength along the undulator's axis has the effect of spreading the spectral line to higher frequencies; interference over this broader spectral range results in a more complex line shape. The angular dependence, on the other hand, is not affected by the amount of taper. The polarization of the radiation in the forward direction is determined by the transverse polarization of the undulator, but the polarization changes off axis. The radiation patterns predicted here are distinct from those of untapered undulators and their detection is now feasible. They will provide useful diagnostics of electron trajectories and threshold behavior in free-electron-laser oscillators using tapered undulators.