Absolute triple-differential probabilities for the emission of $\delta$ electrons in the near-symmetric collision system 10-MeV ${\mathrm{F}}^{q+}+\mathrm{Ne}$, for $q=6,8\mathrm{}$, and $9$, have been measured as a function of the impact parameter, the $\delta$-electron energy, and the $\delta$-electron emission angle. The impact-parameter dependence of these probabilities features for all observed collision systems, electron energies, and emission angles a sharp rise to a constant maximum at about 1.5 times the neon $K$-shell radius $r_K$ and fall off for impact parameters $b>\mathrm{}{r}_K$ somewhat exponentially with increasing electron energy. For an electron emission at 52.5° with respect to the beam axis this energy dependence is distorted by the occurrence of a binary-encounter peak. The $\delta$-electron emission probabilities show a strong asymmetry for electrons emitted in forward beam direction. A comparison of the experimental data obtained in 10-MeV ${\mathrm{F}}^{9+}$ + Ne at an electron emission angle of 90° with a recent semiclassical-approximation-type calculation shows discrepancies in both the impact-parameter dependence and in magnitude of the emission probabilities. However, the energy dependence is reproduced reasonably well in this model.

An algebraic approach for evaluation of the bound-free transition form factor $〈{\overrightarrow{\mathrm{v}}}^{-}\left|\exp \right(i\overrightarrow{\mathrm{Q}}·\overrightarrow{\mathrm{r}}\left)\right|n,l,m〉$ between arbitrary hydrogenic initial states $|n,l,m〉$ and continuum final states $|{\overrightarrow{\mathrm{v}}}^{-}〉$ in the low-velocity limit $v\ll \frac{Z}{n}$ is developed. This form factor determines the initial-state dependence of the electron-loss-to-continuum (ELC) cusp in the Born approximation. The method extends the well-known algebraic O(4,2) approach for bound-bound transitions to lowlying continuum states by exploiting the continuity across the ionization limit. A correspondence between scattering states and Rydberg bound states is established using the fact that the Runge-Lenz vector $\overrightarrow{\mathrm{A}}$ and the velocity vector $\overrightarrow{\mathrm{v}}$ become collinear near the ionization threshold. The present method takes explicitly into account the dynamical symmetry of the Coulomb field. We use the result for a systematic investigation of the doubly differential cross section and the shape of ELC cusps as a function of the initial state, its binding energy, the target, and the projectile velocity ($v_P$) within the Born approximation. Comparison is made with recent experimental data from our laboratory for highly charged projectiles. We find qualitative—and sometimes quantitative—agreement with the data.

We present approximate off-shell wave functions and $T$-matrix elements obtained using a uniform semiclassical propagator. The approximate off-shell wave function is valid near turning points and stationary-phase points for the incoming or outgoing momenta. Our results for the off-shell $T$-matrix elements reduce to the primitive semiclassical results in appropriate limits but extend the range of validity of the available semiclassical approximations.

Kinetic equations for the spin-density operators of the diamagnetic and paramagnetic states of the positive muon are obtained for the description of the slowing-down process encountered when high-energy muons thermalize in a single-component gas. The motion of this two-species system is generated by the Liouville superoperators associated with the diamagnetic and paramagnetic spin Hamiltonians and by time-dependent rate superoperators which depict the probabilities per collision that an electron is captured or lost. These rates are translational averages of the appropriate Boltzmann collision operators. That is, they are momentum and position integrals of the product of either the electron capture or loss total cross section with the single-particle translational density operators for the muon (or muonium) and a gas particle. These rates are time dependent because the muon (or muonium) translational density operator is time dependent. The initial amplitudes and phases of the observed thermal spin polarization in muon-spin-rotation ($\mu \mathrm{SR}$) experiments are then obtained in terms of the spin-density operators emerging from the stopping regime.

Our recently proposed several-electron theory of collisional excitation in quasi-one-electron systems is applied to the resonance excitation process ${\mathrm{Be}}^{+}\mathrm{}\left(2s\right)+\mathrm{He}\to {\mathrm{Be}}^{+}\mathrm{}\left(2p\right)+\mathrm{He}$. The general theory is reduced to that of a quasi-one-electron model by neglecting collisional excitation of the helium target atom. The velocity-dependent, nonlocal interactions of this theory give rise to strong short-ranged forces which account rather well for values of the excitation cross section, polarization of impact radiation, and coherence parameters observed experimentally for impact energies in the range $0.4<E<\mathrm{}2\mathrm{}$ keV. The calculations have been made using limiting forms of the theory which are appropriate to low and high impact energies.

A simple model of electron scattering resonances near electronic excitation thresholds is discussed. The model consists of a single discrete electronic state coupled to several electronic continua. The vibrational dynamics in the resonance state is treated, taking proper account of non-Born-Oppenheimer effects in near-threshold electron-molecule scattering. The effect of long-range potentials is included via the threshold expansion of the partial decay widths of the resonance. The analytic properties of the fixed-nuclei $S$ matrix are analyzed in detail for two special cases ($s$-wave scattering in the absence of long-range potentials and scattering from a strongly polar target molecule). The dipole potential is shown to lead to a qualitatively new behavior of the trajectories of resonance poles near excitation thresholds. The model yields a qualitative description of the measured excitation function of the $B^1{\Sigma }^{+}$ state of the CO molecule, where a strong and narrow threshold peak is observed.

When two atoms are in proximity, their resonance lines are broadened because of the formation of molecular potentials, between which photon transitions can occur. The level of experimental refinement in measuring excimer and collisional far-wing spectra calls for interpretive theoretical methods that accurately treat the observed structure in line shapes. Of particular interest are satellites and undulations, for they can give much information on intermolecular potentials. We derive an expression for $T$-matrix elements, based on JWKB wave functions and stationary-phase techniques, that is universally applicable to situations with one, two, or more Condon points. Each transition point is treated individually, with effects of potential shape, wave-function phases, and interference separately highlighted. The expression is tested against quantum-mechanical line shapes of the red and blue wings of the Rb $D$ lines broadened by Xe perturbers. Agreement is quite good for both the red-wing undulations and the blue-wing satellite-supernumerary structure.

The $K\alpha$ satellite and hypersatellite spectra of alkali-metal and alkaline-earth fluorides, excited by 80-MeV Ar ions, and the $K\alpha$ satellite spectra of a variety of gaseous fluorine compounds, excited by 48-MeV Mg ions, have been measured with a curved-crystal spectrometer. Analysis of these spectra using primary vacancy distributions deduced from spectra of Ne and HF, excited by the same projectiles, yielded rate constants for $L$-vacancy filling. The rate constants obtained from the satellite and hypersatellite distributions of the solid compounds are about the same (30×${10}^{-4\mathrm{}}$ a.u.), but those obtained for the gaseous compounds are much smaller. A two-step mechanism involving electron transfer from outer levels of surrounding atoms to high-$n$ states of the target atom, followed by subsequent $L$ Auger decay is proposed.

When a beam of spin-polarized metastable ${\mathrm{He}}^{+}\left({2s}_{\frac{1}{2}}\right)$ ions is quenched by an electric field $\overrightarrow{\mathrm{E}}$, the emitted radiation intensity contains an asymmetry term proportional to $\left(\hat{k}·\hat{E}\right)(\overrightarrow{\mathrm{P}}·\hat{k}\times \hat{E})$, where $\overrightarrow{\mathrm{P}}$ is the spin-polarization vector and $\hat{k}$ is the direction of observation. The resulting asymmetry is nearly proportional to the level width of the ${2p}_{\frac{1}{2}}$ state in ${\mathrm{He}}^{+}$. The measured asymmetry 0.007 602 7±0.000 020 3 corresponds to a lifetime ${\tau }_{2p}=(0.9992\mathrm{}\pm 0.0026)\times {10}^{-10\mathrm{}}$ sec, in fair agreement with the theoretical value ${\tau }_{2p}=0.9972\mathrm{}\times {10}^{-10\mathrm{}}$ sec.

In model problems involving the "decay" of discrete states into electron and photon continua there is frequently a final-state coupling between the two continua which must be considered. Armstrong, Theodosiou, and Wall have shown that this coupling can change the relative decay probabilities into the two channels. We examine and interpret this continuum-continuum coupling further, paying particular attention to questions of unitarity violation and the validity of the pole or Markov approximation for the continuum-continuum coupling. We also examine unitarity violation and the pole approximation in a more general context, and discuss criteria under which the approximation can be made in sequential diagonalizations. Finally, we interpret the square of the Fano $q$ value as the ratio of two rates in the pole approximation.

X-ray wavelengths, Auger energies, and decay rates have been calculated for various states of the ${\mathrm{P}}^{4+}$ ion, with configurations $\left(1\mathrm{}{s}^{2}2s^{2}2p^5\right)3s3p,3s3d,3p3d,3s^2,3\mathrm{}{p}^2$, and $3d^2$. Intermediate coupling and configuration interaction have been taken into account. The energies and decay rates are found to be strongly affected by configuration interaction. The theoretical results are compared with recent observations in ion-atom collision experiments. Good agreement with measured spectra is found, and the calculations characterize a number of lines that had not previously been identified.

Relative photoabsorption cross sections for the $1{\left(\frac{1}{2}\right)}_u\to 2{\left(\frac{1}{2}\right)}_g$ band of $\mathrm{Xe}_2^{}{}_{}{}^{+}$ have been determined at several discrete wavelengths between $\lambda =248\mathrm{}$ and 351 nm, the spectral region in which the absorption peaks. ${\mathrm{Xe}}^{+}$ ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ ions are produced by two-photon ionization of Xe at 193 nm (ArF laser) which dimerize to form $\mathrm{Xe}_2^{}{}_{}{}^{+}$ ions in the $1{\left(\frac{1}{2}\right)}_u$ ground state. A second excimer-laser pulse subsequently photodissociates the molecular ion. The results agree with the theoretical $1{\left(\frac{1}{2}\right)}_u\to 2{\left(\frac{1}{2}\right)}_g$ ultraviolet absorption curve of Wadt [J. Chem. Phys. 73, 3915 (1980)] except that the cross sections reported here indicate that the band is nearly symmetrical around $\lambda \simeq 340$ nm, rather than skewed towards the visible.

Radiative lifetimes of four ${}_{}{}^1{}_{}{}^{}S$ levels ($n=6-9\mathrm{}$) and seven ${}_{}{}^1{}_{}{}^{}P$ levels ($n=7-13\mathrm{}$) of He I have been measured using the high-frequency deflection technique. The ${}_{}{}^1{}_{}{}^{}S$ lifetimes, with estimated limiting errors of about 3-7%, agree well for $n=6-8\mathrm{}$ with theoretical lifetimes based on transition probabilities computed from central-field wave functions with exchange and configuration interaction. An apparent discrepancy between theory and experiment in the case of the $9{}_{}{}^1{}_{}{}^{}S$ measurement is largely removed when blackbody-radiation-induced emission and absorption processes are included in the theoretical lifetime. Radiative lifetimes for the ${}_{}{}^1{}_{}{}^{}P$ levels were determined under conditions where, in favorable cases ($n=8-12\mathrm{}$), the zero-pressure lifetimes differed by no more than 10-20% from the values measured at low pressures. In these cases, the estimated accuracy of the measurements is comparable to that of theory, and the agreement is deemed within the combined uncertainties. Quenching cross sections for the $n{}_{}{}^1{}_{}{}^{}S$ levels are also reported.

The first cross-section measurements have been made for the process $h\nu +{\mathrm{He}}^{-}\to {\mathrm{He}}^{+}+2\mathrm{}{e}^{-}$, from threshold (4.845 eV) to 0.41 eV above, where it attains a value of only 2×${10}^{-20\mathrm{}}$ ${\mathrm{cm}}^2$. Details of its energy dependence in this region were obscured by uncertainties due to a large background of ${\mathrm{He}}^{+}$ ions produced by the photodetachment-photoionization sequence, and the data do not permit a choice between existing theories. However, these are the first absolute cross sections for such a process, and provide the first determination of the branching ratio between the ejection of two electrons compared to a single electron in the threshold region for ionization.

The excitation and ionization of barium vapor by resonant laser irradiation was investigated in detail. Measurements were taken on a moderately dense vapor (${10}^{19}$ to ${10}^{21}$ ${\mathrm{m}}^{-3\mathrm{}}$) that was illuminated by an intense (7 GW ${\mathrm{m}}^{-2\mathrm{}}$) 1-μs-long dye-laser pulse. The laser was tuned to the Ba resonance line at $\lambda =553.5\mathrm{}$ nm, and burned through the 0.25-m-long vapor column in less than 50 ns. The excitation histories of twelve Ba and ${\mathrm{Ba}}^{+}$ levels were determined with a time resolution of 5 ns by use of hook-interferometry spectra. The emission, which reflected the population of high-lying levels, was also analyzed. For the higher densities investigated, almost complete ionization was achieved within 400 ns. Ionization was highly density-dependent and this pointed to collision-dominated ionization mechanisms. Strontium atoms—present as an impurity in the Ba vapor, yet not in resonance with the laser radiation—were also found to ionize rapidly. This provided further confirmation of the dominance of collisions. We established that seed electrons were heated in superelastic collisions with laser-excited atoms, and that subsequent electron-impact excitation and ionization, as well as photoionization of high-lying levels lead to the creation of more electrons. Electron density and concomitant ionization then increase rapidly. The observed transfer of the excitation energy to the electrons by superelastic collisions requires contributions not only from the laser-pumped resonance level, but also from the lower-lying metastable Ba levels. These are, in fact, populated very rapidly and efficiently via the resonance level.

The atomic-beam, laser-rf double-resonance technique has been used to make precise measurements of the dipole and quadrupole hyperfine constants of the ${}_{}{}^3{}_{}{}^{}H_{6,5,4}^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}F_{4,3,2}^{}{}_{}{}^{}$ states of the $4f^{12}6s^2$ configuration of ${}_{}{}^{167}{}_{}{}^{}\mathrm{Er}$ I. The hyperfine integrals $〈r^{-3\mathrm{}}〉$ are extracted and compared with published ab initio calculations.

Multiphoton ionization in the region near a three-photon resonance is treated for focused, plane-polarized Gaussian beams with diffraction-limited beam divergence. In this situation, a third-harmonic field is generated within the laser beam. At, and very near, three-photon resonance the driving rate for the upper-state probability amplitude due to one-photon absorption of third-harmonic light becomes nearly equal to the corresponding three-photon rate due to the laser field, but these effects are 180° out of phase. As a consequence of this cancellation between two pumping terms, the three-photon resonance line essentially disappears at moderate concentrations and the observed ionization has a line shape that is close to the phase-matching curve for third-harmonic generation. The ionization signal, near but not on the resonance, is due almost entirely to absorption of third-harmonic photons plus other laser photons; three-photon resonantly enhanced multiphoton ionization by the laser is much weaker. This is particularly true on the blue side of the three-photon resonance at detunings where phase matching occurs. The problem is treated quite generally with predictions of the full line shape for $n$-photon ionization and third-harmonic light generation near three-photon resonance, including the rather strong influences of positively dispersive buffer gases. We also show that the cancellation between the one-photon and the three-photon process is partially spoiled in the presence of a counterpropagating beam at the same frequency.

A general expression for the four-wave—mixing profiles in situations involving autoionizing resonances is derived by taking fully into account the spontaneous-emission characteristics of the autoionizing states. The signals are valid for arbitrary values of Fano asymmetry parameters, field strengths, and spontaneous-emission rates. The dramatic increase in the four-wave—mixing signal for field strengths corresponding to the confluence is demonstrated. The spontaneous emission is shown to affect the line shapes not only in weak fields but also in strong fields. The effects of spontaneous emission are found to be most important for field strengths corresponding to confluence which is similar to the problem of laser-induced autoionization.

A fully self-consistent theory of the free-electron laser is derived in the collective regime which includes all transverse variations in the wiggler field as well as the effects of a finite waveguide geometry. A general orbit theory is derived by perturbation about the steady-state trajectories in a configuration which consists of an axial guide field in addition to the helical wiggler field, and used to obtain the source current and charge density for the Maxwell-Poisson equations. By this means, a set of coupled differential equations is found which describes an arbitrary radial beam profile. A dispersion equation is obtained under the assumption of a thin monoenergetic beam, and solved numerically for the growth rates of the T${\mathrm{E}}_{11}$ and T${\mathrm{M}}_{11}$ modes in a cylindrical waveguide. A selection rule is found by which the ${\mathrm{TE}}_{\mathrm{lm}}$ or ${\mathrm{TM}}_{\mathrm{lm}}$ modes are resonant at the $l\mathrm{th}$ free-electron-laser Doppler upshift.

Saturation inhomogeneity produced by a Gaussian field in a gas laser and population inhomogeneity are responsible for lens effects which depend on frequency. They give rise to frequency-dependent transverse parameter variations which, in general, result in an asymmetric line shape. The main objective of this paper is to give a method which yields closed-from expressions for these variations and permits their analytical discussion. As an application we determine a laser structure which minimizes the variations in the region around one of the mirrors. It gives a laser which is stabilized in its transverse parameters and is characterized by a symmetric Lamb dip. We experimentally confirm this result using the 3.39-μm line of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$.