With the use of projection operators, the formal expressions of distorted-wave and coupled-channel-wave transition amplitudes for rearrangement collisions are derived. Use of projection operators (for the transition amplitudes) sharpens our understanding of the structural differences between the two transition amplitudes. The merit of each representation of the transition amplitudes is discussed. Derived perturbation potentials are found to have different structures. The rigorously derived distorted-wave Born-approximation (DWBA) transition amplitude is shown to be a generalization of the earlier DWBA expression obtained from the assumption of the dominance of elastic scattering in rearrangement collisions.

The decay curves for the delayed emission of 2p-1s and 3p-1s transitions in 40-MeV He- and H-like Ne projectiles excited by passage through a thin carbon foil have been measured. The decay curves, when compared to theoretical calculations, indicate that the l distribution is uniform in the high-n Rydberg states. Various structural features in the delayed x-ray emission spectra of 40-MeV Ne and 48-MeV Mg ions have also been examined.

Dissociative electron-attachment cross-section measurements for the production of ${\mathrm{H}}^{\mathrm{-}}$ and ${\mathrm{Cl}}^{\mathrm{-}}$ from HCl have been performed with use of a crossed target-beam–electron-beam collision geometry and a quadrupole mass spectrometer. The relative-flow technique is employed to determine the absolute values of cross sections. The attachment energies corresponding to various cross-section maxima are 7.1±0.1 eV and 9.05±0.1 eV for ${\mathrm{H}}^{\mathrm{-}}$/HCl; 0.85±0.02 eV for ${\mathrm{Cl}}^{\mathrm{-}}$/HCl. The cross sections at these maxima are 2.07×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ and 0.93×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ for ${\mathrm{H}}^{\mathrm{-}}$/HCl; 26.59×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ for ${\mathrm{Cl}}^{\mathrm{-}}$/HCl, respectively.

A theory for multipole-multipole collision under intense laser field is studied, and the formulas of transition probability and cross section are given. An application of this theory is made on the process given in the title.

It has been shown that the approximate solutions of the Fredholm integral equation for the scattering amplitude obtained by demanding that $f_{\mathrm{out}=f_{\mathrm{in}={\lambda }_p}}$,n${\mathrm{f}}_{\mathrm{Bn}}$ on the mass shell in the integral equation (where $f_{\mathrm{Bn}}$ is the scattering amplitude in the nth Born approximation, n and p are nonzero positive integers, and ${\lambda }_p$,n is a scattering-angle- and energy-dependent complex multiplying factor) are identical to those obtained from the Schwinger variational principle with incoming and outgoing trial wave functions which are correct to (p-1)th and (n-1)th order in the interaction potential in a Born approximation. Further, the scattering amplitude obtained from the Schwinger variational principle, with outgoing and incoming scattering waves correct up to first order in the interaction potential in the Born approximation, has been employed to calculate total collisional cross sections for $e^{\pm }$-H scattering in the 20–500-eV energy range. The results are in good agreement with the adopted cross section of de Heer et al. and those obtained in the modified Glauber approximation and the [2,2] Padé approximant for E≥30 eV.

We report the first application of the Schwinger multichannel formulation to low-energy electron collisions with a nonlinear polyatomic target. Integral and differential cross sections are obtained for e-${\mathrm{CH}}_4$ collisions from 3 to 20 eV at the static-plus-exchange interaction level. In these studies the exchange potential is directly evaluated and not approximated by local models. An interesting feature of the small-angle differential cross section is ascribed to polarization effects and not reproduced at the static-plus-exchange level. Our differential cross sections are found to be in reasonable agreement with existing measurements at 7.5 eV and higher energies.

The 1s-1s proton-hydrogen radiative electron capture is studied within the nonrelativistic semiclassical approximation. Several three-particle theoretical methods currently used in collision theory are applied. Double, single, and total cross sections are computed. The continuum distorted-wave method is found to present a projectile angular distribution with two critical angles, i.e., two enhancements, which can be physically visualized in terms of combined processes of a mechanical collision followed (or preceded) by an interaction with the radiation field. It is shown that for high projectile velocities, the contribution of these critical angles to the total cross section is negligible. Prior and post impulse approximations are also calculated.

A six-state coupled-channel calculation has been performed on the laser-assisted charge-transfer collision ${\mathrm{H}}^{+}$+Na+ħω. A greatly enhanced charge-transfer cross section is observed for low-energy collisions if the photon energy is matched to the classical satellite frequency. This frequency is determined by the location of an extremum in the difference of potential energies between the laser-pumped initial and final molecular states. The stationary-phase method has been used to reproduce the general features and the magnitude of the cross-section structure.

The optical-microwave atomic-beam magnetic resonance technique has been used to measure four hyperfine transitions in the $2^3$P state ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. These were used to determine the three hyperfine interaction constants (in MHz) as follows: contact, C=-4283.${84}_{\mathrm{-}0.01}^{+0.02\mathrm{}}$; nuclear-moment-electron-orbit, D=-28.06±0.06; nuclear-moment-electron-momment, E=+7.10±0.02. THe results, which are in excellent agreement with theory, give a clear indication of the effects of core polarization on the hyperfine structure. We conclude that to the accuracy indicated the structure of the 2 ${}_{}{}^3{}_{}{}^{}$P state, including mass-dependet and quantum electrodynamic corrections to the fine structure, and relativistic and core-polarization corrections to the hyperfine structure, is well understood.

A derivation and geometrical interpretation of multichannel quantum-defect theory (MQDT) is presented. An alternative set of MQDT parameters is suggested which separates into two independent groups, one representing the quantum defect of a Rydberg series in the absence of channel coupling and the other representing the channel coupling itself. An equivalent N-level system is developed so that the MQDT boundary conditions are replaced by a simple energy restriction on the N-level system, resulting in easier solutions of the equations. The equations are solved and spectra are presented for the simple two-channel case and for the three-channel case, where channel interactions lead to interferences in the spectra.

When an atom is irradiated by two light beams whose sum frequency corresponds to an allowed two-photon transition between two ${}_{}{}^1{}_{}{}^{}\mathrm{S}$ states, no radiation is absorbed if the electric vectors of the two beams are perpendicular to each other. Application of a magnetic field in a direction perpendicular to the plane defined by the two electric vectors permits two-photon absorption to take place. According to quantum theory the effect is interpreted as an interference phenomenon. That is, if no field is applied, the intermediate states are degenerate and the interference is destructive; when a magnetic field is applied, two different paths through intermediate states are possible, permitting population of the upper state. The effect is related to the Hanle effect and likewise provides the basis for an experimental method of determining Landé factors.

X-ray and Auger transition rates and fluorescence yields have been calculated for the [2p,3p] vacancy states of Ar. The standard Hartree-Fock procedure leads to radial 2p wave functions with a node in the tail region. The calculated transition rates agree well with experiment. A calculation in which special techniques are employed to obtain nodeless 2p wave functions leads to rather poor estimates of the lifetimes, similar to results of earlier Hartree-Fock-Slater calculations. The frozen-core approximation, widely used to calculate Auger rates, yields erroneous results. Reasons for these difficulties are discussed.

The 6s${\left[\mathrm{}\right(3/2\left)\mathrm{}\right]}_2$-6d${\left[\mathrm{}\right(3/2\left)\mathrm{}\right]}_2$ and 6s${\left[\mathrm{}\right(3/2\left)\mathrm{}\right]}_2$-6d${\left[\mathrm{}\right(1/2\left)\mathrm{}\right]}_1$ transitions in xenon have been observed in modest electric fields (E≤4500 V/cm). Their appearance is due to Stark mixing with nearby 7p levels. A calculation of the expected mixing coefficients is in good agreement with the observations. We suggest that Stark mixing in the cathode fall region of dc glow discharges is the mechanism by which the 6s${\left[\mathrm{}\right(3/2\left)\mathrm{}\right]}_2$-6d${\left[\mathrm{}\right(3/2\left)\mathrm{}\right]}_2$ transition is seen in discharge emission spectra.

The spectrum for absorption and emission of radiation by colliding atoms or a diatomic molecule is calculated for spectral regions dominated by an avoided level crossing. Example processes are absorption during an atom-atom collision with separation to either crossing atomic state, total absorption to both crossing states, and spontaneous emission during a collision with either state initially populated. Absorption and emission by bound diatomic molecules (including photodissociation) is described by the theory, and as an example it is applied to the ${\mathrm{Cs}}_2$ A-X band. Spectra due to single-velocity and impact-parameter collisions, as well as thermal and impact-parameter averages, are given. The shapes of the resulting spectra are parametrized by the interaction strength (or excitation transfer probability) between the crossing levels and the slopes of the ground- and excited-state potentials (assumed constant) in the region of the level crossing. The theory is applied to two observations of such regions that have been reported. We conclude that measurements of spectra in the region of level crossing is a very powerful diagnostic of the potentials and transfer probability in the level-crossing region, which is responsible for most inelastic atom-atom energy-transfer processes.

Accurate ab initio nonperturbative $L^2$ non-Hermitian Floquet calculations for intensity-dependent threshold shifts and ground-state total ionization widths (rates) for one-, two-, and three-photon-dominant intense-field ionization of atomic hydrogen are presented. The results show the importance of both the ac Stark shift and the pondermotive potential in the determination of the net threshold shift. In addition, branching ratios to individual continua have been estimated, yielding physical insights regarding the general features and mechanisms of the frequency- and intensity-dependent continuum-continuum transitions and ‘‘peak switching’’ phenomena in the above-threshold ionization processes.

A systematic investigation of N-level inversion schemes, with use of ‘‘chirped frequency lasers,’’ in and beyond the adiabatic limit is presented. (1) It is shown that, contrary to intuition, the favorable scheme for adiabatic inversion requires that, during the process, resonances occur in reversed order, i.e., first the (N-1)-N transition and then backward along the atomic-level ladder down to the transition 1-2. (2) A new multilevel inversion process at fast rates (far beyond the adiabatic limit) is found. Surprisingly, the process occurs for pulse area equal to π in spite of large (time-dependent) detunings. Full analytic explanation of this generalized π pulse inversion is presented. General new properties of the multilevel adiabatic approximation are also derived and discussed.

Recently, DeVoe and Brewer [Phys. Rev. Lett. 50, 1269 (1983)] observed a striking deviation from a prediction of the optical Bloch equations by monitoring optical free-induction decay in the impurity-ion crystal ${\mathrm{Pr}}^{3+}$:${\mathrm{LaF}}_3$. At low optical fields, the ${\mathrm{Pr}}^{3+}$ optical dephasing time $T_2$ arises from magnetic fluctuations of the local environment, but at elevated optical fields, $T_2$ is no longer a constant, as assumed in the Bloch equations, because the magnetic line-broadening process is quenched. Several theories have been developed to explain the phenomenon. In this paper we present a simple theory of relaxation in solids which allows for comparison with earlier work. A ‘‘strong-redistribution’’ model is proposed where the optically excited impurity ions experience frequency shifts ε induced by a thermal bath. Frequency jumps occur at an average rate Γ and with an rms value of ${\epsilon }_0$/ √2 , where ${\epsilon }_0$ is the thermal width associated with the frequency shifts. Modified Bloch equations (MBE) follow that are solved explicitly for two limiting cases, ${\epsilon }_0$≪Γ and ${\epsilon }_0$≫Γ, and qualitatively for the more general case where the ratio Γ/${\epsilon }_0$ is arbitrary. Since many of the earlier theories are equivalent to the strong-redistribution model in the limit ${\epsilon }_0$≪Γ, we can assess the validity of the approximations made by these authors. Finally, we compare our MBE to the analogous transport equations that describe the effects of collisions in atomic vapors. We conclude that the problem addressed here is a general one, common to solids and gases alike, and is not restricted to impurity-ion crystals but will occur whenever frequency fluctuations are important.

A theory of photoelectron counting is presented which combines the perturbation-theory approach of Glauber with the damped field model of Mollow. It is shown that, to first order in field spectral bandwidth, broadband photodetectors respond to photon flux rather than power. By phenomenologically including the effect of the detector on the field, the drawbacks and inconsistencies which limit the validity of traditional perturbative calculations to cases of very low quantum efficiency are eliminated.

We analyze the main features of transient bimodality in optically bistable systems. This phenomenon is proved to exhibit a nonmonotonic behavior in its dependence on the noise level, because a decrease of noise first enhances and subsequently damps the transient bimodality. Hence we identify a range of noise levels which characterizes the phenomenon. In this range the most probable switching time exhibits a remarkably linear dependence on the logarithm of the noise parameter. We discuss the dependence of the phenomenon on the distance from the critical point, especially in connection with the experiments on critical slowing down. Our results show a very satisfactory qualitative agreement with the recent experiments on transient bimodality performed by Lange and collaborators. We argue that our picture holds in general for a large class of systems which exhibit the phenomenon of transient bimodality.

We study the inverse free-electron-laser (IFEL) accelerator and show that it can accelerate electrons to the few hundred GeV region with average acceleration rates of the order of 200 MeV/m. Several possible accelerating structures are analyzed, and the effect of synchrotron-radiation losses is studied. The longitudinal phase stability of accelerated particles is also analyzed. A Hamiltonian description, which takes into account the dissipative features of the IFEL accelerator, is introduced to study perturbations from the resonant acceleration. Adiabatic invariants are obtained and used to estimate the change of the electron phase-space density during the acceleration process.