A semiclassical coupled dressed-quasimolecular-states (DQMS) approach is presented for nonperturbative treatment of multichannel charge-transfer reactions at low collision velocities and high laser intensities, incorporating the implementation of the generalized Van Vleck (GVV) nearly degenerate perturbation theory. The GVV technique allows block partitioning of the infinite-dimensional Floquet Hamiltonian into a finite-dimensional model DQMS space, and thereby reduces greatly the number of effective coupled channels. Further, the GVV-Floquet basis allows minimization of the (usually large in amplitude) field-induced nonadiabatic radial couplings without the need to explicitly construct the transformation between the adiabatic and diabatic DQMS basis. This yields a new set of coupled GVV-DQMS equations (neither adiabatic nor diabatic) which are particularly convenient for multichannel calculations. The method is applied to the study of the laser-assisted charge-transfer process: ${\mathrm{Li}}^{3+}$+H(1s)+ħω→${\mathrm{Li}}^{2+}$(n= 3)+${\mathrm{H}}^{+}$, using 2-, 5-, and 15- GVV-DQMS basis. It is found that while the 5-state results agree well with the 15-state calculations even up to very high intensities for the (LiH${)}^{3+}$ system, the 2-state basis is inadequate at high-intensity and lower-wavelength regimes. Detailed results and nonlinear dynamical features are presented for the process at small impact velocity ${10}^7$ cm/s and strong laser fields with intensity ranging from 1 to 100 TW/${\mathrm{cm}}^2$ and wavelengths from 1500 to 3000 Å.

We report results for vibrationally elastic scattering over the energy range 0.0006–11.6 eV. The interaction potential is composed of a near-Hartree-Fock static term plus a parameter-free model of the correlation-polarization potential. The exchange interaction is included exactly through a separable expansion. Results with a model-exchange potential (free-electron-gas plus orthogonalization) are also reported. A resonance appears in Π symmetry near 2.7 eV (width 1.9 eV) that may be the same feature observed in several experiments. In the model-exchange calculation the Π resonance is shifted toward higher energy (3.8 eV, width 2.4 eV). The Σ symmetry was also found to be very sensitive to the treatment of exchange and to the effect of polarization. Differential and rotational excitation cross sections are evaluated in the multipole-extracted adiabatic-nuclei approximation. Results are compared with the available experimental and theoretical data.

We study the discrete eigenvalues $E_{\mathrm{nl}}$ of the Schrödinger Hamiltonian H=-(1/2)Δ+V(r), where V(r)=g(-1/r) is an increasing concave transformation of the Coulomb potential, and n is the principal (radial) quantum number. It is demonstrated by the method of potential envelopes that upper bounds are provided by the simple formula $E_{\mathrm{nl}}$≤ ${\min }_{\mathrm{s}>0\mathrm{}}$ {(1/2)s+V((n+l)/${\mathrm{s}}^{1/2}$)}, where s is a real variable. Numerical results are compared with previous work for two specific screened Coulomb potentials. In the case of the Yukawa potential V(r)=-(v/r)exp(-λr), it is shown that the inequality (n+l${)}^2$λ/v<2/e is sufficient to guarantee the existence of the eigenvalue $E_{\mathrm{nl}}$: In the case of S states, sharp upper and lower bounds are also provided by a different method.

Absolute total cross sections for electron detachment have been measured for collisions of ${\mathrm{Na}}^{\mathrm{-}}$ and ${\mathrm{K}}^{\mathrm{-}}$ with rare gases at relative collision energies ranging from a few eV to about 200 eV. These alkali-metal anions, which are characterized by angularly correlated ${\mathrm{ns}}^2$ electrons, are observed to be extremely stable with respect to collisional electron detachment. For the ${\mathrm{Na}}^{\mathrm{-}}$-Ne and ${\mathrm{K}}^{\mathrm{-}}$-Ar,Kr,Xe systems, the salient features of the detachment cross sections are described by a simple curve-crossing model. Cross sections for ${\mathrm{Na}}^{\mathrm{-}}$-He,Ar,Kr,Xe and ${\mathrm{K}}^{\mathrm{-}}$-He,Ne remain small (<0.5 A${̊}^2$) throughout the energy range studied. Striking similarities are observed between the energy dependence of these detachment cross sections and that of the cross sections for projectile excitation which results from neutral-alkali-metal–rare-gas collisions.

Differential cross sections for the elastic scattering of 344-, 411-, 444-, 723-, 779-, 868-, 964-, 1005-, 1086-, 1112-, 1275-, and 1408-keV γ rays by ${}_{29}{}^{}{}_{}{}^{}\mathrm{Cu}$, ${}_{42}{}^{}{}_{}{}^{}\mathrm{Mo}$, ${}_{50}{}^{}{}_{}{}^{}\mathrm{Sn}$, ${}_{73}{}^{}{}_{}{}^{}\mathrm{Ta}$, ${}_{82}{}^{}{}_{}{}^{}\mathrm{Pb}$, and ${}_{92}{}^{}{}_{}{}^{}\mathrm{U}$ have been measured for scattering angles of 2°, 3°, 5°, 7°, and 10°. These cross sections generally agree to better than 15% with theoretical cross sections for Rayleigh plus nuclear Thomson scattering, where the Rayleigh scattering amplitudes have been represented by relativistic Hartree-Fock-Slater modified form-factor amplitudes.

First-order many-body theory has been used to calculate the differential, integrated, and momentum-transfer cross sections for the electron-impact excitation of the 5s’${\left[\mathrm{}\right(1/2\left)\mathrm{}\right]}_1^0$(${}^1$$P_1$ ), 5s${\left[\mathrm{}\right(3/2\left)\mathrm{}\right]}_1^0$(${}^3$$P_1$), 5s’${\left[\mathrm{}\right(1/2\left)\mathrm{}\right]}_0^0$(${}^3$$P_0$), and 5s${\left[\mathrm{}\right(3/2\left)\mathrm{}\right]}_2^0$(${}^3$$P_2$) states of krypton for the incident energies of 20, 30, 50, 60, and 100 eV. Electron-photon coincidence parameters for the optically allowed states have been obtained. The results are compared to available experimental results.

Electron-hydrogen scattering to the 1s, 2s, and 2p states is calculated at 54.42 and 200 eV, and compared with experimental data. Higher-energy reaction channels, including the continuum, are taken into account in two different ways: first, in approximate polarization potentials involving explicit integration over the appropriate kinematic degrees of freedom; second, in a set of seven pseudostates for which the 10-channel pseudoproblem is solved in full. In anticipation of larger and better pseudostate sets, approximations to the pseudoproblem are investigated. They involve second-order treatment of coupling to the pseudostates.

Cross sections for the K-shell ionization of medium-heavy atoms by relativistic electrons have been calculated in a relativistic framework in the Coulomb gauge to order ${\alpha }_0$ (=$e^2$/ħc) in the interaction Hamiltonian. Here exchange is neglected. The incident- and scattered-electron wave functions are described by Dirac plane waves. Only the bound- and ejected-electron wave functions are described nonrelativistically for a screened Coulomb potential, used earlier by the present authors. Thus the screening effect is taken into account in this calculation in a satisfactory manner. The calculation is a repetition of what has been published recently by the present authors with one important exception: Here, the ejected-electron continuum state wave function that is used is determined variationally for the above screened Coulomb potential. Thereby some perturbation approximation of ad hoc nature could be avoided. As a consequence, considerable improvement is noticed in the total cross-section results. Comparison with experimental results for ${}_{}{}^{29}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{47}{}_{}{}^{}\mathrm{Ag}$, and ${}_{}{}^{79}{}_{}{}^{}\mathrm{Au}$ shows a good agreement. The calculation may easily be extended to ionization from other shells.

Vibrational excitation and dissociative electron attachment via the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ shape resonance in ${\mathrm{H}}_2$ is treated within the framework of Feshbach’s projection-operator formalism. The problem of nuclear motion in the complex, energy-dependent, and nonlocal potential of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ resonance is solved with the use of a separable expansion of the nonlocal potential. The resonance energy, width function, and level-shift function, which characterize the resonance in the fixed-nuclei limit, are taken from recent ab initio calculations based on the many-body optical-potential approach [M. Berman, C. Mündel, and W. Domcke, Phys. Rev. A 31, 641 (1985)]. Integral cross sections for vibrational excitation of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ up to v=4 and for dissociative electron attachment to ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ molecules in the vibrational levels v=0, 1, and 2 have been calculated. The calculations provide a good overall description of the experimental data for both ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$. Pronounced isotope effects and a strong dependence of the attachment cross section on the vibrational state of the target molecule are found, in qualitative agreement with experimental observations. The accuracy of two widely used approximations, the adiabatic-nuclei approximation and the local-complex-potential model, is quantitatively assessed for this prototype resonance. While the off-shell adiabatic-nuclei approximation provides a qualitatively satisfactory description of vibrational excitation, we observe a stunning failure of the local-complex-potential model. Empirical local complex potentials, fitted to reproduce experimental vibrational excitation and dissociative attachment data in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ within the local-potential model, lack any physical meaning.

We have obtained necessary conditions for the mapping of the reduced first-order density operator γ into the density ρ. These conditions are given as restrictions on the elements of Γ, the reduced first-order density matrix. The implications of these conditions for a density-functional theory based on γ, with built-in pure-state n-representability conditions, are discussed.

Total photon attenuation coefficients near absorption edges are determined in certain suitable elements and compounds. Photoelectric cross sections for elements are deduced from these by subtracting the coherent and incoherent scattering cross sections as well as other elemental cross sections in the cases of compounds. Certain deviations are observed on comparison with the available theoretical and experimental compilations. The & x-ray intensity ratio measured by photon excitation near threshold is found to agree better with the theory than the other available experimental data.

The description of ion-atom collisions in a mean-electric-field approximation is discussed. In this method the sum of the interactions between the projectile and the electrons of the target is expressed as the sum of the Coulomb field acting on the center of charge of the target electrons and a residual interaction. For distant (high-energy) collisions the residual interaction can be neglected. The calculation of the scattering amplitude corresponding to the mean electric field is performed within the framework of the first Born approximation. It is shown that for high-energy collisions the scattering amplitude is a product of single-electron scattering amplitudes and the cross sections of the multiple ionization follow the binomial distribution. A simple expression is derived for the cross section of n-vacancy production. The calculated ionization cross sections and mean numbers of outer-shell vacancies in the presence of an inner-shell vacancy are in satisfactory agreement with experimental values for high projectile energies.

Dispersive line shapes have been observed in the population of the intermediate level of a three-level Λ configuration in a fast beam of metastable ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}_{}^{\mathrm{*}}{}_{}{}^{}$ atoms. A steady-state calculation in the weak-probe approximation is used to identify the main physical processes in the interaction of the system with a weakly saturating pump field and a weak probe field. It is shown how optical-pumping effects between the lower levels can be used to select one particular two-photon process. The selection is enhanced by the narrow Doppler profile of the fast beam. Our simple analysis explains the resulting dispersive line shapes both qualitatively and quantitatively.

The nonlinear coupling of 193-nm radiation to a range of atomic and molecular materials has been experimentally explored up to a maximum intensity on the order of ∼${10}^{17}$ W/${\mathrm{cm}}^2$. Studies of collision-free ion production clearly exhibit anomalous behavior which strongly implies that the atomic shell structure is the principal determinant in the observed response. On the basis of the observed coupling strength and the measured atomic-number (Z) dependence, the experimental evidence points to a coherent atomic motion involving several electrons, possibly an entire shell, as the main physical mechanism enabling the scale of energy transfers seen. Therefore, states representing multiple excitations appear to play a central role in the coupling, a consideration that fundamentally distinguishes the nonlinear interaction of a multielectron atom from that of a single-electron system. Comparison of the experimental findings with standard theoretical treatments, of either a perturbative or nonperturbative nature, does not produce satisfactory agreement. Conversely, the formulation of a simple classical estimate qualitatively conforms to several features of the observed behavior including the shell character of the interaction, the maximum energy transfer, the dependence of the average energy transfer on the intensity of irradiation, the frequency dependence of the observed energy transfer, and the weak influence of polarization.

Zeros in dipole matrix element are found for heavy ions, even when highly ionized, from our relativistic calculation. While the photon energy at which a zero occurs does vary slowly with degree of ionization, the disappearance of bound continuum transition zeros in high-Z elements is primarily associated with the increase in the binding energy of a given subshell with increasing degree of ionization. The stabilization of the value in photoelectron energy of the Cooper minima, as a function of degree of ionization and of principal quantum number n, is also discussed.

Theoretical and experimental investigations of the quartet system of C iv are reported. Twenty-seven quartet-state energies are calculated. Based on this work, several lines observed for the first time in the extreme-ultraviolet beam-foil spectra of carbon (10–200 nm) are classified as 1s2pnl ${}^4$L–1s2pn’l’ ${}^4$L’ and 1s2snl ${}^4$L–1s2sn’l’ ${}^4$L’ (n=2,3; n’=4,5) transitions. The calculated fine structures for the quartet states are also reported. In addition, a list of new observed lines classified in C iii and C iv is given.

The internally excited 4$p^5$4$d^2$ configuration gains notoriety in the Rb isoelectronic sequence from Y iii onwards for appreciably disturbing levels of the nf and np series of the one-electron spectra. We have worked out, on the basis of the spectra recorded in collaboration with J. O. Ekberg at Lund University and with the help of R. D. Cowan’s computations, transitions from this configuration to the ground configuration 4$p^6$4d. Of the 45 levels of 4$p^5$4$d^2$, all 38 that can combine with 4$p^6$4d are established. Many levels of 4$p^5$4$d^2$ are computed to be highly mixed within the configuration, as well as with levels of 5f ${}^2$F, 4f ${}^2$F, 6p ${}^2$P, and 5p ${}^2$P in descending order of magnitude. This is evidenced experimentally by the observation of transitions connecting some 4$p^5$4$d^2$ levels with those of ns, nd (other than 4d), and ng.

The measurement of the interaction in barium of five bound, doubly excited perturber states with singly excited Rydberg series is reported. The five perturbers are the 5d7d ${}^1$$D_2$, 5d7d ${}^3$$F_2$, 5d7d ${}^1$$P_1$, 5d7d ${}^3$$S_1$, and 5d7d ${}^3$$P_0$ states. The J=2 perturbers interact with the 6snd ${}^3$$D_2$ and 6snd ${}^1$$D_2$ Rydberg series; the J=1 perturbers interact with the 6snd ${}^3$$D_1$ and 6sns ${}^3$$S_1$ series; and the J=0 perturber interacts with the 6sns ${}^1$$S_0$ series. We observe the relative cross section for photoexcitation of the 6p7d autoionizing resonance from each of the perturbers and interacting states nearby in energy where the photon energy roughly corresponds to the energy separation of the 5d and 6p ${\mathrm{Ba}}^{+}$ states. The relative strength of the transition is directly related to the 5d7d character of the bound states. Good agreement with extensive previous work is obtained for the 5d7d ${}^1$$D_2$ and 5d7d ${}^3$$P_0$ states. General agreement with previous work is obtained for the 5d7d ${}^3$$F_2$, 5d7d ${}^1$$P_1$, and 5d7d ${}^3$$S_1$ states and specific discrepancies are clarified.

Three-body calculations of photon spectra associated with radiative electron capture are carried out by using the first-order Born approximation. Shell-to-shell results are presented. The theory is compared with experimental results measured at 90° to the incident beam. Structures occurring in the experiments are explained in terms of transitions to higher shells of the projectile coming from K or higher shells of the target.

The dynamical behavior of a multimode dye laser with an intracavity absorber has been investigated theoretically as well as experimentally. This behavior is described by a system of rate equations which has to include the influence of saturation in the case of large absorption coefficients. With the rate-equation-system model calculations have been performed for the cases of saturated and unsaturated intracavity absorption. Saturation of the absorption is shown to severely reduce the sensitivity of intracavity absorption. In general, the sensitivity is governed by the average lifetime of the individual modes. This mode lifetime is limited by large intensity fluctuations which are capable of quenching individual modes. The probability for mode quenching is shown to increase with increasing spectral power density. For this reason, intracavity absorption gains sensitivity close to the lasing threshold. The theoretical results are found to be in excellent agreement with our measurements. In addition, discrepancies in previous work have been resolved within the framework of our theory. With the detailed understanding of the intracavity absorption, reliable measurements of very small, absolute absorption coefficients have become possible.