An integral transformation is given which when applied to hydrogenic-type wave functions converts them into Gaussian form. This is particularly needed in the evaluation of the two-particle matrix elements of the interaction operator. Further examples of the use of the transformation are given by calculating the Wigner transform for the ground state of the H atom and matrix elements of the powers of the z coordinate.

We have evaluated explicitly from the current of the electron in a nonstationary superposition state the near and far potentials and fields, then the radiated flux, and with it, the rate of spontaneous emission with retardation. The Schrödinger current gives a power which is four times smaller than the observed rate of spontaneous emission.

We have calculated unified photorecombination cross sections and independent-processes photorecombination cross sections for ${\mathrm{U}}^{90+}$ in the vicinity of the KLL resonances. For this case, where the radiative width of a level dominates the Auger width, we find relatively strong interference effects between the direct (radiative) and indirect (dielectronic) recombination processes. In particular, we find that the unified photorecombination cross section for the 1${\mathit{s}}^2$+${\mathit{e}}^{\mathrm{-}}$→1${\mathit{s}}^2$2s+hν line is suppressed by a factor of 2 in the presence of the 1s2s(1)2p(3/2) resonance. Overall, however, the KLL recombination cross section is reduced by only 2–3 %, at most.

Photodetachment from negative chlorine and sulfur ions has been studied in the presence of electric fields ranging from 0.5 to 2.7 kV/cm. While the applied electric field oscillated at 2.7 GHz, the data are consistent with the assumption that the field was constant during each detachment event. A simple model for the photodetachment cross section in a constant electric field is presented, appropriate to any ion where zero-field detachment is dominated by an s-wave continuum. The model is in good agreement with the data.

Starting from a scattering-theory formulation, cross sections for Auger and x-ray decay from energetically shifted inner-shell states are derived. Two situations are studied: (i) when there are several close-lying intermediate core-hole states with no vibrational excitations, in which case a state interference effect is identified; and (ii) when there are several close-lying intermediate states with vibrational excitations, in which case a vibronic interference effect is identified. In the latter case, the present formalism is a many-state generalization of the vibrational interference effects derived from the same type of scattering formalism in our previous paper [A. Cesar, H. Ågren, and V. Carravetta, Phys. Rev. A 40, 187 (1989)]. Applications are carried out for spectra of some few-state model systems. It is found that a conventional analysis in terms of discrete noninteracting (noninterfering) states, such as the one-center decomposition model, is only valid when the ratio (R) between energy shift and lifetime is sufficiently large. For states with small R, a more complete theoretical account must be undertaken, including, e.g., the calculation of phases of the respective transition moments. The presented formalism applies to resonance Auger or x-ray emission spectra, to Auger and x-ray emission from core-electron shake-up states, and also, under certain circumstances, to emission from chemically shifted core-hole states.

K-shell ionization cross sections induced by 1.1–8-MeV oxygen ions in Al, Si, S, Ca, and Zn were measured using different target thicknesses. The cross sections for vanishingly thin and for charge-equilibrium targets were obtained by extrapolation. The experimental results are compared to the perturbed stationary-state approximation with energy-loss, Coulomb, and relativistic corrections (ECPSSR) cross sections [Brandt and Lapicki, Phys. Rev. A 23, 1717 (1981)], to the modification of the ECPSSR theory (MECPSSR) [Benka, Geretschläger, and Paul, J. Phys. (Paris) Colloq. Suppl. 12, C9-251 (1987)], to the theory for direct Coulomb ionization of the 1sσ molecular orbital [Montenegro and Sigaud, J. Phys. B 18, 299 (1985)], and to several semiclassical approximation codes using either the united atom binding procedure or the variational approach of Andersen et al. [Nucl. Instrum. Methods 192, 79 (1982)]. The cross sections were also compared to the statistical molecular-orbital theory of inner-shell ionization for (nearly) symmetric atomic collisions [Mittelman and Wilets, Phys. Rev. 154, 12 (1967)]. For fast collisions (ξ∼1), the ionization cross sections are well reproduced by theories for direct Coulomb ionization. For slower collisions (ξ<1), the experimental cross sections are systematically higher than the direct-ionization values, but they agree satisfactorily with the summed cross sections for direct Coulomb ionization and for molecular-orbital ionization. Best agreement (within a factor of 2) was found for the sums of MECPSSR and statistical cross sections.

Experimental and theoretical data pertaining to the doubly differential electron emission occurring in collisions between structured projectiles and atoms are presented. How one or two loosely bound projectile electrons influence the ionization process was investigated for fast H- and He-atom impact on helium. Standard noncoincidence and ionized projectile–emitted-electron coincidence techniques were used to study the electron emission for 0.5- and 1-MeV/amu impact energies. The experimental data demonstrate the importance of events where both the projectile and the target are ionized in a single collision. From a comparison of theoretical calculations made using the first-order Born approximation and the experimental data, it is concluded that single ionization of the target and of the projectile are adequately described by such a model but that improved models are essential in order to account for the observed simultaneous projectile-target ionization events.

An analytic-calculation method enabling the evaluation of the real part of the anomalous scattering factor f¯’ from attenuation measurements in the x-ray range is presented. This method utilizes a power law to fit the variation of the experimentally observed mass attenuation coefficients as a function of the photon energy. It uses an analytic expression involving Gauss hypergeometric functions to calculate the dispersion term. A derivation of the relativistic correction to the dispersion term shows it to be smaller than the one used in the scattering-factor tabulation. The calculations using this method are tested for seven elements of medium Z: Pd, Ag, Cd, In, Sn, I and Xe, between 15 and 45 keV. Since they compare favorably with the ab initio calculation, the present approach can be considered as an advantageous alternative to the full calculation.

A dynamic theory is presented for the description of dissipative charge transfer in molecular systems. The quantum dynamics of the coupled electron-vibration motion are described in the framework of the density-matrix theory. The equations of motion of the density matrix are given in a representation that uses the Born-Oppenheimer states of the different localization centers of the electron together with the vibrational modes coupling to the electron. A dissipative environment is introduced by separating all molecular vibrations which do not couple to the transferred electron and providing thermal equilibrium for them. The description allows (a) the introduction of any type of potential surfaces, (b) the description of any microscopic model for the coupling between the vibrational modes and the dissipative environment, and (c) the consideration of any strength of electronic intercenter coupling. Therefore the approach allows one to study the transition from the wavelike to the hoppinglike electron motion between the centers as well as nonadiabatic transfer, adiabatic transfer, and any intermediate type. Besides the derivation of the basic density-matrix theory, the numerical solution of the density-matrix equations is presented for the model of a two-center single-vibrational-mode system. The exact results of the density-matrix equations are compared with those of approximate rate equations.

Iodine and bromine atoms produced by the laser-induced dissociation of, respectively, molecular iodine and bromine have been photoexcited in the region of the 4d→np (n>5) and 3d→np (n>4) excitations. Total ion-yield spectra show numerous lines whose positions and extensions are attributed to open-shell effects. The decay of the 4d→6p transition in atomic iodine has been investigated. The relaxation of this resonance is dominated by resonant Auger processes accompanied by strong shake processes. The comparison with the decay of the 4d→5p resonances in atomic iodine and with the 4d→6p resonances in xenon shows a strong sensitivity of the decay mechanisms of inner-shell resonances to the nature of the orbital into which the core electron has been promoted.

We report total and differential cross sections for electron-impact excitation of the T (ã ${}_{}{}^3{}_{}{}^{}$${\mathit{B}}_{1\mathit{u}}$) and ${(}^1$${\mathrm{B}}_{1\mathrm{u}}$) states of ethylene from threshold to 20 eV. The calculations were carried out using the complex Kohn variational method. For collision energies above the threshold for excitation of the V state, we carried out three-state close-coupling calculations using accurate multiconfiguration target states. An averaged natural orbital technique was used to obtain a compact representation of the V-state wave function that properly reflects the mixed valence-Rydberg character of this state. The total and small-angle differential cross sections for exciting the optically allowed V state are sensitive to the inclusion of high partial-wave contributions, which were computed using a simple perturbative scheme. In the energy range between the T and V states, where only two electronic states are open, we carried out dressed two-state calculations using optical potential techniques to incorporate the effect of closed channels. We found significant d-wave resonance behavior in the T-state excitation cross section near 5 eV. At higher energies, the T-state differential cross sections are backward peaked, while the V state cross sections show strong forward peaking that is typical of an optically allowed transition.

Transient molecular ions of ${\mathrm{CO}}^{\mathit{q}+}$ (where q=2–7) were produced in single collisions of 97-MeV ${\mathrm{Ar}}^{14+}$ projectiles with neutral CO molecules. The resulting dissociation products were identified by coincidence time-of-flight spectroscopy in which the time of flight of the first ion to reach the detector and the time difference between the first ion and its partner were recorded event by event. An iterative matrix-transformation procedure was employed to convert the time-difference spectra for the prominent dissociation channels into total-kinetic-energy distributions. Analysis of the total-kinetic-energy distributions and comparisons with the available data for ${\mathrm{CO}}^{2+}$ and ${\mathrm{CO}}^{3+}$ from synchrotron radiation experiments led to the conclusion that ionization by Ar-ion impact populates states having considerably higher excitation energies than those accessed by photoionization.

‘‘Symmetry-resolved’’ photoabsorption spectra of free ${\mathrm{N}}_2$ molecules in the K-shell excitation region have been obtained using a technique of angle-resolved photoion spectroscopy combined with linearly polarized undulator radiation. The obtained Σ- and Π-symmetry component spectra have nicely demonstrated the symmetry decomposition of the photoabsorption spectrum. These spectra have been compared with theoretical calculations in the photon-energy regions below and above the ionization threshold.

Absolute cross sections for the processes of single capture, transfer ionization, and single and double ionization were measured for ${\mathrm{C}}^{6+}$, ${\mathrm{N}}^{7+}$, ${\mathrm{O}}^{8+}$, and ${\mathrm{F}}^{9+}$ projectiles incident on a helium target in the projectile velocity range of 0.25–2.0 MeV/amu. The cross sections were determined by measuring projectile-ion final charge states in coincidence with target recoil-ion final charge states. The single-capture and transfer-ionization cross sections were corrected for ionization from impurity charge states in the beam and for double-collision processes in the target gas cell. These corrections, which are necessary for the relative as well as the absolute cross sections, were found to be as large as 50% of the cross section. The measured cross sections are compared to the multistate, coupled-channel calculations of Shingal and Lin using an independent-electron model.

The electron-impact single-ionization cross section of ${\mathrm{Ar}}^{7+}$ has been measured from 18 to 1186 eV using a crossed-beams technique. The present results are higher than previous measurements at the higher energies and are in good agreement with recent distorted-wave calculations that include contributions from excitation autoionization. Below the threshold for direct ionization at 144 eV, the cross section contains contributions due to space-charge modulation and excitation of metastable ions in the target beam into autoionizing states. These transitions are predominantly spin allowed and dipole forbidden. Scaling laws for sodiumlike ions are discussed.

Transfer and excitation, resulting from simultaneous electron capture and K-shell excitation in a single collision, has been measured 280–310-MeV ${\mathrm{Ti}}^{20+}$ ions channeled in the 〈100〉 axis of a thin Au single crystal. The 19+ charge-state fraction of the Ti ions exiting the Au crystal was measured as a function of ion energy and showed no narrow peak attributable to resonant transfer and excitation (RTE). The number of Ti Kα x rays, emitted by the Ti ions due to RTE, in coincidence with ${\mathrm{Ti}}^{19+}$ was also measured at two energies, on and off the previously reported narrow resonance, and again no evidence for a narrow resonance was observed.

The phase-space formulation of quantum scattering is discussed and the asymptotic quantities describing potential scattering in one and three dimensions (transmittances, cross sections) are analyzed. It is found that under certain conditions the transmittance in time-dependent scattering only depends on the momentum distribution of the incident packet, being independent of its particular shape in coordinate space. For three-dimensional scattering, generalized cross sections are defined for momentum coherences and a physical interpretation of the generalized optical theorem is proposed.

We have measured the doubly differential cross sections, in angle and energy, of secondary electrons ejected from atomic hydrogen by electron impact. The incident energies used were from 25 to 250 eV. The energy and angular range of secondary electrons measured were from 1.0 eV to one-half of the difference between the incident energy and the ionization potential of hydrogen atom and from 12° to 156°, respectively. Singly differential cross sections and total-ionization cross sections were obtained from the doubly differential cross sections. The present total-ionization cross sections were compared with previous measurements and theoretical results. Discrepancies have been found between the present results and those measurements and theoretical results.

We have measured the energy distributions of the ${\mathrm{H}}^{+}$ and the ${\mathrm{H}}^{\mathrm{-}}$ ions resulting from the collisional dissociation ${\mathrm{H}}_3^{+}$→${2\mathrm{H}}^{+}$+${\mathrm{H}}^{\mathrm{-}}$ in argon at a projectile energy of 2700 keV. The fragment ions were separated by an analyzing magnet and detected by silicon surface barrier detectors, with the ${\mathrm{H}}^{+}$ and the ${\mathrm{H}}^{\mathrm{-}}$ ions being detected in coincidence. The energy distributions of the fragments in the projectile center-of-mass frame were extracted from their transverse spatial distributions observed at a position 150 cm downstream from the collision chamber. These distributions were used subsequently to determine the total kinetic energy of the fragments and the correlation angle ${\mathrm{\theta }}_{12}$ between the ${\mathrm{H}}^{+}$ momenta. A comparison is carried out with recently published data obtained in the low-velocity regime in helium.

Double-electron capture by the impact of heavy projectiles on heliumlike atoms is studied with a two-electron model. The process is here considered a two-step collision, which in the frame of the distorted-wave formalism is related to the second order. This second order is evaluated by using an on-shell Green function representing one electron in each center, and it is found to be related, after some approximations, to the independent-electron model. In particular, the exact impulse approximation is used to calculate the single-capture T-matrix elements, and the electronic repulsion is included as a dynamic perturbation in first order. A configuration-interaction wave function is employed to describe the ground state of helium for double capture 1${\mathit{s}}^2$→1${\mathit{s}}^2$ in a ${\mathrm{He}}^{2+}$-He collision. For this benchmark, differences with the use of a Hartree-Fock wave function instead are found to be negligible. Thereafter, capture to single excited states for the same system is calculated by using Hartree-Fock and variational electronic wave functions. Also, double capture for multiply charged ions on helium is calculated. Differential cross sections for double-capture ${\mathrm{He}}^{2+}$-He collisions at 60 keV/amu impact energy are presented and compared with previous experiments. The present theory produces good agreement with the available data.