We present nonrelativistic convergent close coupling calculations of electron scattering from the ground state of barium at energies ranging from 1 to 987 eV. At selected energies the effect of the inclusion or neglect of the target continuum is estimated. Very good agreement is found with measurements of the $\mathrm{}\left(6s6p\right)\mathrm{}{}^1{P}^o$ apparent cross section at all energies. In addition, good agreement is obtained for differential cross sections of elastic scattering, and $\mathrm{}\left(6s6p\right)\mathrm{}{}^1{P}^o$ and $\mathrm{}\left(6s5d\right)\mathrm{}{}^1{D}^e$ excitations. The calculated $\mathrm{}\left(6s6p\right)\mathrm{}{}^1{P}^o$ electron-photon angular correlations are in good agreement with experiment.

A relativistic distorted wave method for calculating cross sections for excitation of ions to specific magnetic sublevels by impact with an electron beam is expanded to include the generalized Breit interaction between the bound and free electrons. Illustrative numerical results are given for heliumlike iron and xenon. The effect of inclusion of the generalized Breit interaction is very large for xenon and is even non-negligible for iron.

Resonant photofragmentation of core-excited water molecules has been studied with high-resolution partial-ion-yield spectroscopy. Both the single and coincidence channels were monitored simultaneously. A steep increase in the coincidence yield curves above the ionization threshold, where the normal Auger decay produces doubly charged or multiply charged species that yield two or more charged fragments, has been observed. By comparing the single and coincidence channels the relative weight of H neutral fragments has been qualitatively assessed, and found to be higher for the O $1\overrightarrow{s}{4a}_1$ primary excitation. The presented ion-yield data provide strong evidence for a branching between atomic Auger decay and molecular fragmentation in the ${\mathrm{O}}^{+}$ channel. The most unexpected result is the formation of ${\mathrm{H}}_2^{+}$ species being detected and attributed to a highly excited bending mode.

Using a Spline-Garlekin and inverse iteration method, we studied in detail the photodetachment cross section of the ${\mathrm{He}}^{-}$ $\left(1s2s2p{}^4{P}^o\right)$ state in the region of the $1s$ detachment threshold. Details of the cross section from threshold to 44 eV are presented. The effects of core excitation and continuum channel coupling are studied. A very narrow $2s3s4s{}^{4}S$ resonance was found at 42.866 00 eV with a width of 0.103 meV. Other resonance structures are also found and analyzed. We studied the ${2s2p}^2{}^{4}P$ resonance state that lies immediately below the $1s$ threshold. The width and position of this state, obtained from this calculation, are 37.669 eV and 9.850 meV, respectively. This result is in good agreement with other theoretical calculations.

Angle-resolved $M_{4,5}{N}_{4,5}{N}_{4,5}$ Auger spectra of xenon have been measured near the Xe $3d$ threshold by using synchrotron radiation excitation. The angular anisotropy parameters extracted from the experimental data generally agree with the recent theoretical results based on multiconfiguration Dirac-Fock calculations. The angle-resolved measurements have also been employed in order to study the character of the resonance structures below the $M_4$ threshold.

An extensive and detailed mapping of the resonant Auger decay of all the photoexcited ${3d}_{3/2,5/2}^{-1}\mathrm{np}$ states in Kr has been performed using angle-resolved two-dimensional photoelectron spectroscopy at the Advanced Light Source at Lawrence Berkeley National Laboratory. This has allowed us to obtain angular distributions and spectator and shake probabilities for the Kr ${3d}^{-1}n\overrightarrow{p}{4s}^{-1}{4p}^{-1}{(}^1{P)mp+e}^{-}$ $(n=5\mathrm{}–9,$ $m=5\mathrm{}–11)$ resonance Auger decays. The results show that the spectator-core coupling is strong at lower n $\mathrm{}(n=5,6\mathrm{})\mathrm{}$ but lessens for higher n, with a shake-up of $m=n+1\mathrm{}$ preferred. The observed trend is in good agreement with the previous experimental and theoretical spectator and shake probabilities for these transitions and also with the analogous decay to the ${4s}^2{4p}^4\mathrm{mp}$ states [H. Aksela et al., Phys. Rev. Lett. 25, 4970 (1997)]. However, to our knowledge, no prior angular distribution measurements for the Kr ${3d}^{-1}n\overrightarrow{p}{4s}^{-1}{4p}^{-1}{(}^1{P)mp+e}^{-}$ $(n=5\mathrm{}–9,$ $m=5\mathrm{}–11)$ resonant Auger decay has been reported. These are found to also show similar behavior to the decay to the ${4s}^2{4p}^4\mathrm{mp}$ states.

The dynamics of the fragmentation of ${\mathrm{Na}}_2^{+}$ dimer ions in keV collisions with He is investigated theoretically in the framework of the semiclassical coupled wave-packet method. The fast collisional motion is treated classically, whereas both the electronic motion and the vibrational or dissociative motion of the dimer are treated quantally. The frozen vibrational and rotational approximations are used to lighten the computational effort. The method is able to describe both the impulsive and electronic fragmentation mechanisms. The calculations are undertaken in a basis of 14 electronic states of the ${\mathrm{Na}}_2^{+}-\mathrm{H}\mathrm{e}$ system. Aside from the entrance ${\Sigma }_{g}3s$ channel, the main contributions to the ${\mathrm{Na}}_2^{+}$ fragmentation are those of the ${\Sigma }_{u}3s,$ ${\Sigma }_{g}3p,$ and ${\Pi }_{u}3p$ channels. For each electronic state dissociation probabilities as functions of the impact parameter are presented for various dimer orientations to extract physical insight in the fragmentation mechanism. This analysis shows in particular that the contribution of the electronic mechanism is due to collisions where the He atom passes between the two Na nuclei. Doubly differential cross sections for dissociation are calculated for the $v=0\mathrm{}$ initial state of the dimer and for the distribution of vibrational states. Good agreement with experiment is obtained assuming a small amount of initial vibrational excitation of the dimer.

The charge-transfer rate coefficient for the reaction ${\mathrm{Si}}^{4+}+\mathrm{H}\overrightarrow{e}\mathrm{products}$ was measured at an equivalent temperature of $4.6\times {10}^3\hspace{0.5em}\mathrm{K}$ using a laser-induced plasma ion source and ion storage. The rate coefficient is $4.54\left(0.48\right)\mathrm{}\times {10}^{-12}\hspace{0.5em}{\mathrm{cm}}^3{\mathrm{}\mathrm{s}}^{\mathrm{-}1}$ and is at least an order of magnitude smaller than the available theoretical values.

We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit, for the asymptotic channel solutions of the Dirac equation, and elucidate their close connection with gauge transformations which transform the dynamics into a representation in which the interaction between the electron and a distant ion is of short range. We describe the implications of this relationship for solving the time-dependent Dirac equation for extremely relativistic collisions.

${\mathrm{H}}_2$ is bombarded by 400-eV electrons. Electrons scattered 18° with an energy loss of 36 eV are detected in coincidence with 7.6-eV ${\mathrm{H}}^{+}$ fragments from the $2p{\sigma }_u$ state of ${\mathrm{H}}_2^{+}.$ The collision time and dissociation time are very small compared to the rotation time of the molecule. Therefore, the ${\mathrm{H}}^{+}$ fragments leave the collision region along the line of the internuclear axis at the time of the interaction with the projectile. Angular distribution measurements of the ${\mathrm{H}}^{+}$ ions yield the relative cross section for excitation of the $2p{\sigma }_u$ state of ${\mathrm{H}}_2^{+}$ as a function of orientation of the internuclear axis. The data show a cosine-squared distribution relative to the momentum transfer vector of the collision. Calculations predicting the angular distribution are performed using prolate spheroidal coordinates.

The formulation of a suitable nonlocal model potential for electron exchange is presented, checked with electron-hydrogen and electron-helium scattering, and applied to the study of elastic and inelastic scattering and ionization of orthopositronium (Ps) by helium. The elastic scattering and the $n=2\mathrm{}$ excitations of Ps are investigated using a three-Ps-state close-coupling approximation. The higher $(n>~3)$ excitations and ionization of Ps atoms are treated in the framework of the Born approximation with present exchange. Calculations are reported of phase shifts and elastic, Ps excitation, and total cross sections. The present target elastic total cross section agrees well with experimental results at thermal to medium energies.

We have measured the ratio of cross sections for double to single ionization of helium by Compton scattering, $R_C={\sigma }_C^{++}/{\sigma }_C^{+},$ at photon energies of 40, 80, and 100 keV using cold target recoil-ion momentum spectroscopy. Comparison with calculations involving highly correlated initial states and approximate final states with and without final-state correlations, represented by $3C$ and $2C$ wave functions respectively, shows that the influence of final-state correlations persists to very high photon energies. A comparison with recent charged-particle data is made.

There has recently been much interest in using the notion of a duration time to analyze resonant x-ray Raman scattering (RXS) of atoms, molecules, and solids. This notion implies a selection of processes with different time scales responsible for the formation x-ray Raman spectra, and has been useful for actual predictions of various phenomena associated with RXS and that subsequently have been experimentally verified. However, the notion of a duration time for the x-ray scattering event can also have some paradoxical consequences, as when comparing the RXS duration with the relaxation time of the wave packet evolution in the case when the inverse detuning of the excitation energy is shorter than the time of flight or the lifetime of the core excited state. We present here a solution of this contradiction and give a detailed analysis of the notion of the duration time for RXS. It is shown that this time is complex and consists of two qualitatively different contributions. The first originates in the irreversible decay of the core excited state, while the imaginary part is caused by a reversible dephasing in the time domain. We investigate also the evolution of the wave packets of bound and dissociative states to stationary distributions. The theoretical analysis is accompanied by numerical examples of the time evolution of the wave packet in bound and dissociative core excited states of the ${\mathrm{N}}_2$ and HCl molecules.

We address a growing interest in trapping and cooling of mixed-species alkali-metal atoms. Long-range coefficients that arise in the multipole expansion of molecular potentials for unlike alkali-metal dimers are calculated. The coefficients for the heteronuclear alkali-metal dimers corresponding to different molecular symmetries that separate to $\mathrm{nS}-n^{\prime }S,nS-n^{\prime }P,nS-n^{\prime }D,$ and $\mathrm{nP}-n^{\prime }P$ atomic levels are computed with high precision. We consider cases where in the infinite separation limit, one atom is in the ground state and the other is in one of the lowest S, P, and D excited states and both atoms are in their lowest excited P states. We find the long-range potentials for $\mathrm{Rb}\mathrm{}\left(5S\right)\mathrm{}-\mathrm{C}\mathrm{s}\mathrm{}\left(6S\right),\mathrm{Rb}\mathrm{}\left(6S\right)\mathrm{}-\mathrm{C}\mathrm{s}\mathrm{}\left(6S\right),\mathrm{K}\mathrm{}\left(4S\right)\mathrm{}-\mathrm{R}\mathrm{b}\mathrm{}\left(5P\right)\mathrm{}{\hspace{0.5em}}^{1,3}\Sigma ,\mathrm{K}\mathrm{}\left(4P\right)\mathrm{}-\mathrm{C}\mathrm{s}\mathrm{}\left(6P\right)\mathrm{}{\hspace{0.5em}}^{1,3}\Sigma ,$ and $\mathrm{Rb}\mathrm{}\left(5S\right)\mathrm{}-\mathrm{N}\mathrm{a}\mathrm{}\left(3D\right)\mathrm{}{\hspace{0.5em}}^{1,3}\Sigma$ molecules to be the most attractive. The $\mathrm{K}\mathrm{}\left(4S\right)\mathrm{}-\mathrm{R}\mathrm{b}\mathrm{}\left(5P\right)\mathrm{}$ dimer represents the best candidate molecule for ultracold photoassociative spectroscopy. We also find the $\mathrm{K}\mathrm{}\left(4P\right)\mathrm{}-\mathrm{C}\mathrm{s}\mathrm{}\left(6P\right)\mathrm{}$ and $\mathrm{Rb}\mathrm{}\left(5S\right)\mathrm{}-\mathrm{K}\mathrm{}\left(4P\right)\mathrm{}$ dimers to form, respectively, the most attractive and the most repulsive long-range potentials. The present calculation is in good agreement with experimentally determined value for the ${1/R}^6$ van der Waals coefficient for the interaction between $\mathrm{Cs}\mathrm{}\left(6S\right)\mathrm{}$ and $\mathrm{Li}\mathrm{}\left(2P\right)\mathrm{}$ atoms.

We have carried out a theoretical investigation of charge transfer in collisions of ${\mathrm{H}}^{+}$ ions with neutral phosphorus P atoms both in the ground and metastable states at collision energies below 10 keV/u and above 100 eV/u using a molecular representation. Molecular states for the ${\mathrm{PH}}^{+}$ molecule are obtained by employing the ab initio multireference (single- and double-excitation) configuration-interaction method. In calculating charge-transfer cross sections, we have adopted the semiclassical impact-parameter method. The present charge-transfer cross sections from the ground-state P target are found to reach as large as $2\times {10}^{-15}{\mathrm{cm}}^2$ at 1 keV/u after slowly increasing from lower energies, and the contribution from ${\mathrm{P}}^{+}{(}^{3}P)$ and ${\mathrm{P}}^{+}{(}^5{S}^o)$ formations to the total are found to be comparable at the energy region where the cross section possesses a maximum.

We present a multichannel phase-amplitude formalism that permits us to calculate time and radially dependent wave functions of molecular processes such as preionization and/or predissociation. A model application to the photoionization of ${\mathrm{H}}_2$ is presented showing the time evolution in both closed and open channels.

In an exploratory feasibility study we have measured the angular correlation between Auger electrons that were emitted in a cascadelike decay process after resonant photoexcitation, using synchrotron radiation from the Brookhaven National Synchrotron Light Source. While the monochromator was tuned to the argon $1\overrightarrow{s}4p$ resonance (3203.5 eV) we recorded Ar $\mathrm{LMM}$ Auger electrons in coincidence with ${\mathrm{KL}}_{2,3}{L}_{2,3}{,KL}_1{L}_{2,3},$ and ${\mathrm{KL}}_{2,3}{M}_{1,2,3}$ Auger electrons. We found different nonisotropic angular correlations between distinct energy regions of the $\mathrm{LMM}$ group of Auger lines and the ${\mathrm{KL}}_{2,3}{L}_{2,3}$ Auger electrons, while for other kinetic energies the $\mathrm{LMM}$ Auger electrons exhibit isotropy. Because the $\mathrm{KLL}$ and $\mathrm{LMM}$ Auger energies are so different, we believe that the nonisotropic angular correlation observed is due to an alignment effect rather than a dynamical postcollision interaction effect.

One-dimensional scattering problems are of wide physical interest and are encountered in many diverse applications. In this paper I establish some very general bounds for reflection and transmission coefficients for one-dimensional potential scattering. Equivalently, these results may be phrased as general bounds on the Bogolubov coefficients or statements about the transfer matrix. A similar analysis can be provided for the parametric change of frequency of a harmonic oscillator. A number of specific examples are discussed. In particular I provide a general proof that sharp step function potentials always scatter more effectively than the corresponding smoothed potentials. The analysis also serves to collect together and unify what would otherwise appear to be quite unrelated results.

We have measured and calculated scattering parameters (differential cross sections and four electron-impact coherence parameters) for electron-impact excitation of the $\left(\dots {6s5d}^1{D}_2\right)$ to $\left(\dots {6s6p}^1{P}_1\right)$ transition in barium in the low to intermediate impact energy regime (10, 20, and 40 eV). Measurements were carried out by the superelastic scattering technique in which collisional deexcitation from the laser-excited $\left(\dots {6s6p}^1{P}_1\right)$ state to the metastable $\left(\dots {6s5d}^1{D}_2\right)$ level was detected by electron-energy-loss spectroscopy in a crossed-beam apparatus. Supporting calculations were carried out in the convergent close-coupling scheme. Measured differential cross sections were significantly lower than those measured for $\left(\dots {6s6p}^1{P}_1\right)$ excitation out of the ground $\left(\dots {6s}^{21}{S}_0\right)$ state and good agreement with theory was found. Measured and calculated coherence parameters show strikingly different behavior from that associated with ${}^1{P}_1$ excitations out of the ground state. Agreement between measured and calculated coherence parameters was found to be less satisfactory than in the case of the differential cross sections but was, nevertheless, encouraging considering the weak nature of the transition.

The double-ionization process, which is mainly governed by the electron-electron correlation effect (static/dynamic), has been studied for the ${\mathrm{Li}}^{+}$ ion by fast electron impact $\mathrm{}(e,3e)\mathrm{}$ for both symmetric and asymmetric geometries. The correlation effect in the initial channel has been incorporated by choosing a correlated wave function for the ${\mathrm{Li}}^{+}$ ion in its ground state. Some partial account of the dynamic correlation has also been considered in the final channel. The long-range Coulomb attraction in the initial channel arising due to the ionic target has been taken into account in the framework of the Coulomb-Born approximation. The evaluation of the fully differential cross sections finally reduces to a four-dimensional integration which has been evaluated numerically.