Two studies are carried out on the density functional for the Hartree-Fock exchange energy. (1) Becke’s semiempirical formula for the exchange energy [Phys. Rev. A 38, 3098 (1988)] is reparametrized and applied to selected molecules. The results are excellent. (2) A new theoretical derivation is given of the coefficient β in the standard second-order gradient expansion for the exchange energy. The β value obtained is 0.001 429.

We demonstrate that the functional form of the Padé approximant of the second-order density gradient correction of Rasolt and Geldart [Phys. Rev. Lett. 35, 1234 (1975)] for the inhomogeneous electron gas yields excellent results when applied to atoms. The gradient correction employed by us uses the 10/7 factor as suggested by Kleinman and Lee [Phys. Rev. B 37, 4634 (1988)] with the constants of Rasolt and Geldart replaced by an empirically derived set, based upon numerical fits of the exchange and exchange-correlation energies of the atoms He through Ar. The resulting fitted nonlocal gradient corrections were then used in the minimization of the Kohn-Sham functional to solve for the exchange-only and exchange-correlation total energies. The resulting standard deviations in the calculated total energies were 0.0043 for exchange only and 0.0014 for exchange correlation.

An exact correspondence relationship between the classical and quantum-mechanical expectation values of ${\mathit{r}}^{\mathrm{-}\mathit{k}}$ for arbitrary hydrogenic states with quantum numbers n and l is established. The quantum-mechanical result for arbitrary powers of k is explicitly expressed in terms of relatively simple orthogonal polynomials which are intimately related to the Legendre polynomials and which consist of only the minimum of n-l or k+1 terms. The correspondence between the sets of polynomials, and the complete formal analogy of the classical and quantum results, are found to originate in the fact that the correspondence limit of the Pasternack-Kramers recursion relation for the 〈${\mathit{r}}^{\mathrm{-}\mathit{k}}$〉 is the three-term recursion for the Legendre polynomials.

Some aspects related to the behavior of the correlation energy as a functional of the density are not well represented by the density functionals; such is the case of the energy curves for pure states of diatomic molecules, the dependence of the correlation energy on the zeroth-order wave function, or the multiplet splitting in atoms. In this paper we show that these limitations are due to the fact that a complete description of the two-body effects requires one to take into account the two-electron density. It is shown that using very simple approximations to incorporate explicitly the two-body density into the density-functional equations improves their behavior considerably.

We have solved the capture-cascade equations for double x-ray emission following resonant transfer and excitation in collisions of ${\mathrm{S}}^{15+}$ and ${\mathrm{Ge}}^{31+}$ with ${\mathrm{H}}_2$. Configuration mixing within the autoionizing complex enhances the cascade-produced Kα-Kα peak and removes the discrepancy between single-configuration LS-coupling results and experiment for ${\mathrm{S}}^{15+}$. Intermediate coupling increases the population of the metastables and so reduces the Kα-Kα,Kβ,Kγ cross sections by up to 20% over the LS-coupling results. The coincidence cross sections for highly excited states are still about a factor of 2 (Kα-Kγ) or 3 [(Kβ+Kγ)–(Kβ+Kγ)] smaller than experiment for ${\mathrm{S}}^{15+}$, however. In the case of ${\mathrm{Ge}}^{31+}$, the total coincidence cross section lies 10–30 % below experiment, while the Kα–(Kβ+Kγ) cross section is now somewhat larger than experiment. The comprehensiveness of the theoretical calculations suggests that the experimental results may need to be reexamined where significant discrepancies with theory remain.

Multiconfiguration Hartree-Fock calculations for photodetachment cross sections in ${\mathrm{Ca}}^{\mathrm{-}}$ are reported, both to the ${\mathit{ks}}^2$S and ${\mathit{kd}}^2$D final state. Correlation is important to the binding of the 4${\mathit{s}}^2$4p ${}_{}{}^2{}_{}{}^{}$P state and also to the cross section. In the final state, correlation is particularly important for the kd partial cross section. The value of the electron affinity in ${\mathrm{Ca}}^{\mathrm{-}}$ is critical to agreement in the length and velocity form of the cross section. Better agreement is obtained when a theoretical value is used. Agreement with an experimental photodetachment cross section is good.

The eikonal distorted-wave method is applied to single ionization in proton-helium collisions at laboratory energies of 300 keV, 500 keV, 1 MeV, and 3 MeV. The angular distributions of scattered protons agree well with recent experimental results, showing substantial improvement over the plane-wave Born approximation especially at large scattering angles Θ. The momentum distributions of the ejected electrons at fixed values of Θ are calculated. In particular, those of the electrons ejected mainly in binary proton-electron collisions are studied in detail. The momentum distributions of the recoil ${\mathrm{He}}^{+}$ ions at fixed values of Θ are also discussed by comparing with the results of recent coincidence measurements. At such small Θ at which the plane-wave Born and the eikonal distorted-wave approximations give nearly the same cross sections and are expected to be accurate, these approximations lead to average momenta of recoil ions significantly lower than the measured values.

For incident linearly polarized light and randomly oriented molecules, the angular distribution of photofragments has a dipolar pattern. It will be shown that along a Fano profile, the resonance, interference, and continuum terms have different β parameters, each of which will be discussed in a form directly related to an experiment.

Resonances in the differential photodissociation cross section of ${\mathrm{H}}_2$ are studied. Photon excitation from the metastable ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{\mathrm{-}}{}_{}{}^{}$ state occurs around resonances in the ${}_{}{}^3{}_{}{}^{}\mathrm{\Delta }_{\mathrm{g}}^{}{}_{}{}^{}$ state lying in the continuum of the ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathit{g}}^{}{}_{}{}^{}$ state. The ${\mathit{j}}^3$${\mathrm{\Delta }}_{\mathit{g}}$ state is coupled to the continuum by the nuclear rotation. Since direct excitation to the continuum can also occur, interference is present, which expresses itself as a change in anisotropy of the photofragments as the photon energy is scanned over a resonance. Fano parameters, linewidths, and anisotropy parameters are obtained from the measured differential cross sections and are treated theoretically as outlined in the preceding paper [Glass-Maujean and Siebbeles, Phys. Rev. A 44, 1577 (1991)]. The experimental and calculated results are in good agreement.

A standardized Monte Carlo simulation (MCS) procedure is used as a routine test of the accuracy of any interaction potential of an ion-atom binary pair. By capitalizing on the performance of a supercomputer, the procedure achieves a highly realistic simulation of the ionic motion and calculates the resulting mobilities of the ions in the neutral gas. These values are then compared against accurate experimental values, assumed available. For cases where the same interaction potential has also been used as input for kinetic-theory calculations of mobilities, the procedure may be extended to check the accuracy of the theory itself. The interaction potentials of Lamm et al. [J. Chem. Phys. 74, 3042 (1981)]; Budenholzer, Gislason, and Jorgensen [J. Chem. Phys. 78, 5279 (1983)]; and Koutselos, Mason, and Viehland [J. Chem. Phys. 93, 7125 (1990)] for the ${\mathrm{K}}^{+}$-Ar pair as an illustrative case study are examined. The calculations indicate that the potential of Koutselos, Mason, and Viehland is the most accurate currently available. Furthermore, a comparison of the MCS calculations with the two-temperature theoretical mobilities of Lamm et al. and the three-temperature mobilities of Koutselos, Mason, and Viehland suggests that both theories are quite accurate at both the low- and high-ionic-drift-energy regions, but are up to about 2% too high at the intermediate-energy region.

The total cross section for the single-electron-capture reaction, ${\mathrm{H}}^{+}$+ Ar→H+${\mathrm{Ar}}^{+}${(Ne)3${\mathit{s}}^1$3${\mathit{p}}^6$${;}^2$S}, has been measured at energies from 100 to 800 keV. The cross section is tentatively identified with the cross section for capture directly from the 3s single-electron orbital of Ar. A clear indication of a structure in the functional dependence of the cross section on energy is seen. It is suggested that the structure is caused by one of the two radial nodes of the 3s wave function. The cross sections for the simul- taneous charge transfer and ionization reactions, ${\mathrm{H}}^{+}$+Ar→${\mathrm{H}}^{+}$+${\mathrm{Ar}}^{2+}${(Ne)3${\mathit{s}}^1$3${\mathit{p}}^5$${;}^1$P and ${}_{}{}^3{}_{}{}^{}\mathrm{\}}$, ${\mathrm{H}}^{+}$+Ar→H+${\mathrm{Ar}}^{3+}${(Ne)3${\mathit{s}}^1$3${\mathit{p}}^4$${;}^4$P${,}^2$D, and ${}_{}{}^2{}_{}{}^{}$P}, and ${\mathrm{H}}^{+}$+Ar→H+${\mathrm{Ar}}^{4+}${(Ne)3${\mathit{s}}^1$3${\mathit{p}}^3$${;}^3$D}, were also measured within the energy region 100–800 keV. The energy dependence of these cross sections is different from that found for the pure single-electron-capture reaction. The reason for this is, most likely, that the transfer and ionization reactions are influenced by electron capture from the L shell, followed by Coster-Kronig and Auger transitions. It is not known at present whether multielectron transitions due to dynamic electron correlation or multiple interactions with the projectile are important for the present collision systems. If so, the interpretation of the reactions will require a more thorough theoretical analysis.

A theoretical method to calculate the K-shell electron-capture cross section in asymmetric collisions is developed. The correlation effect between the active and the passive electrons and the screening effect in the wave function of the active electron are all considered. Under the Oppenheimer-Brinkman-Kramers approximation, an analytical expression for the total capture cross section is obtained. The calculated results for ${\mathrm{H}}^{+}$–carbon, nitrogen, oxygen, neon, argon and ${\mathrm{He}}^{2+}$-neon collisions, at the intermediate-energy region, show very good agreement with available experimental findings. A comparison with other theoretical results is given.

Absolute total-scattering cross sections (${\mathit{Q}}_{\mathit{T}}$’s) have been measured for positrons and electrons colliding with sodium and potassium in the 3–102-eV range, using the same apparatus and experimental approach (a beam-transmission technique) for both projectiles. Comparing the present measured ${\mathit{Q}}_{\mathit{T}}$’s for positron and electron scattering by each separate alkali-metal atom shows that (1) they are very similar in shape and magnitude over the entire energy range investigated, (2) they tend to merge near (and above) the relatively low energy of about 40 eV, and (3) the positron ${\mathit{Q}}_{\mathit{T}}$’s become higher than the corresponding electron values as the projectile energy is decreased below about 40 eV. These positron and electron ${\mathit{Q}}_{\mathit{T}}$ comparison measurements differ markedly from the situation for room-temperature gases, but are supported by recent theoretical calculations both for the positron and electron ${\mathit{Q}}_{\mathit{T}}$ comparisons and for their respective absolute values.

Resonant transfer excitation (RTE) was observed and RTE Auger-electron cross sections were measured for the formation of ${\mathrm{F}}^{6+}$ (1s2l2l ’) states in collisions of 0.25–2 MeV/u ${\mathrm{F}}^{7+}$(1${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$S,1s2s ${}_{}{}^3{}_{}{}^{}$S) with ${\mathrm{H}}_2$ and He at zero degrees with respect to the beam direction. The measured Auger-electron differential cross sections agreed well with a modified treatment of the usual impulse approximation and the recent angular dependence theory of RTE by Bhalla [Phys. Rev. Lett. 64, 1103 (1990)], thus confirming the selective population of the ${\mathit{M}}_{\mathit{L}}$=0 magnetic substate in RTE processes. The extracted resonant excitation scattering strengths for the 1s2${\mathit{p}}^2$ ${}_{}{}^2{}_{}{}^{}$D and 1s(2s2p ${}_{}{}^1{}_{}{}^{}$P${)}^2$${\mathit{P}}_{+}$ states were found to be (35±2)×${10}^{\mathrm{-}19}$ and (14±2)×${10}^{\mathrm{-}19}$ ${\mathrm{cm}}^2$ eV, respectively. These two states showed the strongest KLL RTE signature as predicted by theory.

A comprehensive semiempirical model for singly and doubly differential and total ionization cross sections for electron production by electron impact is presented. The model is discussed in relation to several theoretically required constraints. Available experimental data for hydrogen and helium targets are examined, and recommended values of the data are given for all ranges of primary and secondary energies and angles of ejection.

We have measured K x-ray spectra and yields from ${\mathrm{Ar}}^{17+}$ ions slowly approaching a single-crystal Ge surface. The yields were measured as a function of the projectile velocity component perpendicular to the surface. From the data a characteristic time of approximately 1 psec was extracted for the in-flight filling above the surface of the Ar K vacancy.

Quantum-mechanical and semiclassical molecular-orbital expansion methods are employed to investigate a single-electron-capture mechanism in ${\mathrm{N}}^{5+}$+H collisions in the energy range from 10 meV/amu to 10 keV/amu. The dominant electron-capture channels in the entire regime are found to be ${\mathrm{N}}^{4+}$(4s), ${\mathrm{N}}^{4+}$(4p), and to some extent ${\mathrm{N}}^{4+}$(4d). The ${\mathrm{N}}^{4+}$(4f) channel is found to make small contributions at any energy because of its near diabaticity with respect to the initial channel. Agreement for total and n-shell captures with recent measurements is excellent in the entire energy regime, and agreement for l-shell capture with measurements is reasonable for most cases. Furthermore, several shape resonances due to rovibrational states of the transient quasimolecule are found below 1 eV, and a large, broad structure arising from trajectory effects due to the weak attractive polarization potential is found below 60 meV/amu. The origins of differences between the present results and the measurements and other theoretical calculations are also discussed.

In this work, we study the formation of doubly excited projectile states near the double-escape threshold in collisions of 0.1-MeV/u ${\mathrm{Ag}}^{4+}$ ions with He, ${\mathrm{H}}_2$, and Ar gas targets under single-collision conditions. We detect projectile states in which one electron occupies a high Rydberg state and a second electron occupies a low-lying continuum state. The cross sections for producing these doubly excited projectile states are on the order of ${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^2$. The production probabilities are measured as a function of the continuum-electron laboratory-frame energy with the detected Rydberg electrons arising from a fixed band of energy levels. The width of the continuum-electron energy distribution measured in coincidence with a Rydberg electron is smaller than the width of the energy distribution measured without the coincidence requirement for ${\mathrm{H}}_2$ and Ar targets but not for He targets. The width of the continuum-electron energy distribution measured in coincidence with a Rydberg electron decreases as the fraction of doubly excited states formed by projectile double excitation and ionization decreases and the fraction formed by double-target-electron capture increases.

The use of numerical optimization algorithms has been investigated for estimating the electron momentum transfer and excitation cross sections for atoms and molecules based on measured electron transport, or swarm data. The downhill or creeping simplex method is investigated. This algorithm has been used to obtain the momentum-transfer cross sections ${\mathrm{\sigma }}_{\mathit{m}}$(ɛ) for helium and argon from E/N dependent drift velocities (${\mathit{v}}_{\mathit{d}}$) and characteristic energies (D/μ). In addition, this technique has been used to obtain ${\mathrm{\sigma }}_{\mathit{m}}$(ɛ) and a vibrational excitation cross section for ${\mathrm{CH}}_4$ from measured ${\mathit{v}}_{\mathit{d}}$ and D/μ data. These results serve as examples of what may be possible using these and, perhaps, other optimization algorithms.

The electron–polarized-photon coincidence technique has been used to study the finer details of the excitation of the first excited states of the heavy noble gases neon, argon, and krypton by electron impact in the regime of large impact parameters (small scattering angles and intermediate impact energies). Measurements with higher statistical accuracy of the ${\mathit{P}}_1$ coherence parameter in forward scattering for excitation of the ${(}^2$${\mathit{P}}_{1/2}$)ns’[1/2${]}_1^0$(‘${\mathrm{‘}}^1$${\mathit{P}}_1$’’) state in neon (n=3) and argon (n=4) are reported along with ${\mathit{P}}_1$ measurements for both the ${(}^2$${\mathit{P}}_{1/2}$)5s’[1/2${]}_1^0$(‘${\mathrm{‘}}^1$${\mathit{P}}_1$’’) state and the ${(}^2$${\mathit{P}}_{3/2}$)5s’[3/2${]}_1^0$(‘${\mathrm{‘}}^3$${\mathit{P}}_1$’’) state in krypton for incident electron energies from 30 to 100 eV. All measurements are consistent with a ${\mathit{P}}_1$ value of +1, which is indicative of the dominance of direct excitation via transfer of orbital angular momentum. No evidence was found that exchange excitation via spin transfer plays a role in forward scattering at these energies, in agreement with theoretical predictions. A series of systematic measurements of the two linear coherence parameters ${\mathit{P}}_1$ and ${\mathit{P}}_2$ was carried out for excitation of the ‘${\mathrm{‘}}^1$${\mathit{P}}_1$’’ state in argon and the ‘${\mathrm{‘}}^3$${\mathit{P}}_1$’’ state in krypton at 50-eV impact energy and electron-scattering angles up to 25°. A detailed comparison with the predictions of the distorted-wave Born approximation and the first-order many-body theory reveals a generally satisfactory agreement and indicates that the theories are capable of reproducing the general features of the measured parameters as a function of scattering angle.

Two parameters characterizing the angular part of the collisionally induced P-state charge cloud, the alignment angle γ, and the linear polarization ${\mathit{P}}_{\mathrm{lin}}$, were extracted from the measured ${\mathit{P}}_1$ and ${\mathit{P}}_2$ values. The agreement between experiment and theory in the case of γ is in general good, whereas it is somewhat poorer as far as ${\mathit{P}}_{\mathrm{lin}}$ is concerned. This indicates that the theoretical models are quite good in predicting the alignment angle of the collisionally induced charge cloud in the scattering plane, but less capable of predicting the exact shape of the charge cloud.