Interaction potentials for the X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ and a ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ states of ${\mathrm{Li}}_2$ are constructed and used in calculations of the elastic scattering of two ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ atoms at ultralow temperatures. The extreme sensitivity of the cross sections to the details of the interaction potentials is demonstrated. The calculated elastic and spin-change cross sections are very large, of the order of ${10}^{\mathrm{-}13}$ ${\mathrm{cm}}^2$ at zero temperature. The predicted scattering length for the triplet state is negative with a value of -17.2${\mathit{a}}_0$. Pronounced shape resonances appear at energies of 4.9×${10}^{\mathrm{-}8}$ a.u. in the singlet scattering and 5.5×${10}^{\mathrm{-}7}$ a.u. in the triplet scattering.

Generally, at excitation energies well above inner-shell ionization thresholds, Auger spectra are independent of the method of excitation. A notable exception to this has been found for the Ar ${\mathit{L}}_{2,3}$MM Auger spectra where different results are obtained via electron-impact ionization at 2 and 4.5 keV and photoionization below the K edge at 3.17 and 2.2 keV. The differences are explained by the variation of the contribution of ${\mathit{L}}_1$ to ${\mathit{L}}_{2,3}$ vacancy transfers with the mode of excitation. Calculations using a simple vacancy transfer model explain the observed spectra.

We have implemented nonlocal exchange effects rigorously in the first-order nondegenerate adiabatic (FONDA) theory. This implementation requires solving integrodifferential equations that involve double integrals. Separable and model exchange approximations that simplify the inclusion of exchange in the scattering calculations have been previously implemented in the FONDA theory. The discrepancy between the exact exchange FONDA cross sections and the separable and model exchange results suggests that one needs to include exchange rigorously to obtain accurate results over a wide range of energies. Specifically, a difference of up to 30% is observed between the exact and separable exchange FONDA cross sections at near-threshold energies. At higher energies the FONDA results from the rigorous and model exchange implementations disagree by as much as 10%.

We show, for the benchmark case of ${\mathrm{He}}^{2+}$+H collisions, that a close-coupling expansion in terms of an atomic basis modified with a common translation factor is competitive with the molecular approach at low and intermediate impact energies.

Experimental, polarization-dependent excitation spectra for excited-state-Mg–rare-gas-atom optical collisions are reported. In these first studies of the process, polarized Mg atoms in the 3p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ level are produced by absorption of linearly polarized light tuned to the 3s ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$→3p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ resonance transition at 285.2 nm. Detuning-dependent, collision-induced polarization spectra are measured in a ±200-${\mathrm{cm}}^{\mathrm{-}1}$ range around the Mg 3p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$→5s ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ transition at 571.2 nm. The spectra correspond to probing transient Mg-Ne and Mg-Ar molecules on 3p ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_1^{}{}_{}{}^{}$→5s ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_0^{+}{}_{}{}^{}$ and 3p ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_0^{+}{}_{}{}^{}$→5s ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_0^{+}{}_{}{}^{}$ electronic transitions. Measurements of these excited-state polarization spectra for Mg-Ne optical collisions reveal that for detunings to the red of the atomic Mg 3p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$→5s ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ transition, electronic linear polarization greater than 50% survives far into the molecular regime. This represents a direct measure of the polarization important to alignment-dependent inelastic processes in alkaline-earth-metal–rare-gas-atom collisions. The polarization spectra are discussed in terms of existing information on the interatomic potentials and through an axial recoil limit for the polarization degree for parallel and perpendicular molecular transitions. Rate coefficients k for disalignment of Mg 3p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ atoms by collisions with Ar [k=9.4(5)×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$/s] and with Ne [k=6.5(7)×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$/s] are also extracted from the data.

The double-differential cross sections for ionization in ${\mathit{e}}^{\mathrm{-}}$+H(nl) collisions are reported as a function of the impact energy E of the projectile, final energy ${\mathit{E}}_{\mathit{f}}$, and angular momentum ${\mathit{L}}_{\mathit{f}}$ of the ejected electron. This process is assumed to occur via an energy-changing and angular-momentum-changing binary collision between the Rydberg electron in a prepared state (nl) and the projectile electron ${\mathit{e}}^{\mathrm{-}}$ or H(1s). The atomic projectile can also be excited during this process. Systematic trends in the variation of the classical ionization cross sections with final angular momentum ${\mathit{L}}_{\mathit{f}}$ of the ejected electron are discussed and are in accord with a previous quantal treatment, whereby the nondipole (Δl>1) transitions are much more important in the low- and intermediate-energy range of relative motion, and that the value of the final angular momentum of the ejected electron depends mainly on the initial value of the principal quantum number n of the Rydberg atom.

The concept of a generalized scattering amplitude is introduced and applied to quantum potential scatterings. After an outgoing spherical wave is factored out from a wave function, the remaining wave envelope is defined as the generalized scattering amplitude. The transformed Schrödinger equation, in terms of the generalized scattering amplitude, can be solved numerically by using a finite-difference method over the entire scattering domain. Example problems of scatterings by a spherical potential well and the (${\mathit{e}}^{\mathrm{-}}$,H) static field interaction potential are solved to validate the theoretical formulation and numerical method. The far-field solutions for the ordinary scattering amplitude and differential cross section agree very well with those obtained from the partial-wave analysis. The radial profiles of the generalized scattering amplitude and particle density function over the entire scattering region are also presented, and their properties are discussed. These results demonstrate that the method can be used to yield a complete and accurate solution to scattering problems involving arbitrary interaction potentials.

The technique of laser-induced fluorescence (LIF) has been applied to measure the cross sections for electron-impact excitation into the metastable levels of argon atoms as well as the number densities of the argon metastable atoms produced by electron excitation. A monoenergetic electron beam excites the ground-state atoms into the 3${\mathit{p}}^5$4s ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$${,}^3$${\mathit{P}}_2$ metastable levels (1${\mathit{s}}_3$ and 1${\mathit{s}}_5$ in Paschen’s notation) and a pulsed laser pumps the atoms of a metastable level to a level in the 3${\mathit{p}}^5$4p configuration (2p in Paschen’s notation). The transient LIF from the 2p level is shown to be proportional to the apparent cross section of the metastable level and to the metastable number densities so that measurements of LIF enable us to determine both metastable cross sections and number densities. Methods for absolute calibration are described. We obtain both the apparent and direct excitation cross sections for each of the two metastable levels for electron energies from threshold to 200 eV and the results are compared with previous experimental and theoretical works. The pulsed LIF technique is also used to determine the disappearance rates of the metastable atoms after the electron beam is turned off. Two distinct decay modes are found and the observed behaviors are consistent with calculations based on diffusion theory.

In an earlier experiment by H. Cederquist et al. [J. Phys. B 18, 3951 (1985)] an unusual Q-value distribution for true double-electron capture was reported for 400-eV ${\mathrm{C}}^{4+}$-Ne collisions: a strong population of reaction channels resulting in Q values between 27 and 35 eV followed by weakly populated channels in the region 18–25 eV and then again a strong channel at Q=16 eV. The last channel is nearly degenerate in Q value with the dominant single-electron capture reaction. Here, we report measured angular distributions for scattered projectiles in single- and double-electron capture at collision energies 0.6–1.0 keV. At 0.6 keV, both single- and double-electron capture exhibit strong forward peaks for Q∼16 eV. The intensity for the latter, but not the former, decreases drastically when the energy is raised to 1 keV. The energy dependence of the angular distribution for double-electron capture with Q>20 eV can be qualitatively understood in simple terms; single-electron captures to 2s and 2p orbitals, however, yield unexpectedly wide and structured angular distributions.

Adiabatic energy eigenvalues of ${\mathrm{H}}_2^{+}$ are computed for complex values of the internuclear distance R. The infinite number of bound-state eigenenergies are represented by a function ε(R) that is single valued on a multisheeted Riemann surface. A region is found where ε(R) and the corresponding eigenfunctions exhibit harmonic-oscillator structure characteristic of electron motion on a potential saddle. The Schrödinger equation is solved in the adiabatic approximation along a path in the complex R plane to compute ionization cross sections. The cross section thus obtained joins the Wannier threshold region with the keV energy region, but the exponent near the ionization threshold disagrees with well-accepted values. Accepted values are obtained when a lowest-order diabatic correction is employed, indicating that adiabatic approximations do not give the correct zero velocity limit for ionization cross sections. Semiclassical eigenvalues for general top-of-barrier motion are given and the theory is applied to the ionization of atomic hydrogen by electron impact. The theory with a first diabatic correction gives the Wannier threshold law even for this case.

Measurements of the binary collision-induced absorption in hydrogen gas in the fundamental band of ${\mathrm{H}}_2$ (near 2.3 μm) are obtained at temperatures of 298 and 78 K. Agreement is observed with existing measurements and with an ab initio quantum calculation of the spectral profile which is based on the isotropic interaction approximation. The comparison suggests that such calculations may be used to generate the most reliable predictions of the binary spectra of hydrogen over the range of temperatures considered here.

We report on experimental studies of the photon energy dependence of the Auger yield and the spin polarization of Auger electrons and photoelectrons after photoionization of the 5p subshell of free Ba atoms with circularly polarized light for photon energies between 22 and 31 eV. Relations between the dynamics of the Auger-decay and the photoelectron emission are derived and their validity is probed from the experimental results. Our data are compared with numerical calculations, which were performed in the Hartree-Fock and in the random-phase approximation with exchange approach.

We present a numerical evaluation of the resonant charge-transfer cross sections for ions of various positive charges. In the calculations we introduce trajectory parameters through the expression for the instantaneous velocity of the projectile. Subsequent analysis reveals the existence of a natural scaling law by which cross sections of ion-ion collisions can be generated from the isoelectronic ion-atom charge-exchange cross section. We obtain a set of simple formulas useful for a semiquantitative description of the features of such cross section curves and we discuss the oscillatory structure of the cross sections.

Electron capture by ${\mathrm{O}}^{7,8+}$ and ${\mathrm{N}}^{7+}$ in collisions with He at 0.2–1.7 a.u. was investigated using coincident recoil momentum spectroscopy. The Q values and angular differential cross sections for single capture, transfer ionization (TI), and double capture (DC) were measured. Our Q-value measurements indicate that the electrons are captured into less tightly bound states with increasing collision velocity. The Q values and angular differential cross sections for DC and TI by ${\mathrm{O}}^{8+}$ are approximately the same, while those for DC and TI by ${\mathrm{O}}^{7+}$ and ${\mathrm{N}}^{7+}$ differ significantly. Our analysis indicates that the population of very asymmetric states (n=2, n’>10) is necessary to explain this difference.

Close-coupling calculations are carried out for the Q values for electron capture processes in collisions of multiply charged ions with atoms over a broad range of energies. For single-capture processes the results for ${\mathrm{N}}^{7+}$+He and ${\mathrm{O}}^{8+}$+He collisions are in good agreement with the experimental data of Wu et al. [preceding paper, Phys. Rev. A 50, 502 (1994)]. To compare with the experimental Q values for the transfer ionization (TI) and the true double-capture (TDC) processes, an independent-electron model was used to calculate double-electron-capture cross sections. By combining with the calculated average fluorescence yields, the theoretical Q values for TI and TDC processes are also found to be in fair agreement with the experimental data. We also compared the Q values calculated by the close-coupling method and by the classical-trajectory Monte Carlo method.

The cross sections and rates of muon transfer between excited states of muonic hydrogen are presented as functions of collision energy for different isotope combinations. Electron screening of the field of the target nucleus is taken into account. The ground-state population, ${\mathit{q}}_{1\mathit{s}}$, of muonic hydrogen is obtained for different collision energies, target densities, and relative hydrogen isotope concentrations, considering cascade processes for the principal quantum numbers n≤12. The obtained results for ${\mathit{q}}_{1\mathit{s}}$ are significantly smaller than the recent experimental data for D-T and H-D mixtures (tenfold and twice, respectively) and indicate that some new effects must be considered to improve the agreement.

Deexcitation and charge exchange of excited muonic hydrogen are considered. The inverse quasiresonant charge exchange process is taken into account. During cascade the inverse charge exchange balances the direct process down to the level with the principal quantum number ñ for which the resonance defect is larger than the collision energy. The density of the muonic atom for n≤ñ is then determined by deexcitation and muon transfer to nuclei of heavier hydrogen isotopes. Energy dependence of the ground-state population of the initial muonic hydrogen, ${\mathit{q}}_{1\mathit{s}}$, is considered. Comparing our results for the ${\mathit{q}}_{1\mathit{s}}$ parameter with the available experimental data, we conclude that the collision energy of the excited muonic atoms is ∼3 eV for D-T and ∼5 eV for an H-D mixture.

Systematic atomic structure calculations of KLL Auger electron spectra from ‘‘hollow’’ atom configurations 1s2${\mathit{l}}^2$3${\mathit{l}}^{\mathit{Z}\mathrm{-}3}$ are performed for atomic numbers 6≤Z≤10. In comparison with the corresponding 1s2${\mathit{l}}^2$ Li-like configurations it is shown that the additional Z-3 M electrons, apart from taking part in LLM Coster-Kronig transitions, can be regarded basically as mere spectator electrons, neither severely influencing the peak structure due to the Li-like core nor affecting the KLL Auger transition rates. However, due to screening effects the spectra are shifted to higher energies by an amount scaling with √Z-3 when adding the Z-3 M electrons. The results facilitate the identification of distinct narrow peaks in projectile K Auger spectra observed in slow highly charged ion-surface interactions. It is shown that especially competing LLM Coster-Kronig transitions have to be considered in order to account for the measured relative peak intensities. A cascade model of the last deexcitation steps of a highly charged ion in front of the surface based on the atomic structure data provides detailed insight into the time scales involved.

We introduce a general method to block diagonalize Hamiltonians with infinite-range interactions and arbitrary lattice sites f. As a working example we consider the case of the quantum discrete self-trapping Hamiltonian on a lattice which is a complete graph. We show the effectiveness of our method by computing the blocks into which the Hamiltonian decomposes for a finite number of quanta and for an arbitrary number f of lattice sites.

The structures and stabilities of ${\mathit{A}}_2$${\mathrm{Sb}}_4$, ${\mathit{A}}_4$${\mathrm{Sb}}_4$, and ${\mathit{A}}_6$${\mathrm{Sb}}_4$ clusters (A=Li, Na, K, and Cs), some of which were detected by Knudsen effusion mass spectrometry, are investigated in this work by Hartree-Fock pseudopotential optimization. For each system examined, we consider two structural alternatives: one involving a tetrahedral ${\mathrm{Sb}}_4$ cluster nucleus and another containing a square of four Sb atoms. The high electronegativity differences between antimony and alkali-metal-atom cluster constituents give rise to a sizable electron transfer from the alkali-metal atoms to the ${\mathrm{Sb}}_4$ unit, which tends to flatten out the ${\mathrm{Sb}}_4$ tetrahedron. From our calculations, the systems ${\mathit{A}}_2$${\mathrm{Sb}}_4$ and ${\mathit{A}}_4$${\mathrm{Sb}}_4$ appear to be highly polar compounds consisting of a symmetric arrangement of alkali-metal atoms above and below an ${\mathrm{Sb}}_4$ square. For ${\mathit{A}}_6$${\mathrm{Sb}}_4$ complexes, in contrast, no unique characterization can be given. While an ${\mathrm{Sb}}_4$ square variant is proposed for ${\mathit{A}}_6$${\mathrm{Sb}}_4$ clusters with A=Na, K, and Cs, for the ${\mathrm{Li}}_6$${\mathrm{Sb}}_4$ cluster a structure that contains a tetrahedral ${\mathrm{Sb}}_4$ unit is more likely. In general, all the ${\mathit{A}}_{\mathit{n}}$${\mathrm{Sb}}_4$ clusters studied here exhibit substantial polarity. The ${\mathrm{Cs}}_6$${\mathrm{Sb}}_4$ system, however, is characterized by metallic bonding features.