We have developed a first-order adiabatic scattering theory for the calculation of low-energy rovibrational cross sections. This theory is more efficient computationally than a full coupled-state method because it transforms coupling of intermediate states into a parametric dependence on nuclear coordinates, and it is more accurate than the conventional adiabatic nuclei method because it correctly conserves energy in the entrance and exit channels. As formulated, this theory can easily be implemented using available computer programs that solve fixed-nuclei scattering equations. We derive this theory for rotational and vibrational excitation with both local and nonlocal potentials and assess it by application to e-${\mathrm{H}}_2$ collisions.

The improved adiabatic representation is used in calculations of elastic and isotopic-exchange cross sections for asymmetric collisions of pμ, dμ, and tμ with bare p, d, and t nuclei and with H, D, and T atoms. This formulation dissociates properly, correcting a well-known deficiency of the standard adiabatic method for muonic-atom collisions, and includes some effects at zeroth order that are normally considered nonadiabatic. The electronic screening is calculated directly and precisely within the improved adiabatic description; it is found to be about 30% smaller in magnitude than the previously used value at large internuclear distances and to deviate considerably from the asymptotic form at small distances. The reactance matrices, needed for calculations of molecular-target effects, are given in tables.

In the artificial-channel method, an N-channel Hamiltonian describing the multichannel decay of a system is embedded in an (N+1)-channel Hamiltonian. The resonance energies and partial widths of the original N-channel physical problem are related simply to the parameters in the Lorentzian forms of the inelastic-scattering probabilities of the (N+1)-channel problem, the artificial-channel method permitting a straightforward study of a half-collision process with algorithms developed for full scattering processes. The utility of the method is demonstrated numerically for a model problem of Child and Lefebvre [Mol. Phys. 34, 379 (1977)].

The R-matrix theory for the vibrational excitation and dissociative attachment in e-HCl collisions is developed. Only one pole in the R-matrix expansion is included. This allows for making a connection between the R-matrix and the nonlocal-complex-potential theories, and for obtaining the expression for the dissociative-attachment cross section without using the R-matrix radius in the internuclear coordinate. All matrix elements in the equation for the vibrational-excitation and dissociative-attachment amplitudes are calculated using the quasiclassical approach. We study how the results depend on the number of vibrational levels of the neutral molecule included in the theory and show how to exclude the vibrational continuum by a modification of the nonlocal-complex potential. The results for the vibrational-excitation cross sections are extremely sensitive to the behavior of the R-matrix potential curve near the point of crossing this curve with the potential curve of the neutral molecule. Particularly in some cases the cross section at the threshold peak exhibits the boomerang oscillations earlier found for HCl by Domcke [in Aspects of Electron-Molecule Scattering and Photoionization, edited by A. Herzenberg (AIP, New Haven, 1989), p. 169]. The dissociative-attachment cross sections are in reasonable agreement with experiment and with other theories.

We propose a three-parameter expression that gives an accurate fit to diatomic potential curves over the entire range of separation for charge transfers between 0≤δZ≤1. It is based on a generalization of the universal binding-energy relation [J. R. Smith et al., Phys. Rev. A 39, 514 (1989)] with a modification that describes the crossover from a partially ionic state to the neutral state at large separations. The expression is tested by comparison with first-principles calculations of the potential curves ranging from covalently bonded to ionically bonded. The expression is also used to calculate spectroscopic constants from a curve fit to the first-principles curves. A comparison is made with experimental values of the spectroscopic constants.

Calculations are reported of the dissociative attachment of low-energy (less than 5 eV) electrons to molecular hydrogen in the states v=0–9 and J=0. The dynamics are treated using resonant scattering theory, fully including the nonlocal and energy-dependent shift and width operators. The necessary coupling terms are taken from the ab initio calculations of fixed-R electron-${\mathrm{H}}_2$ scattering performed by Mündel, Berman, and Domcke [Phys. Rev. A 32, 181 (1985)]. Good agreement with the available experimental data of Schulz and Asundi [Phys. Rev. 158, 2 (1967)] and of Allan and Wong [Phys. Rev. Lett. 41, 1791 (1978)] is achieved. Exploratory calculations were performed to investigate various local approximations to the nonlocal shift operator. The results suggest that the optimum local approximation will, in general, differ from the curve obtained in a fixed-nuclei structure calculation.

Single-electron capture and direct scattering are investigated in ${\mathrm{He}}^{2+}$ collisions with ${\mathrm{D}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{N}}_2$ molecules. For ${\mathrm{D}}_2$, measurements are made at 2.0, 3.0, and 4.0 keV. At the smallest scattering angles, only the exothermic ${\mathrm{He}}^{+}$(1s)+${\mathrm{D}}_2^{+\mathrm{*}}$ channel is excited. Capture to ${\mathrm{He}}^{+}$(n=2)+${\mathrm{D}}_2^{+}$(X) is found to have a threshold at a reduced scattering angle τ near 2 keV deg and its contribution rises rapidly. The direct scattering is primarily elastic. ${\mathrm{O}}_2$ is studied at 4.0 keV and the capture at small angles is dominated by the quasiresonant ${\mathrm{He}}^{+}$(n=2)+${\mathrm{O}}_2^{+}$(X ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathit{g}}^{}{}_{}{}^{}$) and the exothermic ${\mathrm{He}}^{+}$(1s)+${\mathrm{O}}_2^{+\mathrm{*}}$ channels. The direct-scattering channel is electronically elastic for τ<1.6 keV deg. ${\mathrm{N}}_2$ is studied at 4.0 keV. For τ>1.0 keV deg electron capture dominates the collision. The capture is predominantly exothermic for τ<1.2 keV deg.

Differential cross sections for the transitions from the ground state to n=2 states in ${\mathrm{Li}}^{+}$ are calculated using the R-matrix method. The 19 lowest target states are included, using configuration-interaction wave functions. Results are represented for low incident electron energies and are compared with those of the distorted-wave method and with a recent 11-state close-coupling calculation.

The complex Kohn variational method is employed in four-state close-coupling calculations to generate integral and differential cross sections for low-energy electron-impact excitation of the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$→(b ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$, and ${\mathit{c}}^3$${\mathrm{\Pi }}_{\mathit{u}}$) transitions in ${\mathrm{H}}_2$. The integral cross sections for excitation of the ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ and ${\mathit{c}}^3$${\mathrm{\Pi }}_{\mathit{u}}$ states from the ground state are found to be significantly different from earlier two-state calculations. The ${\mathit{a}}^3$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$ cross sections are also larger than the most recent experimental results. This discrepancy is traced to the behavior of the differential cross sections at scattering angles near 0° and 180°, where measurements have not been carried out. The differential cross sections we find for ${\mathrm{H}}_2$ are strikingly similar to cross sections for analogous transitions in He. Previous theoretical studies of these transitions in He have also shown the two-state approximation to be inadequate.

Experimental cross sections for single and double ionization of ${\mathrm{Ba}}^{2+}$ and ${\mathrm{Ba}}^{3+}$ ions are presented for an electron-impact energy range from threshold up to 1000 eV. By the alternative use of a ‘‘hot’’ electron-cyclotron-resonance ion source and a ‘‘cold’’ Penning ion source, beams of ions with and without metastable content could be employed. A fast energy-scanning technique with step widths of about 40 meV and an energy resolution of 0.4 eV revealed fine details in the cross sections, and in particular resonant contributions to single and double ionization could be observed. The data are interpreted on the basis of calculations of energy levels and distorted-wave calculations of direct ionization from various electron subshells. Influences of giant-resonance phenomena are discussed.

Measurements are reported of the energies and linewidths of the J=2, 3, and 4 components of the 6${\mathit{p}}^{1/2}$14f and 6${\mathit{p}}_{1/2}$19f states of barium. These states are anomalously broad, having autoionization lifetimes of approximately 1/2 of a classical Rydberg orbit period, and previously measurements have discerned no differences among the various J components. This work shows that the differences can be observed, and are consistent with calculations. The variations between states would be large if the states were LS coupled, but the large 6p ionic fine-structure forces recoupling into jj configurations. The spherical symmetry of the 6${\mathit{p}}_{1/2}$ ionic state minimizes the differences between J states, but does not eliminate them.

The differential cross sections for Compton scattering of 662-keV photons from K electrons of tin and lead were measured at scattering angles between 15° and 150°. Both cross sections were found to be similar and to exhibit the qualitative features predicted by relativistic calculations. Additional experiments were carried out with two thick silver and platinum targets, and the influence of second-order scattering processes on the values of the cross sections was estimated.

Energy-resolved electron scattering from ${\mathrm{H}}_2$ was measured using high-energy electrons. The 40-kV energy-unresolved data of Ketkar and Fink [Phys. Rev. Lett. 45, 1551 (1980)] were reanalyzed and combined with our 30-keV elastic measurements to calculate the inelastic cross section. Although the angular dependence of the cross section shows good agreement with recent quantum calculations over a large part of the angular region, some discrepancies remain at s≊4 a.u. in the elastic and inelastic cross section and around s≊2 a.u. in the total cross section. The elastic cross section at very small angles is compared with theoretical predictions and values derived from the magnetic susceptibility.

The visible spectrum emitted from ${\mathrm{N}}_2$ under bombardment by 1-MeV ${\mathrm{H}}_3^{+}$ ions has been studied with higher spectral resolution (linewidths down to 0.01 nm) than employed in comparable earlier work. The light yield versus gas pressure has been investigated in the 2–225-mTorr range (0.3–30 Pa) for a number of prominent spectral features attributed to atomic ions and to neutral and ionic molecules. The pressure functions are interpreted in terms of the constituents of the composite projectile. A considerable kinetic broadening observed for emission from ${\mathrm{N}}^{+}$, but not for other radiators, corroborates findings by Aarts and de Heer [Physica 52, 45 (1971), using electron impact] that this excited species results from the breakup of highly excited ${\mathrm{N}}_2^{+}$ ions into electronically excited ionic fragments.

An arbitrary-order phase-integral formula for the residue of the S matrix at a Regge pole is given. This formula is valid when there are two relevant transition zeros that may lie at an arbitrary distance from each other, possibly close together, but far away from all other transition points, the pole at the origin inclusive. It is also shown that the already-known phase-integral formula for the positions of the Regge poles is valid under the same general assumptions.

A phase-integral formula for calculating Regge-pole residues, which has recently been derived by Fröman and Fröman [preceding paper, Phys. Rev. A 43, 3563 (1991)], promises to be a powerful tool in the complex angular-momentum description of scattering. The present authors demonstrate the power, simplicity, and usefulness of that formula already in the first-order approximation. Application to proton-neon elastic scattering reveals that the new residue formula considerably improves the existing semiclassical Regge-pole description of the prominent rainbow oscillations in the differential cross section.

The Coulomb-dipole (CD) theory of the electron-atom impact-ionization threshold law is extended to include the full electronic repulsion ${\mathit{r}}_{12}^{\mathrm{-}1}$ (for the case of e-H ionization). We find that the threshold law is altered to the form ${\mathit{Q}}_{\mathit{a}}$(E)∝E(lnE${)}^{\mathrm{-}4}$M(E) in contrast to the previous angular-independent model [${\mathit{r}}_{12}^{\mathrm{-}1}$→(${\mathit{r}}_1$+${\mathit{r}}_2$${)}^{\mathrm{-}1}$], for which the logarithmic factor was (lnE${)}^{\mathrm{-}2}$. The modulation factor remains the same: M(E)=[(1-D/α)sin(α lnE+φ)]. This form of ${\mathit{Q}}_{\mathit{a}}$(E)—which in our theory is the true threshold law—applies over an energy range E<${\mathit{E}}_{\mathit{a}}$∝${\mathrm{\alpha }}^{\mathrm{-}4}$, where α≃ √2R and R defines a radius beyond which the assumptions of the CD theory apply. A second energy regime, ${\mathit{E}}_{\mathit{a}}$<E<${\mathit{E}}_{\mathit{b}}$, is also identified wherein the ‘‘threshold’’ law reverts to its angle-independent form ${\mathit{Q}}_{\mathit{b}}$(E)∝E(lnE${)}^{\mathrm{-}2}$M(E), where ${\mathit{E}}_{\mathit{b}}$∝${\mathrm{\alpha }}^{\mathrm{-}2}$. In the final part of the paper the dipole parameter α is estimated to be α≃28. This yields numerical estimates of ${\mathit{E}}_{\mathit{a}}$≃3×${10}^{\mathrm{-}4}$ and ${\mathit{E}}_{\mathit{b}}$≃0.25 eV. ${\mathit{Q}}_{\mathit{b}}$(E) is the relevant form for the lowest energy range of current experiments [Donahue et al., Phys. Rev. Lett. 48, 1538 (1982); 52, 164(E) (1984); and a spin-asymmetry experiment of Guo et al., Phys. Rev. Lett. 65, 1857 (1990)]. Their results are consistent with the CD law including the numerical values of those parameters which we have estimated. In contrast the latter experiment gives a confidence factor seven orders of magnitude smaller, when fit by the Wannier law for this process.

To offset the defective behavior of the molecular method of atomic collisions at intermediate energies, we propose a method to approximate the probability flux towards continuum and discrete states not included in the molecular basis. We check the degree of accuracy and limitations of the method for a model case where transition probabilities can be calculated exactly. An application to the benchmark case of ${\mathrm{He}}^{+}$+${\mathrm{H}}^{+}$ collisions is also presented, and yields complementary information on the properties of this approach.

The Schwinger variational principle is combined with the Lanczos algorithm. It is shown that the straightforward approach where the Lanczos basis is generated by V-${\mathit{VG}}_0$V is not very useful. The difficulties arise because of the unboundedness of the Schwinger operator V-${\mathit{VG}}_0$V for unbound potentials (such as, e.g., the Yukawa potential). A modification of the Schwinger operator is presented that resolves the problem. This approach leads to a new Lanczos recursion for nonsymmetric (and non-Hermitian) operators yielding nonorthogonal basis functions. The resulting approach is shown to be equivalent to the continued-fraction method of Horáček and Sasakawa. To illuminate the particular properties of the Schwinger-Lanczos basis we have applied it as well to other variational principles like the C̃ functional, the Newton variational principle, and the Kohn variational principle. To treat the multichannel problem we have adopted a modified band-Lanczos algorithm. This allows for a more efficient computation of the off-diagonal T-matrix elements than previous approaches.

The silicon 2p photoelectron spectra of eleven molecules: ${\mathrm{SiH}}_4$, Si(${\mathrm{CH}}_3$${)}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_5$${\mathrm{SiH}}_3$, (${\mathrm{CH}}_3$${)}_2$${\mathrm{SiH}}_2$, (${\mathrm{CH}}_3$${)}_3$SiH, ${\mathrm{SiF}}_4$, ${\mathrm{SiCl}}_4$, (${\mathrm{CH}}_3$${)}_3$SiCl, (${\mathrm{CH}}_3$${)}_3$SiI, ${\mathrm{Cl}}_2$${\mathrm{SiH}}_2$, and ${\mathrm{CH}}_3$${\mathrm{SiF}}_3$, have been recorded at high experimental resolution. The spectra all exhibit broadening, and in some cases resolved fine structure resulting from the excitation of vibrations in the core-ionized molecules. Extensive use is made of the equivalent-cores approximation to aid in the interpretation of the observed vibrational structure. Chemical effects on the lifetime of the Si 2p core holes are postulated for the alkyl-silane molecular series and ${\mathrm{SiF}}_4$ based on the linewidths obtained from deconvolutions of the experimental spectra with manifolds of vibrational bands.