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We describe the calculation of singly differential (energy-sharing) cross sections for electron-impact ionization. First, using exterior complex scaling, we calculate the outgoing portion of the scattering wave function without explicit use of asymptotic boundary conditions. Once that wave function is known for a finite region of space, the outgoing flux can be calculated and extrapolated to large distances according to behavior that is specific to the ionization problem. The differential cross section is proportional to the outgoing flux in specific directions of a hyperspherical angle in the coordinates. Calculations on the singlet s-wave radial limit (Temkin-Poet and collinear) models of electron-hydrogen atom ionization are presented. {copyright} {ital 1997} {ital The American Physical Society}

We report the results of close-coupling complex Kohn calculations of cross sections for electron-impact excitation of the water molecule into electronically dissociative states in the energy range from 8 to 30 eV. We have coupled five channels including the [sup 1][ital A][sub 1] ground state and excited singlet and triplet states formed by promoting the occupied 3[ital a][sub 1] and 1[ital b][sub 1] electrons to the lowest unoccupied 4[ital a][sub 1] orbital. These states have theoretical vertical energies in the range from 8 to 12 eV and are known to be dissociative. Our calculations have confirmed the existence of Feshbach resonances related to the [ital A][sub 1] and [ital B][sub 1] excited states which are responsible for dissociative attachment in water at rather high energies. We found that these resonances indeed correspond to configurations 3[ital a][sub 1]4[ital a][sub 1][sup 2] and 1[ital b][sub 1]4[ital a][sub 1][sup 2]. Our results include both total and differential cross sections. We also make comparison between theory and available experimental data.

The complex Kohn method, using correlated target states and a projected optical potential, is applied to elastic s-wave scattering of electrons from atomic helium in the energy range of the (1s2s2)2S Feshbach resonance. A projected optical potential is a very useful construct in the study of electron-molecule scattering, but the convergence of this approximation has not been systematically investigated. In this study, the projected optical potential approximation is shown to be convergent and yields an energy and width of the He 2S resonance of 19.357 eV and 14 meV, respectively, in excellent agreement with experiment.

The complex Kohn method is used to calculate elastic electron-Li[sub 2] scattering cross sections. The effect of including target correlation and polarization is systematically investigated. Various levels of [ital ab] [ital initio] treatment of the target ground and excited states are shown to have a major influence on the resulting scattering cross section for energies below 1 eV. Comparisions are made with previous calculations and experiment.

We report the results of a theoretical study of low-energy electron-${\mathrm{NH}}_{3}$ scattering in which target polarization effects are included by using an ab initio optical potential. The calculations employ the complex Kohn variational technique and are undertaken at both the static-exchange and polarized-self-consistent-field levels. Particular attention is paid to the complications attending electron scattering from target molecules that possess a permanent dipole moment. We describe the steps necessary to extract meaningful differential cross sections from fixed-nuclei calculations that ignore the rotational motion of the target. Good agreement is found between our results and recent experimental measurements.

We show how to extend close-coupling calculations into the intermediate energy region without explicitly including a large number of inelastic channels. By discretizing the target continuum in a suitably chosen set of complex functions, we can construct convergent representations of a Feshbach optical potential that represents open inelastic channels including the ionization continuum. The method can be implemented for electron scattering by atomic or molecular targets with minimal modifications to existing electronic structure codes. The method is illustrated by applying it to [ital e][sup [minus]]+Li[sub 2] elastic scattering.

Separable approximations have been used in electron-molecule scattering calculations to avoid the computation of two-electron matrix elements involving continuum functions. We show that such matrix elements involving one continuum function (proportional to a spherical Bessel function at large distances) and three Gaussian functions can be reduced to a single numerical quadrature of an integral involving ordinary two-election integrals over only Gaussian functions. Using these integrals in the Kohn variational method for electron-molecule scattering allows one to avoid the limitations of a primitive separable approximation for exchange interactions by replacing it with a more stable Schwinger separable expansion. The procedure is demonstrated for electron scattering from the 2 {sup 3}{ital S} state of helium.

Previous efforts to extract resonance widths by analytic continuation of stabilization graphs were limited by non-analytic behavior of the eigenvalues as functions of the stabilization parameter. We describe a procedure which avoids this difficulty by numerical analytic continuation of the characteristic polynomial, truncated to low order, of the hamiltonian matrix.

Complex-basis-function calculations of photoionization cross sections of CO/sub 2/ are reported at the static-exchange level, including averaging over ground-state vibrational motion in all normal modes. Previous studies have considered only the symmetric stretch normal mode. In spite of the fact that the bend and asymmetric stretch modes induce a dipole moment in the system and broaden the shape resonance in the 4sigma/sub g/ channel, the authors find the peak height for that resonance is only reduced by 20%. Possible reasons for the absence of this resonance feature in experimental photoabsorption cross sections are discussed, and extensive basis set studies are reported which verify that this feature is not a computational artifact but instead is a consequence of the static-exchange approximation.

We outline a procedure for calculating elastic and inelastic electron scattering amplitudes using expansions in basis sets of square-integrable functions exclusively. The local complex distortion method is illustrated by application to coupled-channel calculations of e − -H and e − -Li scattering.

The energy and lifetimes of metastable states (equivalently, the positions and widths of scattering resonances) are determined by the complex poles of the S -matrix, the Siegert eigenvalues. A variational, basis set method proposed by Bardsley and Junker for calculating these complex eigenvalues has been applied to several examples — a one-dimensional potential resonance and several autoionizing states of He and H − — with encouraging results. The method is seen to converge to the correct results as the basis set is increased, and the convergence is seen to be well-behaved. It is also significant that results of useful accuracy (e.g., lifetimes to ≈ 10% accuracy) can be obtained with reasonably modest basis sets (≈ 10 configurations for He, H − , of a quality that is attainable for systems with more than two electrons.

The complex potential-energy function for nuclear motion in the Born-Oppenheimer approximation for the lowest /sup 2/..sigma../sub u//sup +/ resonance state of H/sub 2/ /sup -/ has been calculated using the complex self-consistent-field (CSCF) method which treats the incident and target electrons equivalently. There is substantial disagreement among various determinations of the complex potential function for the broad /sup 2/..sigma../sub u//sup +/ resonance. The CSCF results agree best with the potential used by Bardsley and Wadehra (Phys. Rev. Lett. 41, 1795 (1978)) to compute dissociative attachment cross sections. The calculated width of the resonance as a function of internuclear distance is in excellent agreement with the form used by Bardsley and Wadehra while the real part of the CSCF potential agrees less well with their function. It is suggested that correlation effects are important in determining the position of the resonance and in determining the width at least near the internuclear distance at which the resonance becomes a bound state.

Difficulties in the straightfoward application of the complex-coordinate method to the calculation of resonance states in many-electron systems are examined. For the case of shape resonances, it is shown that many of these difficulties can be avoided by using complex coordinates only after reduction of the system to an effective one-electron problem. Further simplifications are achieved by the use of an inner-projection technique to facilitate the computation of the complex Hamiltonian matrix elements. The method is first illustrated by application to a model-potential problem. Its suitability for studying many-electron problems is demonstrated by calculation of the position and width of a low-energy /sup 2/P/sup o/ shape resonance in Be/sup -/. We discuss the modifications necessary to study core-excited (Feshbach) resonances.