Propagating Exterior Complex Scaling Research Articles

Electron-heliumS-wave model benchmark calculations. II. Double ionization, single ionization with excitation, and double excitation

The propagating exterior complex scaling (PECS) method is extended to all four-body processes in electron impact on helium in an S-wave model. Total and energy-differential cross sections are presented with benchmark accuracy for double ionization, single ionization with excitation, and double excitation (to autoionizing states) for incident-electron energies from threshold to 500 eV. While the PECS three-body cross sections for this model given in the preceding article [Phys. Rev. A 81, 022715 (2010)] are in good agreement with other methods, there are considerable discrepancies for these four-body processes. With this model we demonstrate the suitability of the PECS method for the complete solution of the electron-helium system.

Electron-heliumS-wave model benchmark calculations. I. Single ionization and single excitation

A full four-body implementation of the propagating exterior complex scaling (PECS) method [J. Phys. B 37, L69 (2004)] is developed and applied to the electron-impact of helium in an $S$-wave model. Time-independent solutions to the Schr\"odinger equation are found numerically in coordinate space over a wide range of energies and used to evaluate total and differential cross sections for a complete set of three- and four-body processes with benchmark precision. With this model we demonstrate the suitability of the PECS method for the complete solution of the full electron-helium system. Here we detail the theoretical and computational development of the four-body PECS method and present results for three-body channels: single excitation and single ionization. Four-body cross sections are presented in the sequel to this article [Phys. Rev. A 81, 022716 (2010)]. The calculations reveal structure in the total and energy-differential single-ionization cross sections for excited-state targets that is due to interference from autoionization channels and is evident over a wide range of incident electron energies.

Application of exterior complex scaling to positron-hydrogen collisions including rearrangement

The application of an exterior complex scaling method to an atomic scattering problem with distinct rearrangement channels is reported. Calculations are performed for positron-hydrogen collisions in an s -wave model employing an electron-positron potential of V12 =- [8+ (r1 - r2) 2] -1/2, using the time-independent propagating exterior complex scaling method. This potential has the correct long-range Coulomb tail of the full problem and the results demonstrate that exterior-complex-scaling-based methods can accurately calculate scattering, ionization,and positronium formation cross sections in this three-body rearrangement collision.

Electron- and positron-impact atomic scattering calculations using propagating exterior complex scaling

Calculations are reported for four-body electron-helium collisions and positron-hydrogen collisions, in the S-wave model, using the time-independent propagating exterior complex scaling (PECS) method. The PECS S-wave calculations for three-body processes in electron-helium collisions compare favourably with previous convergent close-coupling (CCC) and time-dependent exterior complex scaling (ECS) calculations, and exhibit smooth cross section profiles. The PECS four-body double-excitation cross sections are significantly different from CCC calculations and highlight the need for an accurate representation of the resonant helium final-state wave functions when undertaking these calculations. Results are also presented for positron-hydrogen collisions in an S-wave model using an electron-positron potential of V12 = − (8 + (r1 − r2)2)−1/2. This model is representative of the full problem, and the results demonstrate that ECS-based methods can accurately calculate scattering, ionization and positronium formation cross sections in this three-body rearrangement collision.

Atomic hydrogen revisited: electron impact excitation to H(2p) at 54 eV

New measurements of the three reduced Stokes parameters for 54.4 eV electron impact excitation of the 2p state of atomic hydrogen support convergent close coupling and propagating exterior complex scaling theoretical values within two standard deviations and over a larger angular range of 2°–140° than earlier work. Whereas the present measurements and theoretical values of the circular polarization Stokes parameter P3 agree, they differ by up to about four standard deviations from the measurements by Gradziel and O'Neill (2004 J. Phys. B: At. Mol. Opt. Phys. 37 1893) in the vicinity of 30° electron scattering angle and so do not support their explanation of an increased significance of electron exchange for this excitation process at 54.4 eV. We explore some variations in experimental methods and their implications for the measurements.

Differential and integrated cross sections for excitation to the3s,3p, and3dstates of atomic hydrogen by electron impact below then=4threshold

Integrated cross sections for the electron-impact excitation of ground-state hydrogen to the 3s, 3p, and 3d final states have been calculated using propagating exterior complex scaling and convergent close-coupling methods at energies between the n=3 and 4 excitation thresholds. The calculations are in excellent agreement and demonstrate that exterior complex scaling methods can accurately reproduce the resonance structure and magnitude of the excitation cross sections below the ionization threshold. Measurements of the separate 3s, 3p, and 3d differential cross sections were made at 12.24 eV, and are consistent with both calculations within a total experimental uncertainty of about 35%.

Differential cross sections for excitation to the 3s, 3p and 3d states of atomic hydrogen by electron impact at energies from 16.5 to 54 eV

The excitation of atomic hydrogen from the ground state to each of the 3s, 3p and 3d states has been studied for incident electron energies from 16.5 to 54 eV. Measurements of total cross sections and differential excitation cross sections (DCSs) for scattered electron angles from 5° to 150° have been made using a variety of coincidence methods. Within the summed experimental uncertainties of about 10% at best from statistical sources and 25% from absolute calibration sources the values calculated using the propagating exterior complex scaling and convergent close-coupling methods show good agreement with observations. DCS calculations for all s, p, d and f final states with n ⩽ 4 are also presented over this energy range and reveal a systematic trend with respect to increasing n, final-state angular momentum and incident energy.

Threshold Behavior ofe-H Ionizing Collisions

We present accurate ab initio numerical solutions of the full Schrödinger equation for the electron-impact ionization of hydrogen near threshold using the propagating exterior complex scaling method. They provide strong support for the Wannier threshold law [Phys. Rev. 90, 817 (1953)], giving sigma proportional to E(1.122+/-0.015), and also give the energy dependence of the electrons' angular distribution as (pi-theta12) FWHM approximately 3.0E(1/4), in general agreement with classical and semiclassical predictions.

Differential ionization cross-section calculations for hydrogenic targets withZ⩽4using a propagating exterior complex scaling method

A propagating exterior complex scaling method, with iterative coupling, has been adapted for the electron impact of charged hydrogenic targets. Using this fully ab initio method for solving the Schr\"odinger equation, which has no uncontrolled approximations, we present highly accurate total, single-differential, double-differential, and triple-differential cross-section calculations for the electron-impact ionization of hydrogenic targets with nuclear charge $Z\ensuremath{\leqslant}4$ (H, ${\text{He}}^{+}$, ${\text{Li}}^{2+}$, ${\text{Be}}^{3+}$). For a fixed scaled energy, the total and differential cross sections begin to converge with respect to increasing $Z$ when scaled by ${Z}^{4}$ and ${Z}^{6}$, respectively, and converge more rapidly with increasing incident-electron energy. The angular distributions of the differential cross sections change systematically with increasing nuclear charge for energies above the peak total ionization cross section, but for some lower-energy kinematics the triple-differential cross section for charged targets is significantly different from that of atomic hydrogen.