Iteratively-coupled propagating exterior complex scaling method for electron–hydrogen collisions

Abstract

A newly-derived iterative coupling procedure for the propagating exterior complex scaling (PECS) method is used to efficiently calculate the electronimpact wavefunctions for atomic hydrogen. An overview of this method is given along with methods for extracting scattering cross sections. Differential scattering cross sections at 30 eV are presented for the electron-impact excitation to the n = 1, 2, 3 and 4 final states, for both PECS and convergent close coupling (CCC), which are in excellent agreement with each other and with experiment. PECS results are presented at 27.2 eV and 30 eV for symmetric and asymmetric energy-sharing triple differential cross sections, which are in excellent agreement with CCC and exterior complex scaling calculations, and with experimental data. At these intermediate energies, the efficiency of the PECS method with iterative coupling has allowed highly accurate partial-wave solutions of the full Schrödinger equation, for L 50 and a large number of coupled angular momentum states, to be obtained with minimal computing resources.The method for evaluating the scattered wavefunction for the electron-impact of atomic hydrogen using exterior complex scaling (ECS) was pioneered by Rescigno et al (1999), and using integral methods to obtain ionization cross sections (Baertschy et al 2001a), an excellent agreement with experimental results was obtained. The absence of any systematic approximations in the ECS method, and its universal nature (by directly calculating the underlying Schrödinger equation of the collision processes), gives tremendous potential for its application to collisions more complex than electron-hydrogen. Existing implementations of the ECS method for electron-hydrogen, however, are very computationally intensive. So, in order to apply the method to larger systems, it is necessary to find strategies to reduce its computational complexity.

A complete numerical approach to electron–hydrogen collisions

“…All the PECS calculations presented in this tutorial, and other publications emanating from this research [33][34][35][36][37][38][39][40][41][42][43], are in excellent agreement with other state-of-the-art computational methods and measurements, where available. We consider that the PECS method now offers complete solutions for e-H collisions in four important respects.…”

“…Previously [32,36], we have presented PECS coplanar (where the incident, scattered and ejected electron lie in the same plane) double-differential cross section (DDCS) and tripledifferential cross section (TDCS) calculations at 14.6 eV, 17.6 eV, 27.2 eV and 30.0 eV. The results are in excellent agreement with measurements, ECS calculations (where available) and CCC.…”

“…Our first PECS e-H scattering calculations [36] were undertaken above the ionization threshold at E 0 = 30 eV. These differential scattering cross sections for separate final-state orbital angular momenta (n j 4) demonstrated excellent agreement with measurements and CCC calculations.…”

Theory of Electron Impact Ionization of Atoms

“…This allowed us to obtain an integral representation for the ionization amplitude which is free of ambiguity and divergence problems [14]. In part, our analysis has provided a formal justification of the cross sections obtained in the ECS-based method [8][9][10].…”

“…More recently, Jones and Stelbovics [7] used a direct integration method to calculate electron-impact ionization within the framework of the TP model. A major advance in the direct solution of the Schrödinger equation was made using the exterior complex scaling (ECS) technique [8][9][10] when calculations reached the stage of yielding quantitative agreement with measurements of e-H fully differential ionization cross sections. Close-coupling-based methods, such as the convergent closecoupling [11], R matrix [12], T matrix [13], and other methods, have also yielded excellent agreement with experiment.…”