One- and two-electron excitations of helium in the<i>s</i>-wave model

Draeger, M.; Handke, G.; Ihra, W.; Friedrich, Harald

doi:10.1103/physreva.50.3793

Cited by 23 publications

(11 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(60)]. Similar results were reported by Blü mel and Reinhard (1992) for the twodimensional collinear model and by Drä ger et al (1994) for the s-wave model. The most thorough study of the Fourier-transformed helium 1 S e spectrum has so far been undertaken by Qiu et al (1996;see also Burgdö rfer et al, 1997) based on ab initio quantum calculations by Bü rgers et al (1995).…”

Section: Spectral Fourier Analysissupporting

confidence: 86%

“…Collinear collision dynamics have also been studied by Gu and Yuan (1993) and Tang et al (1996) and have been used to develop the classical S-matrix theory for reactive scattering in molecular problems by Miller (1974) and others. Handke et al (1993) and Drä ger et al (1994) studied the so-called s-wave helium, which is similar to the eZe classical collinear dynamics; even so, the quantum arguments motivating this model are quite different. The model treats the electrons as pure s waves, i.e., the classical dynamics of both electrons take place only in the radial direction.…”

Section: A Collinear Helium: the Hamiltonian And General Propertiesmentioning

confidence: 99%

See 1 more Smart Citation

The theory of two-electron atoms: between ground state and complete fragmentation

2000

View full text Add to dashboard Cite

Since the first attempts to calculate the helium ground state in the early days of Bohr-Sommerfeld quantization, two-electron atoms have posed a series of unexpected challenges to theoretical physics. Despite the seemingly simple problem of three charged particles with known interactions, it took more than half a century after quantum mechanics was established to describe the spectra of two-electron atoms satisfactorily. The evolution of the understanding of correlated two-electron dynamics and its importance for doubly excited resonance states is presented here, with an emphasis on the concepts introduced. The authors begin by reviewing the historical development and summarizing the progress in measuring the spectra of two-electron atoms and in calculating them by solving the corresponding Schrö dinger equation numerically. They devote the second part of the review to approximate quantum methods, in particular adiabatic and group-theoretical approaches. These methods explain and predict the striking regularities of two-electron resonance spectra, including propensity rules for decay and dipole transitions of resonant states. This progress was made possible through the identification of approximate dynamical symmetries leading to corresponding collective quantum numbers for correlated electron-pair dynamics. The quantum numbers are very different from the independent particle classification, suitable for low-lying states in atomic systems. The third section of the review describes modern semiclassical concepts and their application to two-electron atoms. Simple interpretations of the approximate quantum numbers and propensity rules can be given in terms of a few key periodic orbits of the classical three-body problem. This includes the puzzling existence of Rydberg series for electron-pair motion. Qualitative and quantitative semiclassical estimates for doubly excited states are obtained for both regular and chaotic classical two-electron dynamics using modern semiclassical techniques. These techniques set the stage for a theoretical investigation of the regime of extreme excitation towards the three-body breakup threshold. Together with periodic orbit spectroscopy, they supply new tools for the analysis of complex experimental spectra.

show abstract

Section: Spectral Fourier Analysissupporting

confidence: 86%

Section: A Collinear Helium: the Hamiltonian And General Propertiesmentioning

confidence: 99%

The theory of two-electron atoms: between ground state and complete fragmentation

2000

View full text Add to dashboard Cite

show abstract

“…to damp the outgoing waves associated with the doubly excited and continuum states of helium. The energies are in excellent agreement with those presented in [14] (to five significant digits for the real part, four significant digits for the imaginary part) and similar agreement with the older calculations of Draeger et al [25] (to five significant digits for bound states, four significant digits for doubly excited states).…”

Section: B Helium Wave Functionsupporting

confidence: 79%

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

Bartlett

Stelbovics

2010

Phys. Rev. A

View full text Add to dashboard Cite

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 Schrödinger 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.

show abstract

“…(i.e., we used 500 points, in place of 150). An exponential fit of the form exp(−͑⌫ /2͒t) to the data (shown in the same figure by a dashed curve) yields a value of ⌫ 2s 2 = 2.7 ϫ 10 −3 a.u., compared to the width determined by Draeger et al [20] of 3.24ϫ 10 −3 a.u.…”

Section: ͑25͒mentioning

confidence: 65%

“…For a summary of our findings, Table III shows our results for the calculated energies E 2s 2 = ⑀ 2s 2 + i⌫ 2s 2 / 2 for the 2s 2 level in He, and ⑀ 1s , the energy of the 1s level in He + , for different numerical grids. [20] −0.7227− i 0.00162 −2.0000…”

Section: ͑25͒mentioning

confidence: 99%

Helium atom in a box: Doubly excited levels within theS-wave model

Mitnik

2004

Phys. Rev. A

View full text Add to dashboard Cite

A complete nonperturbative close-coupling solution of the helium atom in a box problem is presented by developing two numerical techniques. The first technique is the direct solution by diagonalization of the Hamiltonian, and the second is based on a constrained relaxation of the wave functions. A Feshbach projection operator of the direct solutions to the bound-continuum subspaces allows a comparison of the low-lying autoionization levels obtained in both methods. Time-dependent propagation of these doubly excited wave functions is analyzed, allowing the calculation and the visualization of the autoionization process. In this work, results are presented for the S-wave model in which the electrons are restricted to spherical states and all angular correlations have been eliminated.

show abstract

One- and two-electron excitations of helium in thes-wave model

Cited by 23 publications

References 55 publications

The theory of two-electron atoms: between ground state and complete fragmentation

The theory of two-electron atoms: between ground state and complete fragmentation

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

Helium atom in a box: Doubly excited levels within theS-wave model

Contact Info

Product

Resources

About