Classical dynamics of s-wave helium

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

doi:10.1016/0378-4371(93)90461-c

Cited by 17 publications

(3 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

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: 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

mentioning

confidence: 99%

“…( 1 ) Note that chaotic systems without KAM tori may also exhibit an algebraic asymptotic decay. For example, in the classical s-wave helium model such an algebraic decay of N (t) is observed with β = 0.82, see [7]. The magnetic field B = k/qR (where R is the cyclotron radius) is assumed to be confined by a circle with radius rB, which touches the corners of the triangle.…”

mentioning

confidence: 99%

Quantum manifestations of chaotic scattering in the presence of KAM tori

1996

View full text Add to dashboard Cite

We investigate the semiclassical scattering amplitude for systems, where the classical dynamics is non-hyperbolic, i.e. where islands of KAM trajectories exist in an otherwise chaotic phase space. With the help of semiclassical calculations for the three-disk billiard in an external magnetic field, in which a hyperbolic-non-hyperbolic transition is observed as a function of the field strength, we show that the "stickiness" of the KAM tori leads to a much slower decrease of the survival probability, as compared with the hyperbolic case. This is reflected by a much narrower shape of the energy correlation function. However, we also find that the algebraic asymptotic decay of the survival probability in the non-hyperbolic case is not important for the quantum fluctuations. (2) The conclusion in ref. [9] might have been caused by erroneously identifying the survival probability N II (E, t) with P II (E, t).

show abstract

Two-electron atoms: From resonances to fragmentation

Rost

Tanner²

Classical, Semiclassical and Quantum Dynamics in Atoms

View full text Add to dashboard Cite

Classical dynamics of s-wave helium

Cited by 17 publications

References 23 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

Quantum manifestations of chaotic scattering in the presence of KAM tori

Two-electron atoms: From resonances to fragmentation

Contact Info

Product

Resources

About