Quantum numbers for the problem of two coulomb centers

Krivchenkov, V. D.; Liberman, Michael A.

doi:10.1007/bf01106029

Cited by 2 publications

(4 citation statements)

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“…Physically, under condition (25), the quantity ω − is the frequency of small oscillations around the equilibrium in the direction of the normal coordinate δw .…”

Section: An Analytical Solution For a Three-dimensional Motionmentioning

confidence: 99%

“…where p is a linear momentum vector, the subscript z means a z projection. In this form this quantity was introduced in [25], the last term being added to facilitate the transition at R → ∞ to the Stark effect for the HI of the nuclear charge Z slightly perturbed by the charge Z .…”

Section: Crossings Of Classical Energy Termsmentioning

confidence: 99%

“…where v crit (w) is defined in (25). In any case, one should accept only the root w c within the interval (0, 1), the endpoints 0 and 1 being excluded.…”

Section: Crossings Of Classical Energy Termsmentioning

confidence: 99%

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A purely classical description of crossings of energy levels and spectroscopic signatures of charge exchange

Oks¹

2000

J. Phys. B: At. Mol. Opt. Phys.

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Charge exchange and crossings of corresponding energy levels that enhance charge exchange are strongly connected with problems of energy loss and diagnostics in high-temperature plasmas. Charge exchange has also been proposed as one of the most effective mechanisms for population inversion in the soft x-ray and VUV ranges. One area of the most fundamental theoretical importance in the study of charge exchange is the problem of electron terms in the field of two stationary Coulomb centres (TCC) of charges Z and Z' separated by a distance R. This involves fascinating atomic physics: the terms can have crossings and quasicrossings. These rich features of the TCC problem are also manifest in other areas of physics such as plasma spectroscopy: a quasicrossing of the TCC terms, by enhancing charge exchange, can result in an unusual structure (a dip) in the spectral line profile emitted by a Z-ion from a plasma consisting of both Z- and Z'-ions, as has been shown theoretically and experimentally. The paradigm is that these sophisticated features of the TCC problem and their flourishing applications are inherently quantum phenomena. In this paper we disprove this paradigm. We present a purely classical description of both the crossings of energy levels in the TCC problem and the dips in the corresponding spectral line profiles caused by the crossing (via enhanced charge exchange). Our classical description is based on first principles and does not use any model assumptions.

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“…Physically, under condition (25), the quantity ω − is the frequency of small oscillations around the equilibrium in the direction of the normal coordinate δw .…”

Section: An Analytical Solution For a Three-dimensional Motionmentioning

confidence: 99%

Section: Crossings Of Classical Energy Termsmentioning

confidence: 99%

See 1 more Smart Citation

A purely classical description of crossings of energy levels and spectroscopic signatures of charge exchange

Oks¹

2000

J. Phys. B: At. Mol. Opt. Phys.

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“…It can be checked that, at large R, the Redmond vector is recovered. Krivchenko and Liberman considered the Hamiltonian [77]:…”

Section: Oks' Supergeneralized Runge-lenz Vector For the Two-center P...mentioning

confidence: 99%

On Invariant Vectors in the Presence of Electric and Magnetic Fields

Pain

2023

Atoms

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In this non-exhaustive review, we discuss the importance of invariant vectors in atomic physics, such as the Laplace–Runge–Lenz vector, the Redmond vector in the presence of an electric field, the Landau–Avron–Sivardièrevector when the system is subject to a magnetic field, and the supergeneralized Runge–Lenz vector for the two-center problem. The application to the Stark and Zeeman effects are outlined. The existence of constants of motion in the charge-dyon system is also briefly mentioned.

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Quantum numbers for the problem of two coulomb centers

Cited by 2 publications

References 1 publication

A purely classical description of crossings of energy levels and spectroscopic signatures of charge exchange

A purely classical description of crossings of energy levels and spectroscopic signatures of charge exchange

On Invariant Vectors in the Presence of Electric and Magnetic Fields

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