Theory of Slow Atomic Collisions

Nikitin, E. E.; Umanskiĭ, Stanislav I︠A︡kovlevich

doi:10.1007/978-3-642-82045-8

Cited by 459 publications

(463 citation statements)

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“…Mott & Massey 1949;Bates 1962;Macías & Riera 1982;Nikitin & Umansky 1984). Total wave functions of the entire collisional system are expressed in terms of products of electronic molecular-state wave functions ψ mol l(u) (r; R) and nuclear wave functions, e.g., radial nuclear wave functions F l(u) (R)/R multiplied by angular nuclear wave functions; R being nuclear coordinates.…”

Section: Quantum Collision Theorymentioning

confidence: 99%

On inelastic hydrogen atom collisions in stellar atmospheres

Barklem

Belyaev²,

Guitou³

et al. 2011

A&A

109

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The influence of inelastic hydrogen atom collisions on non-LTE spectral line formation has been, and remains to be, a significant source of uncertainty for stellar abundance analyses, due to the difficulty in obtaining accurate data for low-energy atomic collisions either experimentally or theoretically. For lack of a better alternative, the classical "Drawin formula" is often used. Over recent decades, our understanding of these collisions has improved markedly, predominantly through a number of detailed quantum mechanical calculations. In this paper, the Drawin formula is compared with the quantum mechanical calculations both in terms of the underlying physics and the resulting rate coefficients. It is shown that the Drawin formula does not contain the essential physics behind direct excitation by H atom collisions, the important physical mechanism being quantum mechanical in character. Quantitatively, the Drawin formula compares poorly with the results of the available quantum mechanical calculations, usually significantly overestimating the collision rates by amounts that vary markedly between transitions.

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Section: Quantum Collision Theorymentioning

confidence: 99%

On inelastic hydrogen atom collisions in stellar atmospheres

Barklem

Belyaev²,

Guitou³

et al. 2011

A&A

109

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“…The main source of the discrepancy is a small O͑h͒ error in the interference phases, which is intrinsic to the leading order approximation. We stress that this error cannot be eliminated by simply including the so-called dynamic phase [2,3] [5], because there are other terms of the same order represented by the first order correction (42) to the primitive SC solutions (44). Of course, this conclusion is not a surprise.…”

Section: Discussionmentioning

confidence: 99%

“…(52). We have neglected the so-called dynamic phase [2,3], which is O͑h͒, as well as higher order corrections [5] to the off diagonal elements because they are beyond the leading order approximation, but retained exponentially small terms in the diagonal elements. Strictly speaking, this is not quite consistent with the leading order approximation, but such an approach preserves unitarity of the scattering matrix.…”

Section: ͑59͒mentioning

confidence: 99%

“…Historically, the first application of such an approach was the treatment of the rotational and vibrational spectra of diatomic molecules by Born and Oppen heimer [1]; the selected variable here is the internuclear distance and the small parameter is provided by the electron-tonucleus mass ratio. The term semiclassical (or quasiclassical, in Russian tradition) is commonly used for this kind of approximation in time-independent formulations [2][3][4][5]. A similar theoretical scheme in time-dependent problems, in which case the selected variable is time and the small parameter is the characteristic velocity of "slow" subsystem or the rate of variation of external conditions, is usually called the adiabatic approach [6].…”

Section: Introductionmentioning

confidence: 99%

“…There exists a great number of studies devoted to the comparison of SC and QM results for various physical systems, especially in the field of slow atomic and molecular collisions, see [2][3][4][5] and references therein. In this situation, it is natural to ask what is the reason for undertaking yet another study of this type.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum-mechanical and semiclassical study of the collinear three-body Coulomb problem: Inelastic collisions below the three-body disintegration threshold

Tolstikhin

Namba

2004

Phys. Rev. A

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A quantum-mechanical (QM) and semiclassical (SC) study of inelastic collisions in collinear three-body Coulomb systems below the three-body disintegration threshold is presented. The QM results are obtained by solving the stationary Schrödinger equation in hyperspherical coordinates using the slow/smooth variable discretization method. After appropriate rescaling of the hyperspherical coordinates, an asymptotic parameter 0 ഛ h ഛ 1 that depends only on the masses of particles and has the meaning of an effective Planck's constant for the motion in hyperradius emerges. The SC results are obtained in the leading order approximation of the asymptotic expansion in h. The main attention is paid to investigating how the SC and QM results converge as h → 0. It is shown that the overall agreement for a wide spectrum of systems and processes is surprisingly good even for h ϳ 1. However, because of interference effects the convergence is not monotonic, and the SC results may be grossly in error in the situations where a destructive interference occurs. The analysis of hidden crossings clarifies mechanisms of the nonadiabatic transitions. It is shown that if the oppositely charged particle is located between the two others, the nonadiabatic transitions occur near the top of the potential barrier via the well-known T series of hidden crossings. If it is located on one end of the system, then there is no potential barrier for real values of the angular variable, but there still exists an extremum in the complex plane; the mechanism of nonadiabatic transitions in this case is called the complex T series of hidden crossings.

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Assessing the options for identifying critically important potential surface regions: Applications to nonadiabatic transitions

Mishra¹,

Padmavathi²,

Rabitz³

1997

Int. J. Quant. Chem.

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Results from close coupling sensitivity density-based analyses are compared for some Ž . representative nonadiabatic collisions with those from Landau᎐Zener᎐Stueckelberg LZS and adiabatic analyses. These results seem to indicate that while for simple systems modeled by potential energy curves devoid of competing features LZS and adiabatic approaches also offer qualitatively correct insights these can be misleading for dynamics evolving on potential energy curves with competing features. The close-coupling sensitivity densities seem to offer a more reliable guide for detailed understanding of the impact of structure in potential energy curves and coupling matrix elements in the collisional outcome.

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Theory of Slow Atomic Collisions

Cited by 459 publications

References 0 publications

On inelastic hydrogen atom collisions in stellar atmospheres

On inelastic hydrogen atom collisions in stellar atmospheres

Quantum-mechanical and semiclassical study of the collinear three-body Coulomb problem: Inelastic collisions below the three-body disintegration threshold

Assessing the options for identifying critically important potential surface regions: Applications to nonadiabatic transitions

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