Hund's cases for rotating diatomic molecules and for atomic collisions: angular momentum coupling schemes and orbital alignment

Aquilanti, Vincenz̊o; Cavalli, Simonetta; Grossi, Gaia

doi:10.1007/bf01426406

Cited by 30 publications

(17 citation statements)

References 39 publications

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“…The coupling schemes of four angular momenta are illustrated in Ref. [25] as the basic ingredients underlying the classification of the five Hund cases and the relationships among representations. It was shown that the transition from one coupling scheme to another is performed by an orthogonal transformation whose matrix elements can be written in terms of 6j symbols.…”

Section: Atomic Collisions and Molecular Spectroscopymentioning

confidence: 99%

Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity

et al. 2008

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The mathematical apparatus of quantum-mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinatorial aspects. SU (2) recoupling theory, involving Wigner's 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, plays nowadays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory -and of its extension to other Lie and quantum group-by using the collective term of 'spin networks'.Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey Scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only 1 in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper we list and discuss some aspects of these developments -such as for instance the hyperquantization algorithm-as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.

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Section: Atomic Collisions and Molecular Spectroscopymentioning

confidence: 99%

Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity

et al. 2008

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“…In particular, the case of an atom in a state j ¼ 1 was treated in detail [7] and a classical model was elaborated for j ) 1 [8]. It appeared expedient to consider the locking in a framework of successions, when atoms approach or recede, of the Hund coupling cases a, b, c, d, e in a diatom [9,10] or the , , , , " coupling cases for a more complicated system, atom þ diatomic molecule [11]. Basically, the locking occurs at the distance R % R L where the precession frequency of the intrinsic angular momentum about the collision axis, !…”

Section: Introductionmentioning

confidence: 99%

Locking of the intrinsic angular momentum in the capture of quadrupole diatoms by ions

2010

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The capture dynamics of rotationally polarised homonuclear diatoms in low-energy collisions with ions is studied theoretically. The interaction potential includes charge-quadrupole and charge-induced dipole terms. The former, taken in the perturbed rotor approximation, exhibits an R À3 anisotropic dependence and causes an only gradual locking of the intrinsic angular momentum of the diatom to the collision axis. As a result, the capture occurs in a regime of incomplete locking, and the passage over centrifugal barriers is accompanied by considerable gyroscopic effects. The j-specific capture cross-sections for rotationally-aligned diatoms show a marked dependence on the polarisation state which is not described by the conventional adiabatic channel model. The latter, however, provides a fair approximation for the cross-sections of unpolarised diatoms. These features are due to a considerable angle of rotation of the collision axis before the barrier is reached and to a small angle of rotation during the passage across the barrier. The numerically determined, scaled, capture cross-sections are represented by an approximate analytical expression that interpolates between two limiting cases, very small (adiabatic channel model) and very large (fly-wheel model) gyroscopic effects of the rotating diatom.

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“…This is an account of progress on understanding elementary spin networks in view of their ubiquitous occurrence in applications far beyond the theory of angular momentum in quantum mechanics where they were introduced by Wigner, Racah and others. They have been (and are) precious tools for computational nuclear, atomic, molecular and chemical physics: best known examples are vector coupling and recoupling coefficients and 3nj symbols [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Exact and Asymptotic Computations of Elementary Spin Networks: Classification of the Quantum–Classical Boundaries

Bitencourt

Marzuoli

Ragni

et al. 2012

Computational Science and Its Applications – ICCSA 2012

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Increasing interest is being dedicated in the last few years to the issues of exact computations and asymptotics of spin networks. The large-entries regimes (semiclassical limits) occur in many areas of physics and chemistry, and in particular in discretization algorithms of applied quantum mechanics. Here we extend recent work on the basic building block of spin networks, namely the Wigner 6j symbol or Racah coefficient, enlightening the insight gained by exploiting its self-dual properties and studying it as a function of two (discrete) variables. This arises from its original definition as an (orthogonal) angular momentum recoupling matrix. Progress also derives from recognizing its role in the foundation of the modern theory of classical orthogonal polynomials, as extended to include discrete variables. Features of the imaging of various regimes of these orthonormal matrices are made explicit by computational advances -based on traditional and new recurrence relations-which allow an interpretation of the observed behaviors in terms of an underlying Hamiltonian formulation as well. This paper provides a contribution to the understanding of the transition between two extreme modes of the 6j, corresponding to the nearly classical and the fully quantum regimes, by studying the boundary lines (caustics) in the plane of the two matrix labels. This analysis marks the evolution of the turning points of relevance for the semiclassical regimes and puts on stage an unexpected key role of the Regge symmetries of the 6j. V 2 = 1 288 0 J 2 3 J 2 J 2 23 1 J 2 3 0 J 2 12 J 2 2 1 J 2 J 2 12 0 J 2 1 1 J 2 23 J 2 2

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Hund's cases for rotating diatomic molecules and for atomic collisions: angular momentum coupling schemes and orbital alignment

Cited by 30 publications

References 39 publications

Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity

Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity

Locking of the intrinsic angular momentum in the capture of quadrupole diatoms by ions

Exact and Asymptotic Computations of Elementary Spin Networks: Classification of the Quantum–Classical Boundaries

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