Configuration-Space Approach to Three-Particle Scattering

Zickendraht, W.

doi:10.1103/physrev.159.1448

Cited by 43 publications

(23 citation statements)

References 11 publications

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“…23 Equations of motion and conserved quantities for various potentials 23.1 N -stop metrolands and triangleland…”

Section: Three More Pot Facetsmentioning

confidence: 99%

“…However, once this did appear, I quickly noted that its notion of shape is the same as Kendall's [41], and that [37] itself can be considered in scale-shape split form. By this, Kendall's grasp of the requisite mathematics unlocks the classical and quantum mechanics of that model also [7].There are also a number of ties between RPM's and each of Celestial Mechanics [17,18,20] and Atomic and Molecular Physics [22,23,24,25,26,27]. These and the shape space analogy entirely sufficed to solve relational triangleland at all of the following levels: classical, quantum-mechanical, and a local PoT resolution [110,111,112,113,83,20,93,75,7].…”

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confidence: 99%

“…Acknowledgements: I thank those close to me for being supportive of me whilst this work was done. Mr Eduardo Serna for discussions and reading the manuscript and help with Secs 14,[18][19][20][21][22][23][24][25]…”

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confidence: 99%

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Relational Quadrilateralland I: The Classical Theory

Anderson

Kneller

2014

Int. J. Mod. Phys. D

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Relational particle mechanics (RPM) models bolster the relational side of the absolute versus relational motion debate. They are additionally toy models for the dynamical formulation of General Relativity (GR) and its Problem of Time (PoT). They cover two aspects that the more commonly studied minisuperspace GR models do not: 1) by having a nontrivial notion of structure and thus of cosmological structure formation and of localized records. 2) They have linear as well as quadratic constraints, which is crucial as regards modelling many PoT facets.I previously solved relational triangleland classically, quantum mechanically and as regards a local resolution of the PoT. This rested on triangleland's shape space being S 2 with isometry group SO(3), allowing for use of widely-known Geometry, Methods and Atomic/Molecular Physics analogies. I now extend this work to the relational quadrilateral, which is far more typical of the general N -a-gon, represents a 'diagonal to nondiagonal Bianchi IX minisuperspace' step-up in complexity, and encodes further PoT subtleties. The shape space now being CP 2 with isometry group SU (3)/Z3, I now need to draw on Geometry, Shape Statistics and Particle Physics to solve this model; this is therefore an interdisciplinary paper. This Paper treats quadrilateralland at the classical level, and then Paper II provides a quantum treatment.

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“…23 Equations of motion and conserved quantities for various potentials 23.1 N -stop metrolands and triangleland…”

Section: Three More Pot Facetsmentioning

confidence: 99%

mentioning

confidence: 99%

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Relational Quadrilateralland I: The Classical Theory

Anderson

Kneller

2014

Int. J. Mod. Phys. D

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“…Our partitions come from the separation of degrees of freedom induced by the symmetric hyperspherical coordinate representation. 3,5,[33][34][35][36]38,39,43 Such a separation is expected to be more physically motivated, in distinguishing different kinds of motions, than the usual separation of molecular vibrations and rotations, when dynamics is considered for clusters or reactions.…”

Section: Partitions Of the Kinetic Energymentioning

confidence: 99%

Phase-space invariants for aggregates of particles: Hyperangular momenta and partitions of the classical kinetic energy

Aquilanti

Lombardi

Sevryuk

2004

The Journal of Chemical Physics

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Rigorous definitions are presented for the kinematic angular momentum K of a system of classical particles (a concept dual to the conventional angular momentum J), the angular momentum L(xi) associated with the moments of inertia, and the contributions to the total kinetic energy of the system from various modes of the motion of the particles. Some key properties of these quantities are described-in particular, their invariance under any orthogonal coordinate transformation and the inequalities they are subject to. The main mathematical tool exploited is the singular value decomposition of rectangular matrices and its differentiation with respect to a parameter. The quantities introduced employ as ingredients particle coordinates and momenta, commonly available in classical trajectory studies of chemical reactions and in molecular dynamics simulations, and thus are of prospective use as sensitive and immediately calculated indicators of phase transitions, isomerizations, onsets of chaotic behavior, and other dynamical critical phenomena in classical microaggregates, such as nanoscale clusters.

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“…A similar calculation was done later for the photodisintegration of the trinucleon for the isospin T = 3 final state [2]. At the beginning of the seventies a few attempts to use a hyperspherical-harmonic (HH) expansion for solving nucleon-deuteron scattering [3][4][5] failed to produce reliable results because in this process too many partial * Unit6 de Recherche des Universit6s Paris 11 et Paris 6 Associ6e au CNRS 2 M. Fabre de la Ripelle waves are needed to describe accurately enough the asymptotic behaviour of the wave function.…”

Section: Introductionmentioning

confidence: 97%

Green function and scattering amplitudes in many-dimensional space

Fabre de la Ripelle

1993

Few-Body Systems

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Abstract. Methods for solving scattering are studied in many-dimensional space. Green function and scattering amplitudes are given in terms of the required asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many-dimensional space. Phase-shift analyses are performed for hypercentral potentials and for non-hypercentral potentials by use of the hyperspherical adiabatic approximation.

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Configuration-Space Approach to Three-Particle Scattering

Cited by 43 publications

References 11 publications

Relational Quadrilateralland I: The Classical Theory

Relational Quadrilateralland I: The Classical Theory

Phase-space invariants for aggregates of particles: Hyperangular momenta and partitions of the classical kinetic energy

Green function and scattering amplitudes in many-dimensional space

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