Hyperspherical surface functions for nonzero total angular momentum. I. Eckart singularities

Kendrick, Brian K.; Pack, Russell T; Walker, Robert B.; Hayes, Edward F.

doi:10.1063/1.478574

Cited by 99 publications

(128 citation statements)

References 54 publications

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“…The remaining three internal coordinates can be represented by a hyperradius R and two hyperangles θ and ϕ. To define these internal coordinates, we use a slightly modified version of the Smith-Whitten hyperspherical coordinates [15,39,40,42,43].…”

Section: Methodsmentioning

confidence: 99%

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Adiabatic hyperspherical study of triatomic helium systems

2008

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The 4 He 3 system is studied using the adiabatic hyperspherical representation. We adopt the current state-of-the-art helium interaction potential including retardation and the nonadditive three-body term, to calculate all low-energy properties of the triatomic 4 He system. The bound state energies of the 4 He trimer are computed as well as the 4 He+ 4 He 2 elastic scattering cross sections, the three-body recombination and collision induced dissociation rates at finite temperatures. We also treat the system that consists of two 4 He and one 3 He atoms, and compute the spectrum of the isotopic trimer 4 He 2 3 He, the 3 He+ 4 He 2 elastic scattering cross sections, the rates for three-body recombination and the collision induced dissociation rate at finite temperatures.The effects of retardation and the nonadditive three-body term are investigated. Retardation is found to be significant in some cases, while the three-body term plays only a minor role for these systems.

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Section: Methodsmentioning

confidence: 99%

“…Enforcing the boson permutation symmetry is simplified using a modified version of the Smith-Whitten coordinate system [15,39,40]. The R-matrix method [41] is used to obtain the scattering S-matrix.…”

Section: Introductionmentioning

confidence: 99%

Adiabatic hyperspherical study of triatomic helium systems

2008

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“…A widely used publicly available code is the ABC code of Skouteris, Castillo, and Manolopoulos, 198 which is well suited for tunneling dominated atom-diatom reactions. For complexforming reactions which generally involve deep potential energy wells, methods based on adiabatic hyperspherical coordinates of Launay and coworkers 193,195 or Pack and Parker and their co-workers 194,199,200 may be more appropriate.…”

Section: E Field-free Reactive Scattering Calculationsmentioning

confidence: 99%

Perspective: Ultracold molecules and the dawn of cold controlled chemistry

Balakrishnan

2016

The Journal of Chemical Physics

275

271

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Ultracold molecules offer unprecedented opportunities for the controlled interrogation of molecular events, including chemical reactivity in the ultimate quantum regime. The proliferation of methods to create, cool, and confine them has allowed the investigation of a diverse array of molecular systems and chemical reactions at temperatures where only a single partial wave contributes. Here we present a brief account of recent progress on the experimental and theoretical fronts on cold and ultracold molecules and the opportunities and challenges they provide for a fundamental understanding of bimolecular chemical reaction dynamics. Published by AIP Publishing. [http://dx

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“…For a given value of the total angular momentum quantum number, J, and hyperspherical radius, ρ, the wavefunction is expanded onto a basis set of adiabatic functions, which are eigenfunctions of a triatomic hyperangular Hamiltonian. A hybrid DVR/FBR primitive basis set [61] combined with an Implicity Restarted Lanczos algorithm is used to diagonalize the hyperangular Hamiltonian matrix. The timeindependent Schrödinger equation yields a set of differential close-coupling equations in ρ, which are solved using the log-derivative matrix propagation method of Johnson [62].…”

Section: B Quantum Mechanical Approach and Convergence Testsmentioning

confidence: 99%

Formation of molecular oxygen in ultracoldO+OHcollisions

2009

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We discuss the formation of molecular oxygen in ultracold collisions between hydroxyl radicals and atomic oxygen. A time-independent quantum formalism based on hyperspherical coordinates is employed for the calculations. Elastic, inelastic and reactive cross sections as well as the vibrational and rotational populations of the product O2 molecules are reported. A J-shifting approximation is used to compute the rate coefficients. At temperatures T = 10 − 100 mK for which the OH molecules have been cooled and trapped experimentally, the elastic and reactive rate coefficients are of comparable magnitude, while at colder temperatures, T < 1 mK, the formation of molecular oxygen becomes the dominant pathway. The validity of a classical capture model to describe cold collisions of OH and O is also discussed. While very good agreement is found between classical and quantum results at T = 0.3 K, at higher temperatures, the quantum calculations predict a larger rate coefficient than the classical model, in agreement with experimental data for the O + OH reaction. The zero-temperature limiting value of the rate coefficient is predicted to be about 6 × 10 −12 cm 3 molecule −1 s −1 , a value comparable to that of barrierless alkali-metal atom -dimer systems and about a factor of five larger than that of the tunneling dominated F + H2 reaction.

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Hyperspherical surface functions for nonzero total angular momentum. I. Eckart singularities

Cited by 99 publications

References 54 publications

Adiabatic hyperspherical study of triatomic helium systems

Adiabatic hyperspherical study of triatomic helium systems

Perspective: Ultracold molecules and the dawn of cold controlled chemistry

Formation of molecular oxygen in ultracoldO+OHcollisions

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