Space-fixed vs body-fixed axes in atom-diatomic molecule scattering. Sudden approximations

Pack, Russell T

doi:10.1063/1.1681085

Cited by 1,107 publications

(302 citation statements)

References 25 publications

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“…A more convenient and computationally efficient procedure for our purposes is to transform to a system of body-fixed coordinates. These coordinate systems were applied to quantum mechanical problems long ago by Hirschfelder and Wigner 30 and have been discussed extensively by Curtiss, Hirschfelder, and Adler 31 and more recently by Pack,32 and much of the present development will follow that of Pack. In a fully converged calculation, both the body-fixed and space-fixed formalisms lead to the same number of coupled equations and, for fully converged nonreactive atom diatom calculations, they may be implemented with comparable ease. However, body-fixed coordinate systems lead to an approximate decoupling of certain degrees of freedom which is not naturally present in the space-fixed analysis and which is useful in the development of approximate theories.…”

Section: The Body-fixed Schrodinger Equationmentioning

confidence: 99%

Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. I. Theory

Schatz

Kuppermann

1976

The Journal of Chemical Physics

336

165

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A method is presented for accurately solving the Schri:idinger equation for the reactive collision of an atom with a diatomic molecule in three dimensions on a single Born-Oppenheimer potential energy surface. The Schri:idinger equation is first expressed in body-fixed coordinates. The wavefunction is then expanded in a set of vibration-rotation functions, and the resulting coupled equations are integrated in each of the three arrangement channel regions to generate primitive solutions. Next, these are smoothly matched to each other on three matching surfaces which appropriately separate the arrangement channel regions. The resulting matched solutions are linearly combined to generate wavefunctions which satisfy the reactance and scattering matrix boundary conditions, from which the corresponding R and S matrices are obtained. The scattering amplitudes in the helicity representation are easily calculated from the body fixed S matrices, and from these scattering amplitudes several types of differential and integral cross sections are obtained. Simplifications arising from the use of parity symmetry to decouple the coupled-channel equations, the matching procedures and the asymptotic analysis are discussed in detail. Relations between certain important angular momentum operators in body-fixed coordinate systems are derived and the asymptotic solutions to the body-fixed Schri:idinger equation are analyzed extensively. Application of this formalism to the three-dimensional H + H 2 reaction is considered including the use of arrangement channel permutation symmetry, even-

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Section: The Body-fixed Schrodinger Equationmentioning

confidence: 99%

Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. I. Theory

Schatz

Kuppermann

1976

The Journal of Chemical Physics

336

165

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“…Its origin is placed into the center-of-mass of the entire ABM system. The same classical variables Q = (R, , ) are used, 41 but the quantum degrees of freedom are described by Jacobi coordinates q = (r, γ , ϕ ), as shown in Fig. 2.…”

Section: Mqct In the Bf Reference Framementioning

confidence: 99%

Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in space-fixed and body-fixed reference frames

Семенов

Babikov

2013

The Journal of Chemical Physics

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We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complexvalued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by realvalued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the bodyfixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.

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“…where the angle function G JM Ωℓ is expressed by the D-function, D J ΩM (ω ω ω), and the associated Legendre polynomials, P Ω ℓ (cos θ ) [9,10]. The wave-packet method is suited for the body-fixed representation because it can take an advantage of the sparsity of the Coriolis couplings.…”

Section: Tdwp Methods and Applicationsmentioning

confidence: 99%

Fusion reaction of halo nuclei: A real-time wave-packet method for three-body tunneling dynamics

Nakatsukasa¹,

Itô²,

Yabana³

et al. 2006

AIP Conference Proceedings

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Abstract. We investigate fusion cross section of a nucleus with a valence neutron, using the timedependent wave-packet method. For a stable projectile, in which the valence neutron is tightly bound (ε n < −3 MeV), the neutron could enhance the fusion probability when the matching condition of orbital energies are satisfied. In contrast, for a halo nucleus, in which the binding energy of the neutron is very small (ε n > −1 MeV), the fusion probability is hindered by the presence of the weakly bound neutron.

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Space-fixed vs body-fixed axes in atom-diatomic molecule scattering. Sudden approximations

Cited by 1,107 publications

References 25 publications

Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. I. Theory

Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. I. Theory

Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in space-fixed and body-fixed reference frames

Fusion reaction of halo nuclei: A real-time wave-packet method for three-body tunneling dynamics

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