Fock-tani representation for the quantum theory of reactive collisions

Girardeau, M. D.; Gilbert, J.

doi:10.1016/0378-4371(79)90080-3

Cited by 25 publications

(16 citation statements)

References 14 publications

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“…formalism of the Brussels School. In this way a detailed study could contain in a natural way (a) the inclusion of unstable states [23] which permits the treatment of unimolecular reacting processes such as A2*--> A + A (b) the inclusion of quantized electromagnetic radiation, that is photons, permitting the treatment of photoreactions [21,38] as, A2 + hv-+A + A (c) the inclusion of electrons and ions permitting the treatment of ionization processes and reaction processes between ions [22] ;…”

Section: Discussionmentioning

confidence: 99%

“…This method is based on the combination of two potent formalisms which permit, in principle, the study from a statistical mechanics point of view of any reacting gaseous system in non-equilibrium conditions. The first is the hamiltonian formalism, developed by Girardeau et al [17][18][19][20][21][22][23], which by carrying out Tani's unitary transformation permits the exhibition in a natural way of the reactive scattering processes. Consequently, the hamiltonian operator is not postulated as it has been in other treatments [34].…”

Section: Discussionmentioning

confidence: 99%

“…This procedure is based on the combination of the non-relativistic second quantization hamiltonian formalism, showing rearrangement scattering processes, developed by Girardeau and co-workers [17][18][19][20][21][22][23], and the formalism of Non-Equilibrium Statistical Mechanics (N.E.S.M.) developed by the Brussels School [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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On generalized Boltzmann equations for reacting systems

Veguillas¹,

Rivas²

1982

Molecular Physics

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A quantum-statistical treatment of chemical kinetics is presented which does not differ between non-reactive scattering and rearrangement processes. This treatment is done in such a way that the standard methods of nonequilibrium statistical mechanics become applicable. Kinetics equations of the Waldmann-Snider, and Wang Chang and Uhlenbeck type are derived for the reduced density operator of different species related to an homogeneous, dilute gaseous system of the type AB+C~-AC+B~---BC+A. Global rate coefficients for the different rearrangement processes are defined and derived when starting with Waldmann-Snider type equations.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On generalized Boltzmann equations for reacting systems

Veguillas¹,

Rivas²

1982

Molecular Physics

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“…These are (1) simultyeous occurrence of all arrangement channels in a single unperturbed Hamiltonian H,,, (2) simultaneous occurrence but explicit separation of different arrangement channels in a single interaction Hamiltonian V, (3) exact orthogonality of asymptotic states rEferring to different arrangement channels, and (4) explicit vanishing of that term in V representing the decay/formation of an unstable composite in the limit where the composite becomes stable (infinite lifetime). Here only enough of the structure of this representation to illustrate these properties will be exhibited; further details and derivations can be found in the literature [2-41. Although the method is general, notation appropriate to the decay A + B + C of an unstable composite of species A into stable composites and/or elementary constituents of species B and C will be used.…”

Section: Fock-tani Representationmentioning

confidence: 99%

Theory of half‐collision cross sections

Girardeau

1986

Int J of Quantum Chemistry

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Standard Lippmann-Schwinger theory does not apply to decay of metastable or unstable states due to failure of the adiabatic hypothesis. In the Fock-Tani representation, discrete unstable states can be described by state vectors orthogonal to the asymptotic states representing their decay fragments, and a decay/formation interaction is exhibited explicitly as a portion of the total interaction Hamiltonian. This allows a straightforward derivation of a generalized Lippmann-Schwinger "half-collision'' differential decay cross section without the need of projection operators. It reduces in first order to the product of a resonance line shape by a Golden Rule matrix element squared. In the general case the line shape is nonLorentzian and the matrix element factor contains final-state interaction contxibutions. The exact expression is expected to be applicable to a variety of processes such as predissociation, autoionization, and Auger effect. The derivation employs the van Hove resolvent formalism to exhibit the dependence of the cross section on the complex self energy of the decaying state.

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“…Especially, M.D. Girardeau et al developed the generalized Fock-Tani transformation method [7,8,9] which seems to give a satisfactory solution to this problem. The method is based on redundant modes and unitary transformation, which is mathematically strict.…”

Section: Introductionmentioning

confidence: 99%

Idealization Second Quantization of Composite Particles

Zhou¹,

Yu²,

Sun³

2001

Commun. Theor. Phys.

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A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones compared with those of unbound particles. The field operators of the composite particles thus arise naturally in the second quantization Hamiltonian. To be emphasized, the second quantization Hamiltonian has the regular structures which correspond clearly to different physical processes.

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Fock-tani representation for the quantum theory of reactive collisions

Cited by 25 publications

References 14 publications

On generalized Boltzmann equations for reacting systems

On generalized Boltzmann equations for reacting systems

Theory of half‐collision cross sections

Idealization Second Quantization of Composite Particles

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