Three-body ion-neutral association

Consideration is given to the calculation of the rate coefficient of processes of the type A + + B + C → AB + + C. Classical mechanics is used. The impulse approximation is adopted and hard-sphere interactions are taken to describe C – A + and C – B collisions. Formulae are derived for the rate coefficients of binary collisions giving specified changes in the internal energy of the associating pair (without reference to their orbital angular momentum) and also of binary collisions giving specified changes in both the internal energy and in the square of the orbital angular momentum. By using quasi-equilibrium statistical theory, the rate co­efficient for three-body ion-neutral association is expressed in terms of either set of binary rate coefficients. Computations are carried out only Hg + + Hg + He → Hg + 2 + He. As expected, the predicted rate co­efficient is too high if specific account is not taken of the orbital angular momentum. If such account is taken excellent agreement is obtained with a measurement at 370 K made by Biondi (1953, 1972, private com­munication). The rate coefficient falls off slowly as the temperature is increased.

Gas-phase dissociation of fluorine ( 1 Ʃ + g ) molecules in an agron bath at 3000 K was studied by using the 3D Monte Carlo classical trajectory (3DMCCT) method. To assess the importance of the potential energy surface (PES) in such calculations, three surfaces, with a fixed, experimentally determined F 2 dissociation energy, were constructed. These surfaces span the existing experimental uncertainties in the shape of the F 2 potential. The first potential was the widest and softest; in the second potential the anharmonicity was minimized. The intermediate potential was constructed to ‘localize’ anharmonicity in the energy range in which the collisions are most reactive. The remaining parameters for each PES were estimated from the best available data on interatomic potentials. By using the single uniform ensemble (SUE) method (Kutz, H. D. & Burns, G. J. chem. Phys . 72, 3652-3657 (1980)), large ensembles of trajectories (LET) were generated for the PES. Two such ensembles consisted of 30000 trajectories each and the third of 26200. It was found that the computed one-way-flux equilibrium rate coefficients (Widom, B. Science 148, 1555-1560 (1965)) depend in a systematic way upon the anharmonicity of the potential, with the most anharmonic potential yielding the largest rate coefficient. Steady-state reaction-rate constants, which correspond to experimentally observable rate constants, were calculated by the SUE method. It was determined that this method yields (for a given trajectory ensemble, PES and translational temperature) a unique steady-state rate constant, independent of the initial, arbitrarily chosen, state (Tolman, R. C. The principles of statistical mechanics , p. 17. Oxford University Press (1938)) of the LET, and consequently independent of the corresponding initial value of the reaction rate coefficient. For each initial state of the LET, the development of the steady-state rate constant from the equilibrium rate coefficient was smooth, monotonic, and consistent with the detailed properties of the PES. It was found that, although the increased anharmonicity of the F 2 potential enhanced the equilibrium rate coefficients, it also enhanced the non-equilibrium effects. As a result, the steady-state rate constants were found to be insensitive to the variation of the PES. Thus, the differences among the steady-state rate constants for the three potentials were of the order of their standard errors, which was about 15% or less. On the other hand, the calculated rate constants exceeded the experimental rate constant by a factor of five to six. Because within the limitations of classical mechanics the calculations were ab initio , it was tentatively concluded that the discrepancy of five to six is due to the use of classical mechanics rather than details of the PES structure.


2012 ◽  
Vol 20 (4) ◽  
pp. 3563 ◽  
Author(s):  
O. V. Angelsky ◽  
A. Ya. Bekshaev ◽  
P. P. Maksimyak ◽  
A. P. Maksimyak ◽  
S. G. Hanson ◽  
...  

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Fabian Krinner ◽  
Stephan Paul

AbstractThree-body semileptonic $$\tau $$ τ -decays offer a path to understand the properties of light hadronic systems and CP symmetry violations through searches for electric dipole moments. In studies of electro-weak physics, the hadronic part of the final states has traditionally been described using the language of form factors. Spectroscopic information, resolved in terms of orbital angular momentum quantum-numbers, is best being derived from an explicit decomposition of the hadronic current in the orbital angular momentum basis. Motivated by the upcoming large data samples from $$\mathrm {B}$$ B factories, we present the full description of the hadronic currents decomposed into quantum numbers of the hadronic final state using the isobar picture. We present formulas for orbital angular momenta up to three and apply the rules derived from hadron spectroscopy to formulate the decay chain of hadronic three-body systems of arbitrary mass. We also translate this formalism to the language of form factors and thereby correct insufficiencies found in previous analyses of three-body hadronic final states.


1995 ◽  
Vol 48 (3) ◽  
pp. 503 ◽  
Author(s):  
RN Bhave ◽  
R Cooper

The rates of recombination of electrons with Net ions over a wide range of pressure (1001000 Torr) and at temperatures of 133, 233 and 295 K were measured. Two- and three-body recombination processes were resolved. The observed two-body rate coefficient is lower than earlier reports. The three-body rate measured agrees well with predictions from Flarinery's modified theory by Bates for termolecular ion-electron recombination in a monatomic gas.


1983 ◽  
Vol 36 (6) ◽  
pp. 831 ◽  
Author(s):  
R Hegerberg ◽  
RW Crompton

The Cavalieri electron density sampling technique has been used to measure the diffusion and attachment rate coefficients for thermal electrons in O2, and in O2–N2 and O2–C02 mixtures. The observed pressure dependence of the three-body attachment rate coefficient va/N2 is shown to be caused by the selective removal of electrons from the distribution at the attachment resonance energy, and the magnitude of this effect (so-called 'attachment cooling') is shown to be a measure of the magnitude of the rotational excitation cross sections in O2 and N2. Three-body rate coefficients for the formation of O2 involving O2, N2 and CO¯2 as third bodies have been found to be 2.2,011 and 3.5 X 10¯30 cm6 S¯l respectively. The value of the diffusion coefficient ND for thermal electrons in O2 is found to be (37 � 3) x 1021 cm¯1s¯1.


Author(s):  
Ryohei Yamagishi ◽  
Hiroto Otsuka ◽  
Ryo Ishikawa ◽  
Akira Saitou ◽  
Hiroshi Suzuki ◽  
...  

2018 ◽  
Vol 14 (3) ◽  
pp. 5708-5733 ◽  
Author(s):  
Vyacheslav Michailovich Somsikov

The analytical review of the papers devoted to the deterministic mechanism of irreversibility (DMI) is presented. The history of solving of the irreversibility problem is briefly described. It is shown, how the DMI was found basing on the motion equation for a structured body. The structured body was given by a set of potentially interacting material points. The taking into account of the body’s structure led to the possibility of describing dissipative processes. This possibility caused by the transformation of the body’s motion energy into internal energy. It is shown, that the condition of holonomic constraints, which used for obtaining of the canonical formalisms of classical mechanics, is excluding the DMI in Hamiltonian systems. The concepts of D-entropy and evolutionary non-linearity are discussed. The connection between thermodynamics and the laws of classical mechanics is shown. Extended forms of the Lagrange, Hamilton, Liouville, and Schrödinger equations, which describe dissipative processes, are presented.


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