Centrifugal sudden

The original semiclassical version of the centrifugal sudden approximation (SCS) developed by Strekalov [198, 199] consistently takes into account adiabatic corrections to IOS. Since the orbital angular momentum transfer is supposed to be small, scattering occurs in the collision plane. The body-fixed correspondence principle method (BFCP) [200] was used to write the S-matrix for f — jf Massey parameter a>xc. At low quantum numbers, when 0)zc —> 0, it reduces to the usual non-adiabatic expression, which is valid for any Though more complicated, this method is the necessary extension of the previous one adapted to account for adiabatic corrections at higher excitation... 

It is generally accepted that the centrifugal sudden (CS) approximation is the most reliable approximate method. Its results are usually very close to those obtained by ab initio close coupling (CC) calculations. The integral and differential cross-sections of Ar inelastic scattering on nitrogen were performed for a few low-frequency rotational transitions and four different interaction potentials [205]. Much better agreement of CC with CS results was found than with IOS calculations performed in... 

In the semiclassical centrifugal sudden (SCS) approximation some additional simplifications were made, which permit us to estimate the scattering phase by Eq. (5.50). Therefore the accuracy of SCS has to be checked separately. Fortunately, for the Ar-N2 system some cross-sections were calculated by the BFCP method [200] as well as by the CC method [206], which is considered to be the best. Using the same potential as in [209] the SCS cross-sections were found in [191] for fixed total energy of collisions E. The results are compared in Table 5.1. 

CARS see coherent anti-Stokes/Stokes Raman spectroscopy centrifugal sudden (CS) approximation 155, 166... 

Raman scattering Schrodinger equation 138, 262 SCS see centrifugal sudden (CS) approximation... 

The theory behind body-fixed representations and the associated angular momentum function expansions of the wavefunction (or wave packet) in terms of bases parameterized by the relevant constants of the motion and approximate constants of the motion is highly technical. Some pertinent results will simply be stated. The two good constants of the motion are total angular momentum, J, and parity, p = +1 or 1. An approximate constant of the motion is K, the body-fixed projection of total angular momentum on the body-fixed axis. For simplicity, we will restrict attention to the helicity-decoupled or centrifugal sudden (CS) approximation in which K can be assumed to be a constant of the motion. In terms of aU its components, and the iteration number k, the real wave packet is taken to be [21]... 

We had earlier vindicated treating one of the OH bonds in the H2O molecule as a spectator bond in studying the abstraction reaction. Another key assumption that needed to be checked was the centrifugal sudden (CS) approximation which was invoked to reduce the number of rotational basis functions used in the computations.28 Under the CS approximation and using only the K = 0 rotational basis functions, there was a total of 220 million basis functions for J = 15 alone. Relaxing the CS approximation, for example, with K = 0,1 and J = 15 led to 650 million basis functions. To approach the fully coupled-channel (CC) results, i.e. without... 

At low temperature the classical approximation fails, but a quantum generalization of the long-range-force-law collision theories has been provided by Clary (1984,1985,1990). His capture-rate approximation (called adiabatic capture centrifugal sudden approximation or ACCSA) is closely related to the statistical adiabatic channel model of Quack and Troe (1975). Both theories calculate the capture rate from vibrationally and rotationally adiabatic potentials, but these are obtained by interpolation in the earlier work (Quack and Troe 1975) and by quantum mechanical sudden approximations in the later work (Clary 1984, 1985). 

Among those TDQM studies, exact quantum dynamical calculations were usually limited to the total angular momentum / = 0. For / > 0, most of the authors used a capture model (or L-shift model) [77] to estimate the reaction probability from the / = 0 results. Even the direct calculations of reaction probabilities for / > 0 were performed using the centrifugal sudden (CS) approximation. Carroll... 

Figure 7. The coupled channel (CC) and centrifugal sudden (CS) integral cross section for the H + H20f00)f0) abstraction reaction. Other results x CS, Ref. 44 QCT, Ref. 54.

Figure 6. Temperature dependence of the reaction efficiency per collision for the reactions of OD + CH3Cl (open circles), 0D D20 + CH3Cl (filled circles and 0D (D20)2 + CH3Cl (half-filled circles). The reaction efficiency per collision is the experimental rate constant divided by the calculated collision rate constant, calculated by Clary using the adiabatic capture centrifugal sudden approximation (ACCSA) (28). For experimental reasons (29), the measurements were made with completely deuterated...

Reduced-Dimensionality Quantum Calculations of the Thermal Rate Coefficient for the Cl + HCl — HCl -I- Cl Reaction Comparison with Centrifugal-Sudden Distorted Wave, Coupled Channel Hyperspherical, and Experimental Results. 

The centrifugal sudden-adiabatic bend theory we jnst reviewed represents approximations to the partial wave vibrational state-to-state cumulative reaction probability Because that quan-... 

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