Width resonance

Skokov S and Bowman J M 1999 Variation of the resonance width of HOCI (6uq ) with total angular momentum comparison between ab /M/o theory and experiment J. Chem. Phys. 110 9789-92... 

The inclusion of J-dependence into the resonance width generally produces only a small change in the shape of the resonance step. Schatz et al. have noted that such a step feature may occur for the Cl + HC1 reaction.39... 

However at long times a sample of prepared complex molecules will deplete according to the law, N(t) = N(0)e /T, where the lifetime r is related to the resonance width according to r = h/F. Furthermore, the decay flux into each outgoing channel is locked in fixed proportion at all... 

Explicit expressions for the dispersion laws oxk and resonance width qK can be deduced for a model system, with the substrate simulated by a semi-infinite elastic... 

This formula is derived in Appendix 3). With regard to various cubic and quartic anharmonic interactions, the quantity ft is characterized by a certain combination of these anharmonic contributions and becomes dependent on k (see Eq. (4.3.14) for a related quantity and Ref. 140). However, this dependence is insignificant compared to the k-dependence appearing in the denominators of Eqs. (4.3.32) and (4.3.34). Therefore, spectral characteristics defined by formulae (4.3.32) can with good reason be regarded as proportional to certain functions of lateral interaction parameters and of the resonance width 77 ... 

As a main point of this subsection,186 it is shown that due to sufficiently strong lateral interactions of adsorbed molecules on a two-dimensional triangular lattice, the spectral line for collective vibrations manifests some characteristic peculiar relationships between its dephasing-induced broadening and the resonance width 77 for the low-frequency mode The line width changes as Tj n(l/rf) for surface-normal and as rjm for surface-parallel molecular orientations, and takes nonzero values (independent of 77) for inclined molecules with the inclination angle ranging from 47° to 90°. 

The resonance width for low-frequency inodes rjq averaged over wave vectors is given in the Debye approximation as follows 143... 

Tucker, S. C., Thompson, T. C., Lauderdale, J. G., and Truhlar, D. G. (1988), A Vibrational Configuration Interaction Program for Energies and Resonance Widths, Comp. 

The amount of decrease of the resonance width may be simply estimated in the following way 50). Let the motion of the spins be characterized by a time tc, that is t is the average time a spin stays in a definite environment or the correlation time for the motion. This environment will cause a difference 5w in the precessional frequency of the spin which may be positive or negative from some average value to. During the time Tc the spin acquires a phase angle 60 = TcSu in addition to that acquired by the uniform precession at to. If we consider the motion to be a random walk process (51), after n such intervals during a time t the mean square phase acquired will be... 

Table 3 Rate Constant k, Resonance Energy E Resonance Width Electron Density and Cross Section Ch (From Refs. 10 and 11.)...

When the resonance width is narrower than the energy distribution of thermal electrons, the attachment rate constant is expressed as ... 

The resonance width Ts is expressed by the Wigner s threshold rule. In the case of isolated O2, the resonance state O2 (X ITg, v = 4) can couple with only one electronic partial wave with an angular momentum 1 = 2. In the case of vdW molecules, intermolecular interaction may couple with additional partial waves such as p-wave and s-wave with low energy. If a third-body molecule distorts the orbital of O2 (X ITg), new attachment channels can open with lower angular momentum of electrons and the resonance width may increase. 

We note that A iE) and F ( ) are the energy-dependent shift and width of the state 10 ) in Q, which now has become a resonance, since A(5 , c) = (fg c,E ) give rise to a typical (scattering) resonance line shape. We also note that the shift A ( ) for each state vanishes if one neglects the energy variation of the A(i , c), which is the case when the resonance widths are independent of the energy, or equivalently, when an unstructured continuum in the V subspace is assumed. 

There are many interesting facets of this elementary fragmentation process. In this presentation we emphasize primarily the mode specificity, that is, the more or less sytematic dependence of the resonance widths and the final-state distributions on the excited mode and the number of quanta in each mode. (For more complete analyses the reader is referred to Refs. 32 and 33 and some future publications.)... 

Figure 8. Resonance widths (in cm-1) for the dissociation of HCO as a function of the CO stretching quantum number V2 for several series as indicated. The terms ui and vj are the H-CO stretch and H-C-O bending quantum numbers, respectively. (Reprinted, with permission of IOP Publishing, from Ref. 8.)...

R. Schinke We extracted the resonance widths from the spectrum . It is clear that resonances are missed, especially the broader ones. Moreover, the widths have some uncertainty, especially at higher eneigies. Therefore, the statistics of rates is not unambiguously defined. The only point which I want to make is that our results are in qualitative accord with the predictions of random matrix theory. 

Figure 35. Resonance widths T(r) for He + Ar derived from differential scattering TJ, singlet 102 Tbs, singlet 109 rr, triplet.100...

P. Froelich, E. Brandas, Variational Principle for Quasibound States, Phys. Rev. A12 (1975) 1 P. Froelich, E. Brandas, Calculation of Resonance Widths via Expansion Techniques, Int. J. Quant. Chem. Symp. 10 (1976) 353. 

S. Skokov, J.M. Bowman, Complex L2 calculation of the variation of the resonance widths of HOC1 with total angular momentum, J. Chem. Phys. Ill (1999) 4933. 

P.W. Langhoff, Stieltjes-Tchebycheff moment-theory approach to molecular photoionization studies, in T. Rescigno, V. McKoy, B. Schneider (Eds.), Electron-Molecule and Photon-Molecule Collisions, Plenum, New York, 1979 A.U. Hazi, Stieltjes-moment-theory technique for calculating resonance widths, in T. Rescigno, V. McKoy, B. Schneider (Eds.), Electron-Molecule and Photon-Molecule Collisions, Plenum, New York, 1979. 

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