Lifetime matrix

JEC. This leads to (elastic) time delays that diverge at threshold. Since thresholds are quite dense in energy for a typical chemical reaction, this can yield very erratic behavior of the Smith lifetime matrix, and hence the eigenvalues. 

An important perspective of multichannel resonance scattering may be gained from the lifetime matrix Q(E), introduced by Smith [46] as a generalization of the time delay At of Eq. (24) in single-channel scattering. It is now more often called the time-delay matrix or the delay-time matrix. After extending At for matrix elements Qy(E) for multichannel scattering, he proved that... 

The main difference between (2S-D1ABAT1C) and (IS-GP) results is the appearance of broad Fano profiles on the (2S-D1ABAT1C) transition probabilities, which suggests that the upper adiabatic PES can support resonances which do not exist in the single ground adiabatic surface calculation. This can be investigated further with the lifetime matrix formalism described in Sect. 3.4. Smith lifetime matrices for the (2S-DIABATIC) case differ from the (IS-GP) ones only by the appearance of Lorentzian-shape eigenvalues near and above 4 eV. 

V. Aquilanti, S. Cavalli, D. De Fazio, A. Simoni, and T.V. Tscherbul, Direct evaluation of the lifetime matrix by the hyperquantization algorithm Narrow resonances in the F + H2 reaction dynamics and their splitting for nonzero angular momentum. J. Chem. Phys., 123(054314) 1-15, 2005. 

Lifetime Matrix. In the analysis of our RIOS results for both FH and FD., we shall employ the lifetime matrix analysis due to Smith.T22) In this approach, the lifetimes are given by the diagonal elements of the time delay matrix... 

The most precise characterization of the resonances Is obtained using the lifetime matrix analysis of Smith.(22) In Figure 6 we give the elgendelay times for FH- with Y=0, 1=0 and Y 0, 1=10. It Is... 

We use the Bending-Corrected Rotating Linear Model (BCRLM) to Investigate In detail the way In which resonances may affect the angular distribution of reaction products. Using a lifetime matrix method, we separate the resonant and direct parts of the S matrix, and from the direct part we obtain angular distributions In the absence of the resonance. When applied to the F+H2(v= 0) HF(v =2)+H reaction on the... 

In this paper, we will present a detailed analysis of the way In which resonances may affect the angular distribution of the products of reactive collisions. To do this, we have used an approximate three-dimensional (3D) quantum theory of reactive scattering (the Bending-Corrected Rotating Linear Model, or BCRLM) to generate the detailed scattering Information (S matrices) needed to compute the angular distribution of reaction products. We also employ a variety of tools, notably lifetime matrix analysis, to characterize the Importance of a resonance mechanism to the dynamics of reactions. 

All resonances are necessarily characterized by the llfetlsie of the compound state, and Smith s (39) definition of the lifetime matrix... 

Equation 12 tells us three things about the lifetime matrix near an IM when the energy dependence of S Is negligible (1) the trace of 2 1 8 a Lorentzlan form "... 

Let us now analyze the resonance contribution to this angular distribution more closely. Since Figure 2 shows that at E>1.807 eV the resonant contribution to the deflection of products Is greatest near 1 16, we show In Figure 4 a plot of the eigenvalues of the 1 16 lifetime matrix [Equation 11] as a function of total energy E. Over... 

F.T Smith, Lifetime matrix in collision theory, Phys. Rev. 118 (1960) 349. 

Finally, in Fig. 6 we present the collision lifetime matrix eigenvalues associated with the resonances in the partial wave occurring just before the opening of... 

Figure 6. Collision lifetime matrix eigenvalues (in atomic units) for the partial wave just below the opening of the n = 4 H-atom channel as a function of energy. One atomic unit of time is the classical time it takes an electron in the H-atom ground state to traverse one radian. The ordinates of the off-scale peaks of the dashed and full curves occurring at 0.93145 Ryd and 0.93713 Ryd are 1.3 X 10 and 1.9 x 10 atomic units respectively. The arrows locate the positions of the resonances.

A. Kuppermann and J. A. Kaye, Collision lifetime matrix analysis of the first resonance in the collinear F + H2 reaction and its isotopically substituted analogs, Chem. Phys. Lett, submitted for publication. 

Smithsuggested replacing with the following expression z(T) from the lifetime matrix formalism,... 

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