Resonance lifetime

The ratio F/Eq of width F and the mean energy of the transition Eo defines the precision necessary in nuclear y-absorption for tuning emission and absorption into resonance. Lifetimes of excited nuclear states suitable for Mossbauer spectroscopy range from 10 s to s. Lifetimes longer than 10 s produce too... 

When an electron resonance occurs, the temporary capture of an electron at an atomic or molecular site increases the interaction time of the electron at that site in proportion to the resonance lifetime (xa sec) and the inverse of the electron... 

Figure 26 Quadrupole moment Aq2) for the desorption of CO (v = 0) from 0 203(0 001) as a function of J. Filled circles show experimental data, solid lines show calculated Aq2) averaged with respect to the desorption velocity and other marks connected by line are calculated by various imaginary flat PESs. The excited state resonance lifetime tr = 10 fs [79].

Figure 3t Complex eigenvalues for cbe 1 64 1 effective mass ratio for R 2 4 a.u. The longest lived state is 2 x 10 harmonic periods Resonance lifetimes generally decrease as a function of (1) energy above dissociation, (2) increasing coupling strength. However, there are certainly notable exceptions Co these general trends. Reproduced from ref. (16), with permission. Copyright 1983, American Institute of Physics.

H. W. Jang and J. C. Light, Finite range scattering wave function method for scattering and resonance lifetimes, J. Chem. Phys. 99 1057 (1993). 

Dissociative attachment can be divided into resonant and nonresonant cases. The resonant case is fairly amenable to theoretical treatment (Bardsley et ai, 1964 O Malley, 1966). In that case, the dissociation process can often be well modeled semiclassically in terms of the lifetime of the temporary anion and the survival probability for it to move fl om the geometry at which attachment occurs to the point beyond which the anion is more stable than the neutral. While a fully detailed theoretical treatment can be complex (O Malley, 1966), the minimal ingredients to form a useful estimate of the cross section are an anion potential energy surface and a resonance lifetime or width, each of which can be computed in a fairly straightforward manner. 

When the potential energy of the TMA state is repulsive in the Franck-Condon (FC) region, it leads to a DEA process (9) that produces an anion along with one or more radical fragments. It requires that at least one of the fragments has a positive electron affinity and the resonance lifetime is sufficiently long to permit dissociation (>10 s) (Hofftnan et al. 2001) before electron emission by autodetachment (Figure 16.2). The electron-molecule interaction potential affects the resonance parameters and hence the DEA cross section. The DEA cross section can be written as follows (O Malley 1966)... 

Note, please, that resonance width is different for each resonance. The most narrow resonance corresponds to the lowest energy, the widest to the highest energy. The width of resonances is related to the notion of the resonance lifetime r (r is proportional to the inverse of the resonance width). 

Among these features, we will focus our attention in Section 2 on the role which resonance phenomena [IJ play on the rate of flow of the energy within a molecule, thus affecring the characteristics of unimolecular decay. Mode specificity (i.e. strong dependence of the resonance lifetimes not only on energy) may lead to nonstatistical intramolecular vibrational relaxation and selective unimolecular... 

The compound CeBeia crystallizes in the cubic NaZnja structure and has a lattice constant which suggests an intermediate Ce valence (Shoemaker et al., 1952). The magnetic susceptibility of CeBe (Cooper et al., 1971 Bucher et al., 1975a Borsa and Olcese, 1973) shows no evidence of magnetic order and is very similar to the susceptibility of CeSna. The electronic specific heat coefficient (Cooper et al., 1971) is 115 mJ/mole-K and there is a large peak in the thermoelectric power of 60/iV/K at 120 K. The electrical resistivity of CeBe has no sharp anomalies but at room temperature the resistance rise is slower than T. Borsa and Olcese (1973) measured the nuclear magnetic resonance and relaxation rate of the Be nucleus in CeBeu. They interpreted their data in terms of a variable Ce valence with Ce -Ce resonance lifetime of order 10" sec. 

Therefore, increases rapidly by about tt across a strong transmission resonance, such as that of Fig. 9, resulting in a relatively large value for t-j at the resonant energy E j.es- This resonance lifetime is given by... 

Notice that this differs from the analysis of section II.B. Nevertheless, once S is represented by a direct part and a resonance part (in the form of either a product or a sum), the resonance lifetime or delay time is calculated from the energy derivative of the phase of the resonance part in a reasonably consistent way. 

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