Decay of metastable state

This problem can be treated as a resonant scattering, and the scattering matrix S or the elastic scattering phase shift r] are given by 

If the complex resonance energy is denoted as Er - iV/2, then near the resonance position Er is given by 

The WKB treatment and comparison with the instanton theory made by many authors are discussed in the book by Benderskii et al. [17] (see also [52]). We don t go into the details here. 

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B. Decay of Metastable State through Tunneling (Predissociation)... 

R. Graham, Macroscopic theory of activated decay of metastable states, J. Stat. Phys. 60, 675 (1990). 

The interpretation of final state distributions following the decay of metastable states is a very interesting topic. If the intermediate complex lives longer than an internal period, the memory on the parent molecule in the electronic ground state will be essentially erased and the product state distributions will no longer reflect the initial wavefunction. As we will show in Section 10.3, they instead reflect the wavefunction in the transition state of the upper electronic state and the dynamics in the exit channel following the transition region. 

The instanton theory of tunneling splittings in hydrogen-bonded systems and decay of metastable states in polyatomic molecules was studied by Nakamura et al. [182, 192, 195, 201-204, 216] They formulated a rigorous solution of the multidimensional Hamiltonian-Jacobi and transport equations, developed numerical methods to construct a multidimensional tunneling instanton path, and applied this method to HO [201], malonaldehyde [192, 195], vinyl radical [203], and formic acid dimer [202]. Coupled electron and proton transfer reactions were recently reviewed by Hammes-Schiffer and Stuchebrukhov [209]. 

FIG U RE 1.1 Three kinds of tunneling phenomena schematically depicted by one-dimensional potential energy curves (a) mnneling splitting, (b) decay of metastable state, and (c) tunneling in reaction. 

In the first part of this section, the instanton theory [2] is explained by taking the motion of a particle of mass m in one-dimensional potential V x). Tunneling splitting in a symmetric double well potential and decay of metastable state by tunneling through a potential barrier are employed as examples. In the second subsection, it is shown that the results can be reproduced by the WKB method with slight modification. 

Lifetimes for collision complexes and specific rate coefficients for unimolecular decay of metastable states can be derived in several ways in the framework of the adiabatic channel model, resulting in similar fundamental expressions. The major differences between the various derivations of lifetimes are connected to the physical interpretation. 

Fig. 1-7. Dependence of the partial half-life for decay on the decay energy Qp. The filled symbols refer to the decay of the ground state whereas the corresponding open symbols denote the values for the decay of metastable states. The shaded areas show the trends expected according to the microscopic theory using different assumptions in the...

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