Scattering theory, resonances resonance defined

In the case of a scattering resonance, bound-free correlation is modified by a transient bound state of fV+1 electrons. In a finite matrix representation, the projected (fV+l)-electron Hamiltonian H has positive energy eigenvalues, which define possible scattering resonances if they interact sufficiently weakly with the scattering continuum. In resonance theory [270], this transient discrete state is multiplied by an energy-dependent coefficient whose magnitude is determined by that of the channel orbital in the resonant channel. Thus the normalization of the channel orbital establishes the absolute amplitude of the transient discrete state, and arbitrary normalization of the channel orbital cannot lead to an inconsistency. 

The amplitude i j,(t t)) has been previously defined in the theory of resonant Raman scattering (37) and referred to as the Raman wave function. In the present approach,... 

The most accurate method for multilevel curve crossing problems is, of course, to solve the close-coupling differential equations numerically. This is not the subject here, however instead, we discuss the applications of the two-state semiclassical theory and the diagrammatic technique. With these tools we can deal with various problems such as inelastic scattering, elastic scattering with resonance, photon impact process, and perturbed bound state in a unified way. The overall scattering matrix 5, for instance, can be defined as... 

We now want to study the consequences of such a model with respect to the optical properties of a composite medium. For such a purpose, we will consider the phenomenological Lorentz-Drude model, based on the classical dispersion theory, in order to describe qualitatively the various components [20]. Therefore, a Drude term defined by the plasma frequency and scattering rate, will describe the optical response of the bulk metal or will define the intrinsic metallic properties (i.e., Zm((a) in Eq.(6)) of the small particles, while a harmonic Lorentz oscillator, defined by the resonance frequency, the damping and the mode strength parameters, will describe the insulating host (i.e., /((0) in Eq.(6)). 

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