Scattering continuum

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. 

I point out that the analysis in Refs. [47, 48] and, later on, the one by Hazi and Taylor [49] penetrated deeper into the understanding of the empirical behavior of roots in the continuous spectrum by paying attention to the theory of resonance scattering [2,3] and to the properties of the scattering continuum, such as normalization and density of states. 

The 4>n > may contain contributions from the scattering continuum of the same channel. We concluded that "it is reasonable to expect that in reality these optimum conditions cannot be satisfied exactly and thus physical spectra must contain some single-particle excitation character even in regions where the spectrum is characterized mainly by a single, strongly absorbing peak" [143, p. L262]. 

Coherent and incoherently scattered continuum source Strong increases as atomic number decreases has a maximum value at low Bragg angles. 

Coherently and incoherently scattered continuum from tube. 

Fig. 27. Contour diagram of the collinear H + H2 potential energy surface, with the symmetric and as3rmmetric stretch vibrations of the saddle point configuration indicated by double-headed arrows. These vibrations are associated with the first two resonances in the P q curve of Fig. 2 these resonances represent virtual states embedded in the scattering continuum.

---