The local complex-potential LCP model

The complex-potential model originated as a qualitative explanation of dissociative attachment [18]. A fixed-nuclei electronic resonance is described by a complex potential whose width goes to zero at the crossing point with the molecular ground-state potential, and remains zero if the resonance potential remains below the target 

The vibronic Hamiltonian in the one-electron model is H = Hq + V. The kernels of these operators are 

The coupled Schrodinger equations can be projected onto the fa fa subspace by Feshbach partitioning, giving an equation for the coefficient function Xd(q) in the component faxdiq) of the total wave function. The effective Hamiltonian in this equation is tn + Vd(q) + Vopt, which contains an optical potential that is nonlocal in the 7-space. This operator is defined by its kernel in the fa - fa subspace, 

Here kp = 2(E — Ev) for the bound or continuum vibrational state indexed by v. Thus the Feshbach formalism implies energy-dependent, nonlocal energy-shift and width functions for a resonance. 

Neglecting nonresonant scattering, the resonant contribution to the transition matrix is [82] 

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