Analysis of the optical potential with coupled-channel scattering equations: Energy dependence and coordinate-space behavior

We apply a Sturmian-expansion method we have recently developed to perform an exact multichannel analysis of the optical potential. By combining this method with momentum-space integral-equation techniques we can obtain a finite-rank representation of the nonlocal optical potential in which coupling effects are exactly taken into account. In the framework of this approach we provide also detailed expressions of the various contributions arising when couplings are treated perturbatively. These iterative-perturbative approximation schemes are generally employed in phenomenological optical-potential calculations. Our results do not apply to low-order terms only, but can be extended to any desired order. We find that a proper treatment of inelastic-inelastic couplings may be necessary in order to reproduce the detailed nonlocal structure of the optical potential. We then perform an energy-dependent analysis of the resulting optical potential. To this end, the rapid fluctuations in energy due to compound or quasicompound resonances are subtracted off by means of a direct algebraic procedure. The connection of this subtraction method with Feshbach's general reaction theory is clarified. We analyze the energy dependence of the smooth optical interaction in the light of a dispersion-theoretic approach, by resorting to simple analytic parametrizations of the real and imaginary parts. Both a model multichannel problem and the realistic neutron-208Pb case have been considered