Remarks on the inverse problem for an energy-dependent hamiltonian

We consider the inverse problem of potential reconstruction from scattering data concerning a 1D model of optical potential introduced by Morillon and Romain [Dispersive and global spherical optical model with a local energy approximation for the scattering of neutrons by nuclei from 1 keV to 300 MeV. Phys Rev C. 2004;70:014601] in the context of nuclear reactions. We show that the inverse method of Agranovich and Marchenko [The inverse problem of scattering theory. New York: Gordon and Breach; 1963] (real case) and Lyantse [An analog of the inverse problem of scattering theory for a non-selfadjoint operator. Math USSR-Sbornik. 1967;1:485-504] (complex case) can be extended to this model, in order to retrieve the energy-dependent part of the potential.