A basic optimization problem in linear systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48017/1/224_2005_Article_BF01691464.pd

Construction of analytic, unitary scattering amplitudes from a given differential cross-section:A refined analysis

We extend previous work concerning the construction of unitary scattering amplitudes that correspond to the scattering data at a given energy. The dispersive and absorptive parts are by construction analytic in cosϑ in the small and large Lehmann ellipses, respectively. The dispersive and absorptive parts obtained here, in contrast to those obtained before, are shown to have continuous derivatives on the boundary of their domains of analyticity. The continuum ambiguity in the determination of the scattering amplitude, which is associated with a lack of experimental information on the inelastic contribution to unitarity, is present here as well