Fredholm-Uniformization Computation of Elastic Scattering Amplitudes in the Presence of Arbitrarily Many Open Channels

A uniformization technique is used to compute elastic scattering amplitudes at energies where arbitrarily many channels are open. The method takes knowledge of the Fredholm determinant $D\left(z\right)\mathrm{}$ on the physical sheet and uses rational-fraction analytic continuation to continue $D\left(z\right)\mathrm{}$ onto the appropriate Riemann sheet to construct the elastic amplitude and total inelasticity. Numerical examples for two-, three-, and four-channel problems are given, and preliminary results which indicate that the method may be of use in the breakup region are presented.