Jost Function Interpolation of Scattering Cross Sections

The analytic properties of the Jost function or Fredholm determinant for single- and many-channel scattering problems suggest that they may often be less rapidly varying functions of the energy than the $S$ matrix or cross sections. This idea is combined with a pointwise rational-fraction interpolation to give a rapidly convergent and highly accurate method of interpolating scattering information over a continuous range of energies. Narrow resonances are easily found by examination of the zeros of the real part of the Fredholm determinant.