Deformation of the J-matrix method of scattering

Using the tools of the J-matrix method we show that truncating the background interaction in the reference Hamiltonian leads to a significant loss of scattering information. Moreover, this loss is not recoverable by numerical means even if the truncated region in configuration or function space were to be extended substantially. We demonstrate this by calculating the nonrelativistic scattering for a system whose reference Hamiltonian is enhanced by one-parameter linear deformation as a clear and simple example for the background interaction to be truncated. This will result in an additional phase shift, component that could be used to account for persistent deviations in the scattering data from those obtained by proposed potential models. The compensating phase shift component, which is obtained by taking the full effect of the deformation in the II₀-problem, is confined to low energy regions whose extent depends on the value of the deformation parameter. Higher order deformations are briefly discussed and illustrated in a simple example. We also show that the deformation is equivalent to the addition of a separable potential, with Laguerre-type form factors, to the reference Hamiltonian and that the coupling parameters of the potential correspond to the deformation parameters.