Matrix elements of the transition operator evaluated off the energy shell: Analytic results for the hard-core plus square-well spherical potential

An analytic expression is presented for the off-shell T-matrix elements for scattering from the spherical hard-core plus square-well potential. Various analytical properties of the off-shell T matrix, such as symmetry and unitarity, are examined. The typical behavior of the off-shell T matrix is shown numerically. It is found that the behavior strongly depends on the three independent quantities, i.e., the energy and the initial and final momenta, which can be off the energy shell. These results, combined with multiple-scattering theory, can be used to study high-energy many-body collision processes, such as collision-induced dissociation.