One-dimensional model of nucleus-nucleus collision with zero-range force

A formula is presented to calculate in a simple way the exact scattering amplitudes between nuclei in a one-dimensional model with zero-range force. For all the possible pairs of nuclei, the exact scattering amplitudes are calculated and their properties are discussed. Furthermore, for some pairs of nuclei we construct the exact equivalent local potentials which prove to be just soliton potentials and discuss their properties. (author)