The { \sl dressed} Scattering matrix describing scattering of quasiparticles in various models with long-range interactions is evaluated by means of Korepin's method\upref vek1/. For models with ${ 1\over\sin^2(r)}$-interactions the S-matrix is found to be a momentum-independent phase, which clearly demonstrates the ideal gas character of the quasiparticles in such models. We then determine S-matrices for some models with ${ 1\over\sinh^2(r)}$-interaction and find them to be in general nontrivial. For the ${ 1\over r^2}$-limit of the ${ 1\over\sinh^2(r)}$-interaction we recover trivial S-matrices, thus exhibiting a crossover from interacting to noninteracting quasiparticles. The relation of the S-matrix to fractional statistics is discussed.
Categories: cond-mat