Abstract:
The singularities of the partial-wave amplitudes for the diagrams of the multiple
scattering series in a system of three nonrelativistic particles of arbitrary mass are
investigated. For an arbitrary diagram, simple analytic expressions are obtained for
the position of the nonpotential singularities of the partial-wave amplitudes in the
energy plane and necessary and sufficient conditions for the existence of these
singularities on the physical sheet are found. Simultaneously, using the analogy
between the singularities of the diagrams of the multiple scattering series and the
classical problem of the collision of three material points, we determine the maximal
number of possible two-body collisions in a classical system of three point particles of arbitrary mass with contact interaction.
Fulltext:
PDF file (1435 kB)
