College of Liberal Arts & Sciences

# Math Physics Seminar

**Abstract:**

In a many-body scattering reaction it can happen that a large fraction of the total cross section is due to a small number of scattering channels. When this is the case it is useful to find an approximation where all of the scattered flux comes out in the dominant scattering channels. In this talk I use cluster expansions to construct a decomposition of the full many body Hamiltonian as a sum of two operators, when one has scattering only into an important set of channels and the other has scattering only into the complementary set of channels.

The decomposition utilized information that can be obtained by proper subsystem problems. The approximate wave function differ from the exact wave functions by an operator that is a compact perturbation of the identity.