College of Liberal Arts & Sciences

# Math Physics Seminar

**Abstract:**

Many-body nuclear reactions are extremely difficult to model mathematically, due to the large dimension of the many-body Hilbert space. One way of handling this issue is to simply the calculations by extracting the physics from dominant reaction mechanisms. This process involves identifying the most important scattering channels, within the first approximation, and to treat the physics that contributes to those channels to all orders.

In this talk I will discuss how partition combinatorics, based on the Birkhoff lattice, can be used to simply the many-body calculation into a set of coupled few-body calculations. The structure of the Birkhoff lattice allows for the cluster expansion of the Hamiltonian to be expressed as a linear combination of subsystem Hamiltonians resulting in a decomposition by scattering channels. The Hamiltonian will contain coupled channels, associated with different partitions, which result in a set of coupled integral equations. These equations will contain the scattering information relevant to the dominant channels in the system and can be solved using numerical methods.