Many-body fits of phase-equivalent effective interactions

In many-body theory, it is often useful to renormalize short-distance, high-momentum components of an interaction via unitary transformations. Such transformations preserve the on-shell physical observables of the two-body system (mostly phase shifts, hence unitarily connected effective interactions are often called phase equivalent) while modifying off-shell T-matrix elements influential in many-body systems. In this paper, I lay out a general and systematic approach for controlling the off-shell behavior of an effective interaction, which can be adjusted to many-body properties, and present an application to trapped fermions at the unitary limit.