Abstract
We resum the ladder diagrams for the calculation of the energy density E of a spin 1/2 fermion many-body system in terms of arbitrary vacuum two-body scattering amplitudes. The partial-wave decomposition of the in-medium two-body scattering amplitudes is developed, and the expression for calculating E in a partial-wave amplitude expansion is also given. The case of contact interactions is completely solved for any content in partial waves and it is shown to provide renormalized results, expressed directly in terms of scattering data parameters, within cutoff regularization in a wide class of schemes. The S- and P-wave interactions are considered up to including the first three-terms in the effective-range expansion, paying special attention to the parametric region around the unitary limit.
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