Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content
arXiv:2106.02652 · doi:10.1016/j.aop.2021.168741
Abstract
We resum the ladder diagrams for the calculation of the energy density 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 in a partial-wave amplitude expansion is also given. The case of contact interactions is completely solved and is shown to provide renormalized results, expressed directly in terms of scattering data parameters, within cutoff regularization in a wide class of schemes. - and -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.
58 pages, 16 figures, 2 table. New version to match the accepted manuscript in Annals of Physics. Pole content and pairing is further discussed
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- Ultracold spin-balanced fermionic quantum liquids with renormalized -wave interactions
- Effective Field Theories for Neutron Stars Physics