2007/05/07 by H. S. Køhler, H. S. Kohler, Kohler, H. S. · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Crystallography and Radiation Phenomena #FOS: Physical sciences #Nuclear Theory (nucl-th) #Spectral Theory in Mathematical Physics #nucl-th
paper · pdf · doi:10.48550/arxiv.0705.0944
8 pages
arxiv created 2007/05/07 · openalex publication_date 2007/05/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This report concerns the energy of a zero-temperature many-body system of spin 1/2 fermions interacting via a two-body potential with a free space infinite scattering length and zero effective range; the Unitary limit. Given the corresponding phase-shift δ(k)=π/2 a one-term separable potential is obtained by inverse scattering assuming a momentum cut-off Λ such that δ(k)=0 for k>Λ. The \it effective \rm interaction in the many-body system is calculated in a pp-ladder approximation with Pauli-blocking but neglecting mean-field (dispersion) corrections; effective mass m*=1. Using only the zero relative momentum component of this interaction the total energy is ξ=4/9 (in units of the fermigas), a result reported by several previous authors. Integrating the momentum dependent interaction over the Fermi sea this energy is revised to ξ=0.24. This result is independent of density and of the cut-off Λ if Λ> ∼ 3kf. With m*≠ 1 there is however a strong dependence on this cut-off. Including hh-ladders estimates give ξ=0.4↔ 0.6, but a reliable result would in this case require a Green's function calculation.