Long-Range Behavior of 3- and 4-body Fermionic Systems near Unitarity

Few interacting fermions near or at unitarity have been extensively studied in the context of atomic physics. One class of systems near unitarity is the BEC-BCS crossover problem, where the two-body singlet s-wave scattering length (a) is large compared to the range (r₀) of the interaction (|a/r₀|>10). This work is also relevant to the few-neutron problem in nuclear physics. These systems are studied in the adiabatic hyperspherical framework using an explicitly-correlated Gaussian basis. Through an analysis of the lowest few adiabatic potentials, the long-range behavior of the potentials exhibit universal behavior through a deviation from the repulsive ρ^-2 centrifugal barrier of the form Ca/ρ³, where ρ is the hyperradius and C depends only on system size and particle statistics. This long-range coefficient is extracted for both 3-body and 4-body systems through an analysis of adiabatic hyperradial potentials, computed using a correlated Gaussian hyperspherical method. The implications of this universal long-range behavior on low-energy N-body continuum scattering phaseshifts and the Wigner-Smith time delay are also explored.