Three and four identical fermions near the unitary limit

Abstract

This work analyzes the three and four equal-mass fermionic systems near and at the $s$- and $p$-wave unitary limits using hyperspherical methods. The unitary regime addressed here is where the two-body dimer energy is at zero energy. For fermionic systems near the $s$-wave unitary limit, the hyperradial potentials in the $N$-body continuum exhibit a universal long-range ${R}^{\ensuremath{-}3}$ behavior governed by the $s$-wave scattering length alone. The implications of this behavior on the low-energy phase shift are discussed. At the $p$-wave unitary limit, the four-body system is studied through a qualitative look at the structure of the hyperradial potentials at unitarity for the ${L}^{\ensuremath{\pi}}={0}^{+}$ symmetry. A quantitative analysis shows that there are tetramer states in the lowest hyperradial potentials for these systems. Correlations are made between these tetramers and the corresponding trimers in the two-body fragmentation channels. Universal properties related to the four-body recombination process $A+A+A+A\ensuremath{\leftrightarrow}{A}_{3}+A$ are discussed.