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 $R^{-3}$ 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 $L^{\pi }=0^{+}$ 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 $\mathrm{A}+\mathrm{A}+\mathrm{A}+\mathrm{A}\leftrightarrow {\mathrm{A}}_3+\mathrm{A}$ are discussed.

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Cited by in corpus (4)

• Three-body forces and Efimov physics in nuclei and atoms
• Universal trimers with p-wave interactions and the faux-Efimov effect
• Observability of modified threshold behavior near unitarity
• Elastic collision rates of spin-polarized fermions in two dimensions