Three and four identical fermions near the unitary limit

TL;DR

This paper investigates three- and four-fermion systems near the unitary limit using hyperspherical methods, revealing universal long-range behaviors, tetramer states, and implications for four-body recombination processes.

Contribution

It provides a detailed analysis of hyperradial potentials and tetramer states in fermionic systems at unitarity, extending understanding of few-body universal phenomena.

Findings

Hyperradial potentials exhibit a universal R^{-3} behavior near s-wave unitarity.

Existence of tetramer states in the lowest hyperradial potentials.

Connections between tetramers, trimers, and four-body recombination processes.

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 $\mathrm{A+A+A+A}\leftrightarrow \mathrm{A_3+A}$ are discussed.