Three and four identical fermions near the unitary limit
- URL: http://arxiv.org/abs/2205.04564v3
- Date: Fri, 8 Jul 2022 03:01:52 GMT
- Title: Three and four identical fermions near the unitary limit
- Authors: Michael D. Higgins, and Chris H. Greene
- Abstract summary: This work analyzes the three and four equal-mass fermionic systems near and at the $s$- and $p$-wave unitary limits.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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