Recombination in the universal four-fermion system

TL;DR

This paper investigates fermion-fermion-dimer recombination in four-fermion systems near the unitary limit, providing a simple parametrization of the recombination rate's dependence on the effective range, useful for benchmarking methods.

Contribution

It introduces a linear-in-effective-range parametrization of the recombination rate near the unitary limit, enhancing understanding of four-fermion dynamics and aiding method benchmarking.

Findings

Recombination rate is linear in the effective range near unitarity.

Provides a simple parametrization for finite-range effects.

Results are useful for benchmarking four-particle system calculations.

Abstract

In the systems of spin $\frac12$ fermions with resonant $S$-wave interactions supporting only weakly bound dimers the antisymmetry forbids recombination of three (or more) fermions at zero energy. However, the fermion-fermion-dimer recombination is only partially suppressed. It is studied in the framework of momentum-space integral equations for the four-particle transition operators. In the vicinity of the unitary limit the fermion-fermion-dimer recombination rate, rescaled to build dimensionless quantity, is found to be linear in the effective range parameter, enabling a simple and accurate parametrization as well as evaluation of finite-range effects for any potential model. This feature makes the present results very useful in benchmarking different methods for three-cluster breakup and recombination calculations in four-particle systems. The interplay of the three-fermion and fermion-fermion-dimer recombination processes and their consequences for ultracold mixtures of fermions and dimers is discussed.