Observability of modified threshold behavior near unitarity

TL;DR

This paper investigates how close to unitarity a multi-neutron system must be to exhibit modified threshold behavior, concluding that current neutron-neutron scattering lengths are insufficient for such effects to be observed.

Contribution

It quantifies the proximity to unitarity needed for observable threshold modifications in 3- and 4-neutron systems, using both physical and altered scattering lengths.

Findings

Neutron-neutron scattering length is not large enough for unitarity effects in 3n or 4n systems.

Modified threshold behavior requires a larger scattering length than currently observed.

Current neutron systems do not demonstrate the predicted unitarity threshold exponents.

Abstract

A number of recent references have pointed out that an N-particle system having short-range interactions at S-wave and/or P-wave unitarity can exhibit modified threshold behavior for various reactive processes. But the question of how close to unitarity one must get in order to observe such modifications has not been addressed. The present study quantities this question by treating cases involving 3- or 4-neutrons, at the physical value of the neutron-neutron singlet scattering length a and at artificially altered values. One major conclusion is that the neutron-neutron scattering length is not yet sufficiently large for the 3n or 4n systems to demonstrate the unitarity threshold exponent.