Neutron$-^{19}$C scattering near an Efimov state

TL;DR

This paper investigates neutron-19C scattering near an Efimov state, revealing how the phase shift behavior signals the presence of Efimov states, with implications for ultracold atom physics.

Contribution

It demonstrates that the real part of the s-wave phase shift exhibits a zero or pole associated with Efimov states, using a zero-range model with large scattering lengths.

Findings

The phase shift shows a zero or pole when an Efimov state is present.

The pole position scales with the Efimov state's energy.

Results are relevant for ultracold atom systems with tunable interactions.

Abstract

The low-energy neutron$-^{19}$C scattering in a neutron-neutron-core model is studied with large scattering lengths near the conditions for the appearance of an Efimov state. We show that the real part of the elastic $s-$wave phase-shift ($\delta_0^R$) presents a zero, or a pole in $ k\cot\delta_0^{R}$, when the system has an Efimov excited or virtual state. More precisely the pole scales with the energy of the Efimov state (bound or virtual). We perform calculations in the limit of large scattering lengths, disregarding the interaction range, within a renormalized zero-range approach using subtracted equations. It is also presented a brief discussion of these findings in the context of ultracold atom physics with tunable scattering lengths.