Universality in the neutron$-^{19}$C scattering using finite range separable interactions

TL;DR

This paper investigates the low-energy neutron scattering in $^{19}$C near Efimov state conditions, examining the persistence of universal scaling laws with finite-range interactions and identifying universal features in phase-shift behavior.

Contribution

It demonstrates that universal scaling laws from zero-range models approximately hold with finite-range interactions in neutron-$^{19}$C scattering.

Findings

Universal scaling behavior observed in phase-shift data.

Universal characteristics linked to pole positions and effective-range parameters.

Finite-range interactions retain key features of zero-range universality.

Abstract

We report a study on the low-energy properties of the elastic $s-$wave scattering of a neutron ($n$) in the carbon isotope $^{19}$C near the critical condition for the occurrence of an excited Efimov state in the three-body $n-n-^{18}$C system. For the separation energy of the two halo neutrons in $^{20}$C we use the available experimental data. We also investigate to which extent the universal scaling laws, strictly valid in the zero-range limit, will survive when using finite-range interactions. By allowing to vary the $n-^{18}$C binding energy, a scaling behavior for the real and imaginary parts of the $s-$wave phase-shift $\delta_0$ is verified, emerging some universal characteristics given by the pole-position of $k\cot(\delta_0^R)$ and effective-range parameters.