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

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.

Comments: arXiv admin note: text overlap with arXiv:1611.03381