Neutron-${}^{19}\mathrm{C}$ scattering: Towards including realistic interactions

TL;DR

This study investigates low-energy neutron-${}^{19}$C scattering using realistic interactions within a three-body model, confirming Efimov physics signatures and emphasizing the importance of properly treating deeply-bound states.

Contribution

It provides a detailed three-body scattering analysis with realistic potentials, highlighting the effects of Pauli-forbidden states and confirming Efimov physics in neutron-${}^{19}$C interactions.

Findings

Efimov physics signatures confirmed in elastic scattering

Quantitative differences between shallow and deep models

Inelasticity parameter linked to bound state normalization

Abstract

Low-energy neutron-${}^{19}$C scattering is studied in the three-body $n + n + {}^{18}$C model using a realistic $nn$ potential and a number of shallow and deep $n$-${}^{18}$C potentials, the latter supporting deeply-bound Pauli-forbidden states that are projected out. Exact Faddeev-type three-body scattering equations for transition operators including two- and three-body forces are solved in the momentum-space partial-wave framework. Phase shift, inelasticity parameter, and cross sections are calculated. For the elastic $n$-${}^{19}$C scattering in the $J^\Pi=0^+$ partial wave the signatures of the Efimov physics, i.e., the pole in the effective-range expansion and the elastic cross section minimum, are confirmed for both shallow and deep models, but with clear quantitative differences between them, indicating the importance of a proper treatment of deeply-bound Pauli-forbidden states. In contrast, the inelasticity parameter is mostly correlated with the asymptotic normalization coefficient of the ${}^{19}$C bound state. Finally, in the regime of very weak ${}^{19}$C binding and near-threshold (bound or virtual) excited ${}^{20}$C state the standard Efimovian behaviour of the $n$-${}^{19}$C scattering length and cross section was confirmed, resolving the discrepancies between earlier studies by other authors [I. Mazumdar, A. R. P. Rau, V. S. Bhasin, Phys. Rev. Lett. 97 (2006) 062503; M. T. Yamashita, T. Frederico, L. Tomio, Phys. Rev. Lett. 99 (2007) 269201].