Exploring core excitation in halo nuclei using halo effective field theory: an application to the bound states of $^{11}$Be

Abstract

Halo effective field theory (Halo-EFT) has proved to be very efficient for describing halo nuclei within models of nuclear reactions. Its order-by-order expansion scheme enables us to single out the structure observables that are probed in reactions, and therefore improve the accuracy of their values inferred from experiment. This formalism is however limited by its breakdown scale. Structure effects beyond that scale cannot be considered explicitly in reaction models. To extend the usual Halo-EFT, we include core excitation considering a particle-rotor model. We apply it to the case of $^{11}$Be, the archetypical one-neutron halo nucleus. The corresponding set of coupled equations is solved using the R-matrix method on a Lagrange mesh. As a first application, we analyze in detail the structure of both bound states of $^{11}$Be and the $^{10}$Be-n phaseshifts at low energy in the corresponding partial wave as a function of the core deformation. We also compute the electric dipole transition between these bound states. The comparison of our results with existing \textit{ab initio} calculations, show that including core excitation within Halo-EFT can significantly improve the description of the $\frac{1}{2}^+$ ground state of $^{11}$Be over single-particle models. On the contrary, core excitation has a negative effect on the description of the $\frac{1}{2}^-$ bound excited state. This is probably related to the presence of Pauli-forbidden states in our two-body model of $^{11}$Be.