Three-body model of $^{6}$He with non-local halo effective field theory potentials

Abstract

We study the $^6$He Borromean nucleus in coordinate representation within a three-body model with two-body potentials derived from cluster effective field theory (EFT). These potentials are originally developed in momentum space and Fourier transformed to provide non-local potentials in configuration space. We use hyperspherical coordinates in combination with the Lagrange-mesh technique to compute the ground state energy, root mean square radius and the E1 strength distribution of $^6$He. We also introduce a three-body interaction to eliminate dependencies on the cutoff parameter of the two-body potentials on the ground state energy. The E1 strength distribution exhibits a low lying resonance as expected. However it is strongly influenced by the choice of the three-body EFT interaction.