Beryllium-9 in Cluster Effective Field Theory

Abstract

It is aimed to describe the nucleus of $^9$Be in an $\alpha$-$\alpha$-neutron cluster model, where the $\alpha$-$\alpha$ and $\alpha$-neutron interactions are determined via an effective field theory (EFT) for halo nuclei (halo-EFT). Here, only the $\alpha$-$\alpha$ case is discussed more detailed and hence results are given for $\alpha$-$\alpha$ phase shifts and for the ground-state energy of $^{12}$C as a three $\alpha$ cluster. The calculation of the $^{12}$C wave function is made via an expansion on nonsymmetrized hyperspherical harmonics (NSHH) in momentum space.