Three-body systems in the no-core shell model

In this thesis we present the ab initio no-core shell model (NCSM) and we use that framework to study 6He and 6Li computed with a realistic nucleon- nucleon interaction. In particular, we present results for the point-proton radius and the ground-state energy. Since we are limited to use a finite harmonic oscillator basis, we need to apply corrections to compute basis- independent results. A way of doing this is presented and demonstrated in this thesis. Furthermore, we derive an expression for calculating the three-body overlap function from microscopic wave functions obtained in the NCSM. We compute the overlap function, , to study the clusterization of the Borromean two-neutron halo state in 6He. We demonstrate that the clusterization is driven by the Pauli principle. The overlap function framework is also applied to 6Li. Finally, we demonstrate the capabilities of a microscopic model to study the core in a halo system, by computing the core swelling effect in 6He