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Microscopic description of translationally-invariant core+N+N overlap functions

We derive expressions for core + N + N overlap integrals starting from microscopic wave functions obtained in the ab initio no-core shell model. These overlap integrals correspond to three-body channel form factors and can be used to investigate the clustering of many-body systems into a core plus two nucleons. We consider the case when the composite system and the core are described in Slater determinant, harmonic oscillator bases, and we show how to remove spurious center of mass components exactly in order to derive translationally-invariant overlap integrals. We study in particular the Borromean 6He nucleus using realistic chiral nuclear interactions, and we demonstrate that the observed clusterization in this system is a Pauli focusing effect. The inclusion of three-body forces has a small effect on this structure. In addition, we discuss the issue of absolute normalization for spectroscopic factors, which we show is larger than one. As part of this study we also perform extrapolations of ground-state observables and investigate the dependence of these results on the resolution scale of the interaction.