  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.
