  We derive expressions for cluster overlap integrals or channel cluster form
factors for ab initio no-core shell model (NCSM) wave functions. These are used
to obtain the spectroscopic factors and can serve as a starting point for the
description of low-energy nuclear reactions. We consider the composite system
and the target nucleus to be described in the Slater determinant (SD) harmonic
oscillator (HO) basis while the projectile eigenstate to be expanded in the
Jacobi coordinate HO basis. This is the most practical case. The spurious
center of mass components present in the SD bases are removed exactly. The
calculated cluster overlap integrals are translationally invariant. As an
illustration, we present results of cluster form factor calculations for
<5He|4He+n>, <5He|3H+d>, <6Li|4He+d>, <6Be|3He+3He>, <7Li|4He+3H>, <7Li|6Li+n>,
<8Be|6Li+d>, <8Be|7Li+p>, <9Li|8Li+n> and <13C|12C+n>, with all the nuclei
described by multi-hbar Omega NCSM wave functions.
