Normal ordered approximation with symmetry restoration for ab initio nuclear structure and reactions*

Inclusion of three body (3B) forces in ab initio nuclear structure and reaction calculations is necessary but expensive. A normal ordered two body (NO2B) approximation to the 3B interaction can be obtained, by first normal ordering it with respect to a reference state, and then truncating it to two-body contributions. However, violations of rotational and translational symmetry are introduced into the resulting interaction by the non-invariance of the reference state under rotation (for a reference state of nonzero angular momentum) and translation (for a reference state represented in terms of Slater determinants). It is essential for these symmetries to be restored, in order for an NO2B approximated interaction to be usable in ab initio reaction calculations. We study the effects of using an NO2B approximated interaction, with symmetries restored, in ab initio no-core shell model (NCSM) calculations, and present progress towards using this approximation in ab initio reaction calculations.