$^6$Li in a Three-Body Model with Realistic Forces: Separable vs. Non-separable Approach

{\bf Background:} Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. {\bf Purpose:} Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that their solution based on separable interactions agrees exactly with solutions based on non-separable forces. {\bf Results:} The ground state of $^6$Li is calculated via momentum space Faddeev equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-$^4$He force. For the latter the Pauli-forbidden $S$-wave bound state is projected out. This result is compared to a calculation in which the interactions in the two-body subsystems are represented by separable interactions derived in the Ernst-Shakin-Thaler framework. {\bf Conclusions:} We find that calculations based on the separable representation of the interactions and the original interactions give results that agree to four significant figures for the binding energy, provided an off-shell extension of the EST representation is employed in both subsystems. The momentum distributions computed in both approaches also fully agree with each other.