Convergence of 2-Body Effective Range Expansions for $nd$ Quartet Scattering

Abstract

We examine the convergence properties of the 2-nucleon Effective Range Expansion as used in Effective Theories (ET-ERE's) for 3-nucleon calculations. We accomplish this by accounting for the 2-body dynamics with a simple rank-1 separable 2-body potential where the finite range effects can be incorporated systematically in both the 2- and 3-body problems. We make our initial comparisons in the simple context of the $^3S_1$ 2-nucleon channel and the $^4S_{3/2}$ 3-nucleon channel. We find that convergence problems for some of the 3-nucleon scattering amplitudes using the ET-ERE can be traced to its poor account of finite range effects that soften the momentum dependence of the deuteron propagator in the Faddeev kernel. In contrast, our simple separable potential with dipole form factors works very well in all cases considered.