Equivalence of Model Space Techniques and the Renormalization Group for a Toy 2-body Problem Typeset Using Revt E X 1

Lee-Suzuki similarity transformations and Krencigowa-Kuo folded diagrams are two common methods used to derive energy independent model space effective interactions for nuclear many-body systems. We demonstrate that these two methods are equivalent to a Renormalization Group (RG) analysis of a toy 2-body problem. This is accomplished by considering a schematic model that can be solved in closed form. Analytic expressions for the effective low-momentum potentials V ef f are obtained and shown to give the same scaling equation for V ef f that RG arguments predict. This indicates that model space methods should be of interest to those studying low-energy nuclear physics using Effective Field Theories (EFT). We find the new result that all of the different energy independent model space techniques yield a unique low-momentum V ef f when applied to the toy 2-body problem.