Renormalization Group Scale Dependence of Nucleon-Nucleus Optical Potentials

The optical potential for scattering of a nucleon (a proton or neutron) off an atomic nucleus (e.g. O-16, Ca-40) is an effective interaction that results from reducing the (A+1)-body problem to a 2-body problem. There is a long history of empirical fits to determine optical potentials; however, efforts to calculate optical potentials rigorously from the underlying nucleon-nucleon (NN) interaction and microscopic many-body theory are only more recent. One important development from recent years is that the theoretical description of the NN potential is highly dependent on the renormalization group (RG) scale at which one works. In this work, we calculate optical potentials using leading-order multiple scattering theory (MST), and examine the dependence of these potentials to the RG scale. This work sheds light on subtleties associated with the NN potential and MST, which will help practitioners calculate improved nuclear scattering cross sections and assess their error more accurately.