Universality and the Coulomb interaction

We study the relationship between universal effects and the Coulomb interaction. Here, we present our approach and a first illustrative example. Understanding the relationship of universality and the Coulomb interaction is important for weakly bound nuclear few-body systems. The example nucleus we study is the excited state of $^{17}$F which we model as a proton and an $^{16}$O core. We use a Gaussian potential to represent short-range forces together with a Coulomb potential. Our calculation uses the Gaussian Expansion Method (GEM), which is a variational method well-suited to our problem. We find that we need to choose the range of the Gaussian potential in addition to the potential strength that reproduces the right scattering length. We propose to fit the range of the Gaussian potential such that the effective range is reproduced. We show that this approach leads to consistent results for $^{17}$F.