Renormalization of Inverse Power Law Potentials

Inverse power law potentials of the form $1/r^n$ play a central role in nuclear and atomic physics. For $n \ge 2$, their singularity requires an additional boundary condition to solve the 2-body system. I will present the results of examining the renormalization process for these highly singular potentials in the 3-body sector. The results are focused on two particular scenarios. First, I will address the renormalization of the $1/r^3$ potential as it represents the most singular term of the one-pion-exchange potential. I will discuss the necessity of a 3-body force in the 2 and 3-body sectors, basing my conclusions on calculations of bound state and scattering observables. Second, I will discuss the renormalization of van der Waals systems. These systems exhibit universal properties known to exist for a large scattering length which I will also address.