Low Energy Effective Interactions for Atom-Ion Systems

This work develops simple and tunable low-energy effective interactions that retain the correct long-range r^-4 tail corresponding to the polarization potential. The effective interaction is tuned to reproduce the desired low-energy behavior of the energy-dependent quantum defect. In turn, the quantum defect is determined by the low-energy collision observables. For instance, the zero-energy quantum defect can be fixed by the physical scattering length. The resulting effective potential model can be used to accelerate the computation of collision cross sections for a neutral atom and a trapped ion, a fundamentally challenging problem computationally comparable to a three-body collision.