Atomic Collisions with a Trapped Ion

We model the collision of a Lithium atom with a trapped Ytterbium ion within the adiabatic hyperspherical approach in one spatial dimension. We propose a strategy that leverages the energy-analytic solutions of quantum defect theory, which can be used impose a short-ranged two-body boundary condition on the adiabatic eigenfunctions. This boundary condition depends on the hyperradius R, and in our numerical scheme must be translated to a particular b-spline basis set at each value of the hyperradius. We present a straightforward method for the computation of the adiabatic potential energy curves and all nonadiabatic couplings, providing a path forward for the calculation of scattering cross sections. We note that this method opens new possibilities for incorporating long-ranged two-body physics into few-body calculations.