Two particles interacting via a contact interaction on $S^2$

We consider two particles interacting via a contact interaction that are constrained to a sphere, or $S^2$. We determine their spectrum to arbitrary precision and for arbitrary angular momentum. We show how the non-inertial frame leads to non-trivial solutions for different angular momenta. Our results represent an extension of the finite-volume L\"uscher formulas but now to a non-trivial geometry. We apply our results to predict the spectrum of select two-nucleon halo nuclei and compare with experimental results.