Different ground-state potentials for the same ultracold-collision outcome

For ultracold strontium atoms colliding at 1 μK, we search for and determine a class of continuous deformations of the ground-state potential curve, under which scattering results are invariant. We search for these potential transformations by keeping track of the changes in the scattering length and photoassociation probabilities ( X 1 Σ g + → 1 Σ u + ) , as we systematically vary a suitable parametric description of the ground-state potential curve. Through a careful analysis of the numerical data thus obtained, we determine one-parameter transformations leaving the scattering matrix invariant. Moreover, we find that any two of these transformations are quadratically related.