  We derive the generalization of Wigner's causality bounds and Bethe's
integral formula for the effective range parameter to arbitrary dimension and
arbitrary angular momentum. We also discuss the impact of these constraints on
the separation of low- and high-momentum scales and universality in low-energy
scattering. Some of our results were summarized earlier in a letter
publication. In this work, we present full derivations and several detailed
examples.

Nuclear Theory;Quantum Gases;Quantum Physics