A simple expansion of the scattering length in terms of $S$-matrix poles is derived for the angular momenta $l>0$. This expression shows that the dominant role in the low-energy collisions is played by the poles lying close to the origin of the complex momentum plane. Among these poles a peculiar class of virtual states is found to respond very weakly to the scaled perturbation potentials and thus resistant to producing trajectories in the complex momentum plane. Properties and an impact on low-energy collisions of these resistant virtual states are discussed.

• Received 11 May 2023
• Accepted 23 June 2023

DOI:https://doi.org/10.1103/PhysRevA.108.012807