High-fidelity pseudopotentials for the contact interaction

Abstract: The contact interaction is often used in modeling ultracold atomic gases, although it leads to pathological behavior arising from the divergence of the many-body wavefunction when two particles coalesce. This makes it difficult to use this model interaction in quantum Monte Carlo and other popular numerical methods. Researchers therefore model the contact interaction with pseudopotentials, such as the square well potential, whose scattering properties deviate markedly from those of the contact potential. In this article, we propose a family of pseudopotentials that reproduce the scattering phase shifts of the contact interaction up to a hundred times more accurately than the square well potential. Moreover, the pseudopotentials are smooth, resulting in significant improvements in efficiency when used in numerical calculations.