Constructing initial wave packets for time-dependent non-reactive scatterings at low collision energies

The scatterings between cold atoms, molecules, and ions provide an important playground for exploring cold physics and chemistry. Quantum scattering theory is essential to understanding the quantum mechanical nature of reactive and non-reactive scattering processes, providing comprehensive information on the dynamic scattering event. At low collision energies, the time-independent method is commonly used, but it suffers from a steep-scaling law with respect to the problem size. The present work develops the time-dependent wave packet method for non-reactive scatterings at low collision energies by constructing initial wave packets that are free of opposite momentum components, which otherwise emerge from the extended momentum range intrinsic to the finite Gaussian-shaped initial wave packet. These components have no influence on the reactive channel but interfere with the non-reactive elastic parts after being reflected by the barrier. Three schemes-the direct cut, the smooth elimination, and the direct construction-are proposed to alleviate the influence of the opposite components, and they are applied to three examples, a one-dimensional toy model, the H + H2 system, and the O + OH system, to demonstrate their performance in non-reactive scatterings at low collision energies.