High-rank separable atom-atom interaction potential used for solving two-body Lippmann-Schwinger and three-body...

We derive a high-rank separable potential formula of the atom-atom interaction by using the two-body wave function in the coordinate space as inputs. This high-rank separable potential can be utilized to numerically solve the two-body Lippmann-Schwinger equation and three-body Faddeev equation. By analyzing the convenience and stability of numerical calculations for different kinds of the matrix forms of the Lippmann-Schwinger and Faddeev equations, we can find the optimal forms of the kernal matrices in the two- and three-body scattering equations. We calculate the dimer bound energy, two-body scattering phase shift and off-shell t-matrix, the trimer bound energy, atom-dimer scattering length, and three-body recombination rate using the high-rank separable potentials, taking the identical ⁴He atoms as an application example. All the calculations converge quickly for the rank number $$ . The high-rank separable potential is valid for two-body scattering calculation of ⁴He atoms, but not accurate enough for reproducing the three-body scattering results by using only two-body s-wave interaction and describing the contributions of two-body high partial-waves to the three-body scattering for the ⁴He₃ system.