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

• Published in: The Journal of chemical physics 2018-11, Vol.149 (20), p.204109-204109
• Main Authors: Li, Jing-Lun, Cong, Shu-Lin
• Format: Article
• Language: English
• Subjects: Dimers; Faddeev equations; Mathematical analysis; Physics; Scattering; Stability analysis; Trimers; Wave interaction
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.5045084

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 N⩾3. 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.