The Faddeev-Yacubovsky model of four particle scattering problem

The Faddeev-Yacubovsky model of four identical spinless particles with the resonating group approximation is considered. The integral equations of 4-particle scattering problem are formulated in the case of two-body channel (i.e. one particle + bound three particle type, and bound pair + bound pair type). It is shown with resonating group approximation, the four-particle scattering problem can be reduced to solve a set of one-dimensional coupled integral equations. Further, it is noticed that the Faddeev-Yacubovsky approach can be reduced to much more simple form with the nonlocal separable potential, and this is believed to bring the 4-particle problem within the range of modern computers. (author)