Four-body bound states in momentum space: the Yakubovsky approach without two-body $t-$matrices

Abstract

This study presents a solution to the Yakubovsky equations for four-body bound states in momentum space, bypassing the common use of two-body $t-$matrices. Typically, such solutions are dependent on the fully-off-shell two-body $t-$matrices, which are obtained from the Lippmann-Schwinger integral equation for two-body subsystem energies controlled by the second and third Jacobi momenta. Instead, we use a version of the Yakubovsky equations that doesn't require $t-$matrices, facilitating the direct use of two-body interactions. This approach streamlines the programming and reduces computational time. Numerically, we found that this direct approach to the Yakubovsky equations, using 2B interactions, produces four-body binding energy results consistent with those obtained from the conventional $t-$matrix dependent Yakubovsky equations, for both separable (Yamaguchi and Gaussian) and non-separable (Malfliet-Tjon) interactions.