AUTHOR=Mohammadzadeh M. , Radin M. , Mohseni K. , Hadizadeh M. R. 

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

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1232691

DOI=10.3389/fphy.2023.1232691

ISSN=2296-424X

ABSTRACT=<p>This study presents a solution to the Yakubovsky equations for four-body bound states in momentum space, bypassing the common use of two-body <italic>t</italic> − matrices. Typically, such solutions are dependent on the fully-off-shell two-body <italic>t</italic> − 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 does not require <italic>t</italic> − 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 <italic>t</italic> − matrix dependent Yakubovsky equations, for both separable (Yamaguchi and Gaussian) and non-separable (Malfliet-Tjon) interactions.</p>