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This study presents a solution to the Yakubovsky equations for four-body bound states in momentum space, bypassing the common use of two-bodyt− matrices. Typically, such solutions are dependent on the fully-off-shell two-bodyt− 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 requiret− 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 conventionalt− matrix dependent Yakubovsky equations, for both separable (Yamaguchi and Gaussian) and non-separable (Malfliet-Tjon) interactions.
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Relativistic Faddeev 3D equations for three-body bound states without two-body t -matrices
Abstract This paper explores a novel revision of the Faddeev equation for three-body (3B) bound states, as initially proposed in Ref. [J. Golak, K. Topolnicki, R. Skibiński, W. Glöckle, H. Kamada, A. Nogga, Few Body Syst. 54, 2427 (2013)]. This innovative approach, referred to as t-matrix-free in this paper, directly incorporates two-body (2B) interactions and completely avoids the 2B transition matrices. We extend this formalism to relativistic 3B bound states using a three-dimensional (3D) approach without using partial wave decomposition. To validate the proposed formulation, we perform a numerical study using spin-independent Malfliet–Tjon and Yamaguchi interactions. Our results demonstrate that the relativistic t-matrix-free Faddeev equation, which directly implements boosted interactions, accurately reproduces the 3B mass eigenvalues obtained from the conventional form of the Faddeev equation, referred to as t-matrix-dependent in this paper, with boosted 2B t-matrices. Moreover, the proposed formulation provides a simpler alternative to the standard approach, avoiding the computational complexity of calculating boosted 2B t-matrices and leading to significant computational time savings.
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- Award ID(s):
- 2000029
- PAR ID:
- 10486686
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Progress of Theoretical and Experimental Physics
- Volume:
- 2024
- Issue:
- 1
- ISSN:
- 2050-3911
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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