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arXiv · 2002.02615

A three-dimensional momentum-space calculation of three-body bound state in a relativistic Faddeev scheme

M. R. Hadizadeh·M. Radin·K. Mohseni
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Abstract

In this paper, we study the relativistic effects in a three-body bound state. For this purpose, the relativistic form of the Faddeev equations is solved in momentum space as a function of the Jacobi momentum vectors without using a partial wave decomposition. The inputs for the three-dimensional Faddeev integral equation are the off-shell boost two-body $t-$matrices, which are calculated directly from the boost two-body interactions by solving the Lippmann-Schwinger equation. The matrix elements of the boost interactions are obtained from the nonrelativistic interactions by solving a nonlinear integral equation using an iterative scheme. The relativistic effects on three-body binding energy are calculated for the Malfliet-Tjon potential. Our calculations show that the relativistic effects lead to a roughly 2\% reduction in the three-body binding energy. The contribution of different Faddeev components in the normalization of the relativistic three-body wave function is studied in detail. The accuracy of our numerical solutions is tested by calculation of the expectation value of the three-body mass operator, which shows an excellent agreement with the relativistic energy eigenvalue.

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M. R. Hadizadeh, M. Radin, K. Mohseni. 2020-02-07. A three-dimensional momentum-space calculation of three-body bound state in a relativistic Faddeev scheme. https://doi.org/10.1038/s41598-020-58577-4

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