Hadizadeh M R, Radin M, Mohseni K
College of Engineering, Science, Technology and Agriculture, Central State University, Wilberforce, OH, 45384, USA.
Department of Physics and Astronomy, Ohio University, Athens, OH, 45701, USA.
Sci Rep. 2020 Feb 6;10(1):1949. doi: 10.1038/s41598-020-58577-4.
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.
在本文中，我们研究三体束缚态中的相对论效应。为此，在动量空间中求解Faddeev方程的相对论形式，它是雅可比动量矢量的函数，且不使用分波分解。三维Faddeev积分方程的输入是离壳推进两体t矩阵，其通过求解Lippmann-Schwinger方程直接从推进两体相互作用计算得出。推进相互作用的矩阵元通过使用迭代方案求解非线性积分方程从非相对论相互作用中获得。针对Malfliet-Tjon势计算了相对论效应对三体结合能的影响。我们的计算表明，相对论效应导致三体结合能大约降低2%。详细研究了不同Faddeev分量在相对论三体波函数归一化中的贡献。通过计算三体质量算符的期望值来检验我们数值解的精度，结果表明与相对论能量本征值高度吻合。
