论文标题
相对论的FADDEEV方案中三体绑定状态的三维动量空间计算
A three-dimensional momentum-space calculation of three-body bound state in a relativistic Faddeev scheme
论文作者
论文摘要
在本文中，我们研究了三体结合状态下的相对论效应。为此，FADDEEV方程的相对论形式在动量空间中被求解，这是Jacobi动量向量的函数，而无需使用部分波浪分解。三维FADDEEV积分方程的输入是外壳增压两体$ t- $矩阵，通过求解Lippmann-Schwinger方程，它们直接从增强的两体相互作用中计算出来。增强相互作用的矩阵元素是通过使用迭代方案求解非线性积分方程来从非差异相互作用获得的。计算了对马氏-Tjon电位的三体结合能的相对论影响。我们的计算表明，相对论效应导致三体结合能的降低约为2 \％。详细研究了不同FADDEEV成分在相对论三体波函数的归一化中的贡献。通过计算三体质量运营商的期望值来测试我们的数值解的准确性，这表明与相对论能量特征值非常一致。
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.
