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首页> 外文期刊>Physical review, C >Numerical solution of time-dependent three-particle Faddeev equations: Calculation of rearrangement S matrices
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Numerical solution of time-dependent three-particle Faddeev equations: Calculation of rearrangement S matrices

机译：时间依赖性三粒子Faddeev方程的数值解：重排矩阵的计算

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The time-dependent Faddeev equations (TDFEs) are employed for the first time as a computational tool for three-particle scattering problems. Rearrangement transition amplitudes over a wide range of collision energies are extracted from a single numerical wave-packet solution of the TDFE. To numerically solve the TDFE in momentum space for a given initial wave packet, finite-element-type discretizations of Jacobi momenta in terms of local basis functions is employed to convert the TDFE into a set of first-order differential equations in time. Central difference formula for the time derivative is used for the time propagation step. Two forms of TDFE are considered and incorporation of permutational symmetry for three identical particles into these equations is carried out. The proposed method is tested on a three-body model that is often used as a benchmark to compare different computational approaches to three-particle problem. Rearrangement S-matrix elements obtained from the analysis of the wave-packet solution of TDFE at asymptotic times are compared with the results of well-established time-independent methods. These results establish that the TDFE approach is a viable and competitive addition to the existing arsenal of computational methods for the three-body scattering problem.
机译：时间依赖的Faddeev方程（TDFE）首次使用作为三粒子散射问题的计算工具。从TDFE的单个数字波分组溶液中提取宽范围碰撞能量的重排过渡幅度。为了在给定的初始波分组的动量空间中进行数字地解决TDFE，采用了在本地基函数方面的有限元型分子，以便将TDFE转换为一组一定的一阶微分方程。时间衍生物的中心差分公式用于时间传播步骤。考虑两种形式的TDFE并将三种相同颗粒的效率对称掺入这些方程中。在三体模型上测试了该方法，该模型通常用作基准，以比较三种粒子问题的不同计算方法。与渐近时间在渐近时间的TDFE波浪分组溶液的分析中获得的重排S-基质元素与良好的无关的方法的结果进行了比较。这些结果确定TDFE方法是对三体散射问题的现有计算方法的现有武器的可行和竞争性。

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