Hyperspherical calculations of ultralow-energy collisions in Coulomb three-body systems
Hyperspherical calculations of ultralow-energy collisions in Coulomb three-body systems
复制标题
库仑三体系统超低能碰撞的超球面计算
DOI：
10.1103/physreva.92.032713
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
and T. Morishita
中科院分区：
文献类型：
--
作者：
Y. Zhou;S. Watanabe;O. I. Tolstikhin;and T. Morishita
给出了超球椭圆坐标系下库仑三体系统超低能碰撞的量子力学计算。结合矩阵传播技术，采用慢变量离散化方法处理超半径和超角变量之间的非绝热耦合问题。对于散射态的计算，采用Gailitis方法的二维匹配程序[M]。盖利斯，J.物理学家。B 9,843 (1976) jpama40022-370010.1088/0022-3700/9/5/027；C. Noble和R. Nesbet, Comput。理论物理。实现了内部波函数与渐近波函数之间边界条件的确定[j] .文献33,399 (1984)CPHCBZ0010-465510.1016/0010-4655(84)90145-0。该方法被证明是非常有效的，并给出了非常准确的结果。利用这种方法，我们精确地计算了质量比变化几个数量级的库仑三体系统的散射相移和散射长度。在一定的质量比下，我们观察到散射长度的跳跃和两次跳跃之间的单调减小。根据Levinson定理[N]，这些与最高束缚态的结合能密切相关。K.莱文森，丹。Vidensk。Selsk。垫,财政年度。医学杂志，25,9（1949）。我们的计算提供了从库仑三体系统的质量比变化的散射长度的一个全面的视角。
Quantum mechanical calculations of ultralow-energy collision of Coulomb three-body systems in the hyperspherical elliptic coordinates are presented. The nonadiabatic coupling between the hyperradius and hyperangular variables is treated with the slow-variable discretization method in combination with the-matrix propagation technique. For scattering state calculations, the two-dimensional matching procedure using Gailitis's method [M. Gailitis, J. Phys. B 9, 843 (1976)JPAMA40022-370010.1088/0022-3700/9/5/027; C. Noble and R. Nesbet, Comput. Phys. Commun. 33, 399 (1984)CPHCBZ0010-465510.1016/0010-4655(84)90145-0] is implemented to determine the boundary conditions between the internal and the asymptotic wave functions. This method is proved to be very efficient and gives very accurate results. Taking advantage of this method, we accurately calculate the scattering phase shifts and the scattering lengths of Coulomb three-body systems with mass ratio varying over several orders of magnitudes. We observed jumps of the scattering length fromtoat certain mass ratios and monotonic decreases between two jumps. These are closely related to the binding energy of the highest bound state through Levinson's theorem [N. Levinson, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 25, 9 (1949)]. Our calculations provide a comprehensive perspective to the scattering length from the variation of mass ratio of Coulomb three-body systems.