双动力学平衡集在相对论原子结构多体问题中的应用
Application of the dual-kinetic-balance sets in the relativistic many-body problem of atomic structure
摘要：
用双动力学平衡（DKB）有限基组方法求解类氢离子的Dirac方程[V.M. Shabaev等人，物理修订信函93，130405（2004）]推广到具有非局部球对称Dirac-Hartree-Fock势的问题。我们使用B样条基集实现DKB方法，并将其性能与Notre Dame（ND）组[W.R. Johnson和J. Sapirstein，Phys. Rev. Lett. 57，1126（1986）]。通过计算Cs原子的能量、超精细积分、$6s_{1/2}-7s_{1/2}$跃迁的宇称非守恒振幅和价电子去除能的二阶多体修正，比较了ND和DKB方法的性能.我们发现，对于一个相当大小的基组的准确性，这两种方法是类似的矩阵元素积累远离核区域。然而，对于由小距离确定的原子性质，DKB方法优于ND方法。此外，我们提出了一种策略，通过选择越来越高的分波逐步减少基函数的数量来优化基组的大小。这种策略利用抑制贡献的高分波典型的多体相关校正。
英文摘要：
The dual-kinetic-balance (DKB) finite basis set method for solving the Dirac equation for hydrogen-like ions [V. M. Shabaev et al., Phys. Rev. Lett. 93, 130405 (2004)] is extended to problems with a non-local spherically-symmetric Dirac-Hartree-Fock potential. We implement the DKB method using B-spline basis sets and compare its performance with the widely-employed approach of Notre Dame (ND) group [W.R. Johnson and J. Sapirstein, Phys. Rev. Lett. 57, 1126 (1986)]. We compare the performance of the ND and DKB methods by computing various properties of Cs atom: energies, hyperfine integrals, the parity-non-conserving amplitude of the $6s_{1/2}-7s_{1/2}$ transition, and the second-order many-body correction to the removal energy of the valence electrons. We find that for a comparable size of the basis set the accuracy of both methods is similar for matrix elements accumulated far from the nuclear region. However, for atomic properties determined by small distances, the DKB method outperforms the ND approach. In addition, we present a strategy for optimizing the size of the basis sets by choosing progressively smaller number of basis functions for increasingly higher partial waves. This strategy exploits suppression of contributions of high partial waves to typical many-body correlation corrections.
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