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作为典型的单中子晕核，$^{11}$Be在原子及核物理研究中具有独特的意义.本文针对类氦$^{11}$Be$^{2+}$离子，采用相对论组态相互作用方法，高精度计算了主量子数最高达$n=8$的$n\,^{3}\!S_1$和$n\,^{3}\!P_{0,1,2}$态的能量与波函数.通过将有限核质量修正算符直接引入Dirac-Coulomb-Breit哈密顿量，使计算能够同时考虑相对论效应和质量相关修正.基于计算的高精度能量与波函数，本文进一步确定了$k\,^3\!S_1\rightarrow m\,^3\!P_{0,1,2}$($k\leq 5$,$m\leq 8$)电偶极跃迁的振子强度，精度达3到6位有效数字.此外，利用态求和法计算了$n'\,^3\!S_1$($n'\leq 5$)态在宽光子频率范围内的动力学电偶极极化率，在远离共振位置处结果最高可达$10^{-6}$精度水平.上述高精度计算结果为$^{11}$Be$^{2+}$离子在高精度测量中涉及的斯塔克频移评估以及光与物质相互作用的模拟等方面提供了重要的理论依据和关键输入参数.As a typical one-neutron halo nucleus, $^{11}$Be holds unique significance in atomic and nuclear physics research. The nucleus comprises a tightly bound $^{10}$Be core and a loosely bound valence neutron, forming an exotic nuclear configuration that exhibits remarkable differences in both magnetic and charge radii compared to conventional nuclei, thereby establishing a unique platform for investigating nuclear-electron interactions. This study focuses on the helium-like $^{11}$Be$^{2+}$ ion, employing the relativistic configuration interaction (RCI) method combined with high-order $B$-spline basis functions to systematically calculate the energies and wavefunctions of the $n\,^{3}\!S_1$ and $n\,^{3}\!P_{0,1,2}$ states up to principal quantum number $n=8$. By directly incorporating the nuclear mass shift operator $H_M$ into the Dirac-Coulomb-Breit (DCB) Hamiltonian, this work achieves a comprehensive treatment of relativistic effects, Breit interactions, and nuclear mass corrections for $^{11}$Be$^{2+}$. The results demonstrate that the energies of states with $n\leq5$ converge to eight significant digits, showing excellent agreement with existing NRQED values, such as $-9.298\,711\,91(5)$ a.u. for the $2\,^{3}\!S_1$ state. The nuclear mass corrections are on the order of $10^{-4}$ a.u. and decrease with increasing principal quantum number.
Using the high-precision wavefunctions, the electric dipole oscillator strengths for $k\,^3\!S_1 \rightarrow m\,^3\!P_{0,1,2}$ transitions ($k \leq 5$, $m \leq 8$) were determined, with results for low-lying excited states ($m\leq4$) accurate to six significant digits, providing reliable data for evaluating transition probabilities and radiative lifetimes. Furthermore, the dynamic electric dipole polarizabilities of the $n'\,^3\!S_1$ ($n' \leq 5$) states were calculated via the sum-over-states method. The static polarizabilities exhibit a significant increase with principal quantum number. For the $J=1$ state, the difference in polarizability between the magnetic sublevels $M_J=0$ and $M_J=\pm1$ is three times the tensor polarizability. In the calculation of dynamic polarizabilities, the precision reaches $10^{-6}$ in non-resonant regions, whereas achieving the same accuracy near resonance requires higher energy precision. These high-precision computational results provide crucial theoretical foundations and key input parameters for evaluating Stark shifts in high-precision measurements, simulating light-matter interactions, and investigating single-neutron halo nuclear structures. -
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