High-precision calculation of dynamic electric dipole polarizability of <inline-formula><tex-math id="M1">\begin{document}$^{11}\mathrm{Be}^{2+}$\end{document}</tex-math></inline-formula> ion

<sec><sup>11</sup>Be, as a typical one-neutron halo nucleus, is of unique significance in studying atomic and nuclear physics. The nucleus comprises a tightly bound <sup>10</sup>Be core and a loosely bound valence neutron, forming an exotic nuclear configuration that is significantly different from traditional nuclear configuration in both magnetic and charge radii, thereby establishing a unique platform for investigating nuclear-electron interactions. In this study, we focus on the helium-like <sup>11</sup>Be<sup>2+</sup> ion and systematically calculate the energies and wavefunctions of the <inline-formula><tex-math id="M10">\begin{document}$n^{3}S_1$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M11">\begin{document}$n^{3}{\mathrm{P}}_{0,1,2}$\end{document}</tex-math></inline-formula> states up to principal quantum number <inline-formula><tex-math id="M12">\begin{document}$n=8$\end{document}</tex-math></inline-formula> by employing the relativistic configuration interaction (RCI) method combined with high-order <i>B</i>-spline basis functions. By directly incorporating the nuclear mass shift operator <inline-formula><tex-math id="M13">\begin{document}$H_{\mathrm{M}}$\end{document}</tex-math></inline-formula> into the Dirac-Coulomb-Breit (DCB) Hamiltonian, we comprehensively investigate the relativistic effects, Breit interactions, and nuclear mass corrections for <sup>11</sup>Be<sup>2+</sup>. The results demonstrate that the energies of states with <inline-formula><tex-math id="M14">\begin{document}$n\leqslant 5$\end{document}</tex-math></inline-formula> converge to eight significant digits, showing excellent agreement with existing NRQED values, such as <inline-formula><tex-math id="M15">\begin{document}$-9.29871191(5)$\end{document}</tex-math></inline-formula> a.u. for the <inline-formula><tex-math id="M16">\begin{document}$^{3}{\mathrm{S}}_1$\end{document}</tex-math></inline-formula> state. The nuclear mass corrections are on the order of 10<sup>–4</sup> a.u. and decrease with principal quantum number increasing.</sec><sec>By using the high-precision wavefunctions, the electric dipole oscillator strengths for <inline-formula><tex-math id="M17">\begin{document}$k^3{\mathrm{S}}_1 \rightarrow m^3{\mathrm{P}}_{0,1,2}$\end{document}</tex-math></inline-formula> transitions (<inline-formula><tex-math id="M18">\begin{document}$k \leqslant 5$\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M19">\begin{document}$m \leqslant 8$\end{document}</tex-math></inline-formula>) are determined, resulting in low-lying excited states (<inline-formula><tex-math id="M20">\begin{document}$m\leqslant4$\end{document}</tex-math></inline-formula>) accurate to six significant digits, thereby providing reliable data for evaluating transition probabilities and radiative lifetimes. Furthermore, the dynamic electric dipole polarizabilities of the <inline-formula><tex-math id="M21">\begin{document}$n'^3{\mathrm{S}}_1$\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M22">\begin{document}$n' \leqslant 5$\end{document}</tex-math></inline-formula>) states are calculated using the sum-over-states method. The static polarizabilities exhibit a significant increase with principal quantum number increasing. For the <inline-formula><tex-math id="M23">\begin{document}$J=1$\end{document}</tex-math></inline-formula> state, the difference in polarizability between the magnetic sublevels <inline-formula><tex-math id="M24">\begin{document}$M_J=0$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M25">\begin{document}$M_J=\pm1$\end{document}</tex-math></inline-formula> is three times the tensor polarizability. In the calculation of dynamic polarizabilities, the precision reaches 10<sup>–6</sup> 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.</sec>