As a typical one-neutron halo nucleus, ^11Be holds unique significance in atomic and nuclear physics research. The nucleus comprises a tightly bound ^10Be 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 ^11Be^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\!S₁ and n\, ^3\!P₀, ₁, ₂ states up to principal quantum number n=8. By directly incorporating the nuclear mass shift operator HM into the Dirac-Coulomb-Breit (DCB) Hamiltonian, this work achieves a comprehensive treatment of relativistic effects, Breit interactions, and nuclear mass corrections for ^11Be^2+. The results demonstrate that the energies of states with n5 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\!S₁ 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\!S₁ m\, ³\!P₀, ₁, ₂ transitions (k 5, m 8) were determined, with results for low-lying excited states (m4) 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\!S₁ (n' 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 MJ=0 and MJ=1 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.
Fang-fei et al. (Wed,) studied this question.