¹¹Be, as a typical one-neutron halo nucleus, is of unique significance in studying atomic and nuclear physics. The nucleus comprises a tightly bound ¹⁰Be 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 ¹¹Be²⁺ ion and systematically calculate the energies and wavefunctions of the n^3S_1 and n^3\mathrmP_0,1,2 states up to principal quantum number n=8 by employing the relativistic configuration interaction (RCI) method combined with high-order B-spline basis functions. By directly incorporating the nuclear mass shift operator H_\mathrmM into the Dirac-Coulomb-Breit (DCB) Hamiltonian, we comprehensively investigate the relativistic effects, Breit interactions, and nuclear mass corrections for ¹¹Be²⁺. The results demonstrate that the energies of states with n\leqslant 5 converge to eight significant digits, showing excellent agreement with existing NRQED values, such as -9.29871191(5) a.u. for the ^3\mathrmS_1 state. The nuclear mass corrections are on the order of 10^–4 a.u. and decrease with principal quantum number increasing.

By using the high-precision wavefunctions, the electric dipole oscillator strengths for k^3\mathrmS_1 \rightarrow m^3\mathrmP_0,1,2 transitions (k \leqslant 5, m \leqslant 8) are determined, resulting in low-lying excited states (m\leqslant4) accurate to six significant digits, thereby providing reliable data for evaluating transition probabilities and radiative lifetimes. Furthermore, the dynamic electric dipole polarizabilities of the n'^3\mathrmS_1 (n' \leqslant 5) states are calculated using the sum-over-states method. The static polarizabilities exhibit a significant increase with principal quantum number increasing. 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.