High-Precision Calculation of the Dynamic Electric Dipole Polarizability of the ¹¹Be²⁺ Ion

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 ¹¹Be²⁺ 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 ¹¹Be²⁺. The results demonstrate that the energies of states with n≤5 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 (m≤4) 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.