Isotope shifts of the three lowest S1 states of the B+ ion calculated with a finite-nuclear-mass approach and with relativistic and quantum electrodynamics corrections

We present very accurate quantum mechanical calculations of the three lowest S -states [1 s² 2 s² (¹S₀), 1 s² 2 p² (¹S ₀), and 1 s₂ 2s3s (¹S0)] of the two stable isotopes of the boron ion, ¹⁰B⁺ and ¹¹B⁺. At the nonrelativistic level the calculations have been performed with the Hamiltonian that explicitly includes the finite mass of the nucleus as it was obtained by a rigorous separation of the center-of-mass motion from the laboratory frame Hamiltonian. The spatial part of the nonrelativistic wave function for each state was expanded in terms of 10 000 all-electron explicitly correlated Gaussian functions. The nonlinear parameters of the Gaussians were variationally optimized using a procedure involving the analytical energy gradient determined with respect to the nonlinear parameters. The nonrelativistic wave functions of the three states were subsequently used to calculate the leading α² relativistic corrections (α is the fine structure constant; α=1/c, where c is the speed of light) and the α³ quantum electrodynamics (QED) correction. We also estimated the α⁴ QED correction by calculating its dominant component. A comparison of the experimental transition frequencies with the frequencies obtained based on the energies calculated in this work shows an excellent agreement. The discrepancy is smaller than 0.4 cm-1.