Isotope shifts of the three lowest 1S states of the B+ ion calculated with a finite-nuclear-mass approach and with relativistic and quantum electrodynamics corrections

Abstract

We present very accurate quantum mechanical calculations of the three lowest S-states 1s22s2 1S0 , 1s22p2 1S0 , and 1s22s3s 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 thecenter-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 2 relativistic corrections is the fine structure constant; =1/c, where c is the speed of light and the 3 quantum electrodynamics QED correction. We also estimated the 4 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