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Free, publicly-accessible full text available February 13, 2026
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We report high-accuracy calculations of the ground and the lowest eight excited states of the two stable isotopes of the boron atom, and , as well as of the boron atom with an infinite nuclear mass . The nonrelativistic wave function of each of the states is generated in an independent variational calculation by expanding it in terms of a large number, , of all-electron explicitly correlated Gaussian (ECG) functions whose nonlinear parameters are extensively optimized with a procedure that employs analytic energy gradient determined with respect to these parameters. These highly accurate wave functions are used to compute the fine-structure splittings using the first order of the perturbation theory , where is the fine-structure constant, which are then corrected for the electron magnetic moment anomaly . As the nonrelativistic Hamiltonian explicitly depends on the mass of the nucleus, the recoil corrections up to the order of are automatically accounted for in the fine-structure calculations. Furthermore, the off-diagonal corrections to the fine structure are estimated using the multireference methods based on one-electron Gaussian orbitals. The results obtained in this paper are considerably more accurate than those available in the literature. Moreover, we report accurate splittings for a number of excited states, for which there have been no reliable experimental or theoretical data at all. The calculated values presented in this paper may serve as a valuable guide for future experimental measurements of the fine structure of the boron atom. As the fine structure of an atom provides a spectral signature that can facilitate atom's detection, our data can also aid the search for trace amounts of boron in the interstellar medium. Published by the American Physical Society2024more » « lessFree, publicly-accessible full text available December 1, 2025
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