Calculation of energies and hyperfine structure constants of $^{233}$U$^{+}$ and $^{233}$U

With six valence electrons and a very heavy core, uranium represents a major challenge for precision atomic theory even using large-scale computational resources.

We carried out calculations of the energies and magnetic dipole hyperfine-structure constants of the low-lying states of $^{233}$U$^{+}$ and $^{233}$U using two different approaches. The first approach combines configuration interaction (CI) with a method allowing us to include core-valence correlations to all orders of the perturbation theory over residual Coulomb interaction. The second approach is a pure CI method which allows the use of different initial approximations. We present a detailed analysis of all calculated properties and discuss the advantages and disadvantages of each of these methods. We report a preliminary value of the U nuclear magnetic moment and outline the need for further experiments.