  Neutral uranium (U I) is a very difficult atom for theoretical calculations
due to a large number of valence electrons, six, strong valence-valence and
valence-core correlations, high density of states, and relativistic effects.
Configuration-interaction many-body perturbation theory (CI-MBPT) can treat
efficiently valence-core correlations and relativistic effects, but because the
formalism was developed for Dirac-Hartree-Fock (DHF) starting potential that
does not contain valence electrons, quite large CI space is needed to
compensate for +6 charge of such a potential. Much more efficient is
relativistic configuration-interaction (RCI) approach which uses relatively
accurate starting DHF potential that includes some valence electrons to make
the valence electron Hamiltonian diagonally dominated for some states. Here we
report calculations of U I hyperfine constants of several low-energy states
using the RCI method with the starting potential that includes four f valence
electrons. With this starting potential, it is possible to use the
single-configuration approximation or small basis sets to obtain quite accurate
results for hyperfine structure constants. In fact, by scaling nuclear magnetic
moment, the agreement for 5 levels was within 5\%, and a new magnetic moment
can be recommended 0.43(2). The method can be further developed to include more
extensive data sets to improve accuracy and can be applied to other atoms and
for calculations of other properties, for example, relevant to fundamental
symmetry tests.
