Exponential increase of energy level density in atoms: Th and Th II

We present analytical estimates and numerical calculations showing that the energy level density in open-shell atoms increases exponentially with increase of excitation energy. As an example, we use the relativistic Hartree-Fock and configuration interaction methods to calculate the density of states of Th and Th II. The result is used to estimate the effect of electrons on the nuclear transition which is considered for the use in a nuclear clock.