Theoretical study of the experimentally important states of dysprosium

Configuration interaction method is used to calculate transition amplitudes and other properties of the low states of dysprosium which are used in cooling and in study of the time variation of the fine structure constant and violation of fundamental symmetries. The branching ratio for the cooling state to decay to states other than ground state is found to be smaller than $10^{-4}$. The matrix element of the weak interaction between degenerate states at $E=19797.96$ cm$^{-1}$ is about 2 Hz which is consistent with the experimental limit $|H_W| = |2.3 \pm 2.9({\rm statistical}) \pm 0.7({\rm systematic})|$ Hz [A. T. Nguyen, D. Budker, D. DeMille, and M. Zolotorev, Phys. Rev. A {\bf 56}, 3453 (1997)] and points to feasibility of its experimental measurement. Applications include search for physics beyond the standard model using the PNC isotopic chain approach.