  The microscopic description of collectivity in heavy nuclei in the framework
of the configuration-interaction shell model has been a major challenge. The
size of the model space required for the description of heavy nuclei prohibits
the use of conventional diagonalization methods. We have overcome this
difficulty by using the shell model Monte Carlo (SMMC) method, which can treat
model spaces that are many orders of magnitude larger than those that can be
treated by conventional methods. We identify a thermal observable that can
distinguish between vibrational and rotational collectivity and use it to
describe the crossover from vibrational to rotational collectivity in families
of even-even rare-earth isotopes. We calculate the state densities in these
nuclei and find them to be in close agreement with experimental data. We also
calculate the collective enhancement factors of the corresponding level
densities and find that their decay with excitation energy is correlated with
the pairing and shape phase transitions.
