Crossover from vibrational to rotational collectivity in heavy nuclei in the shell-model Monte Carlo approach

Heavy nuclei exhibit a crossover from vibrational to rotational collectivity as the number of neutrons or protons increases from shell closure towards midshell, but the microscopic description of this crossover has been a major challenge. We apply the shell model Monte Carlo approach to families of even-even samarium and neodymium isotopes and identify a microscopic signature of the crossover from vibrational to rotational collectivity in the low-temperature behavior of $<\mathbf{J}^2>_T$, where $\bf J$ is the total spin and $T$ is the temperature. This signature agrees well with its values extracted from experimental data. We also calculate the state densities of these nuclei and find them to be in very good agreement with experimental data. Finally, we define a collective enhancement factor from the ratio of the total state density to the intrinsic state density as calculated in the finite-temperature Hartree-Fock-Bogoliubov approximation. The decay of this enhancement factor with excitation energy is found to correlate with the pairing and shape phase transitions in these nuclei.