Shell Model Monte Carlo Studies of Collectivity in Heavy Nuclei

A microscopic description of the crossover from vibrational to rotational collectivity in heavy nuclei in the configuration-interaction shell model approach is beyond the reach of conventional diagonalization methods due to combinatorial growth of the many-particle model space with the number of valence nucleons and/or valence single-particle orbitals. The shell model Monte Carlo (SMMC) method is viable in such model spaces, and has been successfully applied to calculate thermal and ground-state observables. Recently, a method has been developed that provides access to spectral information encoded in a generalized eigenvalue problem satisfied by imaginary-time response matrices of one-body densities [1]. We have validated the method in an sd-shell nucleus whose excitation energies can be calculated exactly using conventional diagonalization techniques. Application of this method to chains of heavy lanthanide isotopes enables the calculation of a few energy levels for each spin and parity, yielding direct spectral evidence of the crossover from vibrational to rotational collectivity. The generalized eigenvalue problem also encodes information about one-body transition densities, and we discuss extensions of the method to extract this information.