The predictive power of the interacting shell model in describing properties of nuclei is restricted by the limitations of conventional diagonalization techniques. The shell model Monte Carlo (SMMC) method allows the calculation of thermal properties in very large model spaces, much beyond what is possible with exact diagonalization. In particular, the SMMC has become the state-of-the-art method for the calculation of statistical properties of nuclei.

The total state density that is calculated in SMMC includes the magnetic degeneracy of nuclear levels. On the other hand, the quantity that is usually measured experimentally is the level density, in which each level is counted once irrespective of its spin. We present a method to calculate level densities in SMMC and apply it to mid-mass and heavy nuclei. In particular, we present the first calculation of densities for odd-mass nuclei, circumventing a sign problem that originates in the projection on odd number of particles. We find good agreement with various experimental results.

We also introduce and validate a method to calculate low-lying excitation energies, for the first systematic calculation of spectroscopic properties within SMMC. The method is based on the imaginary time-dependent correlation matrix (ITCM) of the one-body densities. We successfully reproduce the first few low-lying excitation energies for each spin and parity in a light nucleus, for which exact diagonalization is possible.