As a strongly interacting finite-size quantum many-body system, the atomic nucleus provides a captivating arena for studying a multitude of phenomena. We explore applications of the shell model Monte Carlo (SMMC) method, a powerful approach to investigate heavy nuclei (A~150) where direct diagonalization is infeasible due to the rapid growth of the model space. The SMMC enables the use of standard Monte Carlo techniques to calculate ground state, statistical, and collective properties of nuclei. In this work, we refine a recently developed method for estimating low-lying excitation energies. This method is based on the imaginary time correlation matrix (ITCM) of one-body densities, and we validate it by comparing results with exact diagonalization in a light nucleus.
Next, we address the challenge of applying the ITCM method to heavy nuclei, focusing on the choice of a suitable residual interaction to reproduce certain experimental quantities. The Hartree-Fock-Bogoliubov (HFB) approximation and the Quasiparticle Random Phase approximation (QRPA) are employed to estimate key observables, guiding the selection of the interaction. The procedure is then applied to two chains of even-even lanthanide isotopes, illustrating the method in heavy nuclei. We successfully reproduce several low-lying excitation energies for each spin and parity, observing the crossover from vibrational to rotational collectivity in these isotope chains via its spectral signatures. This work highlights the versatility and potential of the SMMC method as a probe for studying nuclear spectra microscopically in heavy nuclei.
Thesis Advisor: Yoram Alhassid (yoram.alhassid@yale.edu)
Committee: Nir Navon, Alexis Mercenne, Douglas Stone