Sohan Vartak successfully defends thesis, “Nuclear Spectroscopy of Heavy Nuclei in the Shell Model Monte Carlo Method”

September 12, 2023

On September 6, 2023, Sohan Vartak successfully defended the thesis “Nuclear Spectroscopy of Heavy Nuclei in the Shell Model Monte Carlo Method” (advisor: Yoram Alhassid).

Vartak explained, “The atomic nucleus can be studied at a variety of scales, and my work focuses on a microscopic picture in terms of protons and neutrons. Within this framework, it is a challenge to describe collective excitations of nuclei such as rotations and vibrations, which involve many nucleons moving together. The signatures of these types of collectivity are expressed in the excitation spectra of nuclei. My research has focused on exploring a specific microscopic model (the configuration-interaction shell model) and its ability to describe these collective excitations. To this end, I have applied the shell model Monte Carlo (SMMC) method to calculate excitation energies in several nuclei. These excitation energies are encoded in a generalized eigenvalue problem obeyed by the imaginary-time correlation matrix (ITCM), which describes density-density correlations in the nucleus. I successfully used the SMMC method to calculate the ITCM and extract excitation energies in several samarium and neodymium isotopes. We found that the excitation spectra from the ITCM display clear signatures of the crossover from vibrational to rotational collectivity in two chains of lanthanide isotopes, providing the first direct microscopic evidence of this crossover in SMMC.”

Vartak will join the Amsterdam University of Applied Sciences as an Educational Officer.

Abstract: 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.