On May 21, 2021 **Paul Fanto** successfully defended the thesis: “Statistical properties of nuclei: beyond the mean-field approximation” (Thesis Advisor: Yoram Alhassid).

Fanto explained “The reaction rates of compound-nucleus reactions are important for our understanding of nuclear astrophysics and nuclear technology. Theoretical nuclear physicists predict these reaction rates using a framework known as the statistical model of compound-nucleus reactions. The applicability and accuracy of this model depend on two key ideas: (i) that the compound nucleus can be modeled with a random matrix; and (ii) that we can provide as input to the model accurate estimates of certain average nuclear quantities, known as statistical properties of nuclei. My thesis research addressed questions related to both of these ideas. I developed random-matrix models of compound-nucleus reactions to investigate recent experimental results. I also developed a novel application of a theoretical method–the static-path plus random-phase approximation (SPA+RPA)–to calculate nuclear state densities in heavy nuclei, which are important inputs to statistical reaction codes. We found that the SPA+RPA provided an excellent description of the state densities of heavy samarium isotopes.”

Fanto will be joining the System Evaluation Division at the Institute for Defense Analyses as a research staff member.

**Thesis Abstract**: The statistical model of compound-nucleus reactions has important applications in fundamental nuclear science, nuclear astrophysics, and nuclear technology. This model relies on two theoretical areas: (i) statistical reaction theory, which describes the compound nucleus with the Gaussian orthogonal ensemble (GOE) of random-matrix theory; and (ii) statistical properties of nuclei, i.e., nuclear structure observables that determine statistical-model predictions of reaction rates.

The GOE statistical theory predicts that the partial widths of compound-nucleus resonances follow the Porter-Thomas distribution (PTD) and that total $\gamma$-decay widths have a narrow distribution. However, recent experiments measured width distributions that were broader than statistical-model predictions. We study these results with resonance-reaction models based on the GOE.

Nuclear level densities are important statistical properties of nuclei and inputs to the statistical model. Mean-field methods are widely used to calculate level densities microscopically but neglect important correlations. We introduce two novel methods for symmetry projection after variation in the finite-temperature mean-field approximation and calculate nuclear state densities with exact particle-number projection. Moreover, we calculate state densities in the configuration-interaction shell model framework using the static-path plus random-phase approximation (SPA+RPA). The SPA+RPA includes static fluctuations and small-amplitude time-dependent quantal fluctuations beyond the mean field. We find that the SPA+RPA state densities agree with exact shell model Monte Carlo (SMMC) state densities and improve significantly over mean-field state densities in heavy lanthanide nuclei.