Statistical properties of nuclei in the static-path plus random-phase approximation

Nuclear level densities and $\gamma$-ray strength functions ($\gamma$SFs) are important inputs to the Hauser-Feshbach theory of compound-nucleus reactions. To calculate these statistical properties, we apply the static-path plus random-phase approximation (SPA+RPA), which includes large-amplitude static fluctuations and small-amplitude quantal fluctuations beyond the mean field. We find excellent agreement between SPA+RPA state densities and exact state densities calculated with the shell model Monte Carlo (SMMC) method in lanthanide nuclei [1]. We also discuss a computational method to extend SPA+RPA calculations to larger model spaces. In addition, we benchmark finite-temperature SPA+RPA $E2$ and $M1$ $\gamma$SFs by comparing them with exact configuration-interaction (CI) shell model and quasiparticle random-phase approximation (QRPA) $\gamma$SFs in $sd$ shell nuclei. We find that the SPA+RPA reproduces qualitative aspects of the exact CI shell model results. We discuss the current limitations of the SPA+RPA for $\gamma$SFs and outline possible extensions of this method. [1] P. Fanto and Y. Alhassid, arXiv:2008.13722.