Abstract: Traditional nuclear models can be divided into two categories, namely, the spherical shell model (SM) based on diagonalization and the mean field (MF) method based on the variational principle. The former is considered an exact model within the restricted model space. Space limitations hinder the application of SM in heavy nuclei and highly excited states. The latter is an approximate method, but more versatile in application. However, MF methods usually only study near ground states rather than highly excited states. Furthermore, MF models are not suitable for computing general observables due to not well-defined wavefunctions. Since these traditional methods do not describe highly excited states, statistical concepts (e.g., Shell Model Monte Carlo-SMMC) are introduced into nuclear models.
There is a need for an approach that combines the advantages of all the above methods. This novel shell model, designed for arbitrarily heavy systems, starts from a deformed MF solution, transforms the basis states from the intrinsic to the laboratory frame through angular–momentum-projection, builds the configurations in the projected space, and then performs shell-model diagonalization in the laboratory frame like SM. The obtained states are eigenstates of spin and parity, and the well-defined wavefunctions can be used to calculate any observables. With new breakthroughs in many-body calculations, shell-model calculations for highly excited states are now achieved through the Projected Shell Model (PSM).
This talk introduces PSM with recent examples in application and discusses potential future applications. With deformed heavy nuclei as examples, we demonstrate how eigenvalue problems, H |Ψ> = E |Ψ>, can be solved to obtain microscopic nuclear level density (NLD) and g strengths. Attractive properties in the calculation are that our NLDs are presented with precise spin-distribution and dipole g strengths can distinguish E1 and M1. Excited scissors states are included in the calculation. We discuss how the scissors M1 resonances and the low-energy enhancements (LEE) in magnetic dipole transitions naturally appear in our calculation. Electron-capture rates, Gamow-Teller and first-forbidden transitions of b decay for highly excited states are discussed with calculated examples.