Quantum Choreography of the Nucleus: Rotations, Vibrations, and Emergent Structure

Nuclei are complex many-body quantum systems where interactions of the neutrons and protons via the strong, the weak, and the electromagnetic forces lead to the emergence of simple patterns of energy states that have been described by various theoretical approaches. One of the goals of all the theoretical models is the development of a universal theory that can be applied across the entire chart of nuclides. Significant progress has been made by experiments as well as the increasing sophistication of models, but a universal theory has yet to be established. A recent reviewof nuclei in the Z = 50–82 region of the chart of nuclides has analyzed all the available compiled data from several decades of studies towards a clarification of the low-lying structure of nuclei. Other reviews have reported and explained the emergence of multiple different shapes in nuclei at somewhat higher excitation energies than the ground state. Somehave challenged the interpretation of the first excited K${}^{\pi }=0^{+}$ band as a vibration of ground state. This work attempts to provide a guide to determining the nature of the first excited K${}^{\pi }=0^{+}$ band in nuclei by the combined use of nuclear lifetimes, energy level evolutions, dynamic moments of inertia, and intrinsic quadrupole moments extracted from transition probabilities. The result is that for a subset of the nuclei in this region, the K${}^{\pi }=0^{+}$ band is consistent with the traditional $\beta$-vibration description of an oscillation built on the ground state.