Simple Patterns in Nuclei

We review state-of-the-art no-core shell model (NCSM) work that exploits symmetries which bare the emergence of simple patterns from Quantum Chromodynamics (QCD)-inspired effective interactions. Our theory of choice for this is the Symplectic Model (SpM) and a recent implementation that includes mixing of configurations of the no-core shell-model type, called NCSpM. The SpM is a fully microscopic theory that respects exact and exploits partial symmetries and hence, can uncover simple patterns hidden within the complexities of nuclei. Making use of the algebraic features of the SpM, the NCSpM complements the NCSM by “vertically extending” a physically relevant subspace into a model space that is needed to fully capture the collectivity of nuclei.