2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119534A microscopic theory is presented for identifying shape-phase structures and transitions in interacting fermion systems. The method provides a microscopic description for collective shape-phases, and reveals detailed dependence of such shape-phases on microscopic interaction strengths. The theory is generally applicable to fermion systems such as nuclei, quarks, and in particular trapped cold atoms, where shape-phases may be observed and investigated in a controlled manner.4 pages, 6 figuresNuclear Theorytext