Dynamical symmetry of isobaric analog 0+ states in medium mass nuclei

An algebraic $\mathit{s}\mathit{p}(4)$ shell model is introduced to achieve a deeper understanding and interpretation of the properties of pairing-governed ${0}^{+}$ states in medium mass atomic nuclei. The theory, which embodies the simplicity of a dynamical symmetry approach to nuclear structure, is shown to reproduce the excitation spectra and fine structure effects driven by proton-neutron interactions and isovector pairing correlations across a broad range of nuclei.