*Review* **Isospin-Symmetry Breaking within the Nuclear Shell Model: Present Status and Developments**

**Nadezda A. Smirnova**

Laboratoire de Physique des Deux Infinis Bordeaux (LP2IB), Centre National de la Recherche Scientifique, Institut National de Physique Nucléaire et de Physique des Particules (CNRS/IN2P3), Université de Bordeaux, 33175 Gradignan, France; nadezda.smirnova@u-bordeaux.fr

**Abstract:** The paper reviews the recent progress in the description of isospin-symmetry breaking within the nuclear shell model and applications to actual problems related to the structure and decay of exotic neutron-deficient nuclei and nuclei along the *N* = *Z* line, where *N* is the neutron number and *Z* the atomic number. The review recalls the fundamentals of the isospin formalism for two-nucleon and many-nucleon systems, including quantum numbers, the spectrum's structure and selection rules for weak and electromagnetic transitions; and at the end, summarizes experimental signatures of isospin-symmetry breaking effects, which motivated efforts towards the creation of a relevant theoretical framework to describe those phenomena. The main approaches to construct accurate isospin-nonconserving Hamiltonians within the shell model are briefly described and recent advances in the description of the structure and (isospin-forbidden) decay modes of neutron-deficient nuclei are highlighted. The paper reviews major implications of the developed theoretical tools to (i) the fundamental interaction studies on nuclear decays and (ii) the estimation of the rates of nuclear reactions that are important for nuclear astrophysics. The shell model is shown to be one of the most suitable approaches to describing isospin-symmetry breaking in nuclear states at low energies. Further efforts in extending and refining the description to larger model spaces, and in developing first-principle theories to deal with isospin-symmetry breaking in many-nucleon systems, seem to be indispensable steps towards our better understanding of nuclear properties in the precision era.

**Keywords:** nuclear shell model; isospin symmetry and its breaking; structure of neutron-deficient nuclei; superallowed Fermi beta decay; fundamental interactions; astrophysical *rp*-process
