*2.3. Microscopic Approaches*

A recent breakthrough in the construction of the *NN* interaction from effective field theories and advances in nuclear many-body methods led to the appearance of the first semi-microscopic and fully microscopic effective charge-dependent Hamiltonians. In particular, large-scale calculations for proton-rich nuclei in the extended *sdf*7/2 *p*3/2 and *pfg*9/2 model spaces with effective Hamiltonians, derived within many-body perturbation theory from *χ*EFT *NN*+3*N* interactions, have been reported in Ref. [30].

Later on, valence space Hamiltonians were constructed within the IMSRG approach [35] based on two forces obtained within *χ*EFT. The author tested the ability of their fully ab initio methods to reproduce the experimental IMME *b* and *c* coefficients for a large selection of nuclei of interest for superallowed *β*-decay applications with *A* between 10 and 74. Their conclusion is that although the major trend comes out correctly, their results are interaction-dependent and not precise enough to get the fine details.

Numerous modern theoretical investigations of nuclear properties are performed nowadays within ab initio approaches using charge-dependent realistic interactions (for example, those from *χ*EFT). We believe that specific issues of isospin-symmetry breaking will definitely be addressed in forthcoming studies.

## **3. Structure and Decay of Neutron-Deficient Nuclei**

Development of charge-dependent Hamiltonians has its ultimate goal of providing an accurate description of nuclei along the *N* = *Z* line and proton-rich nuclei, making it possible to describe the signatures of isospin-symmetry breaking. This Section gives examples of how theoretical IMME coefficients can serve to predict nuclear masses and excited states in mirror nuclei, and it summarizes the progress in the description of isospinforbidden transitions. The latter provide important tests of isospin mixing in nuclear wave functions to validate theoretical models.
