The proxy-SU(3) symmetry predicts, in a parameter-free way, based only on the Pauli principle and the short-range nature of the nucleon–nucleon interaction, non-vanishing values of the collective variable γ almost everywhere across the nuclear chart. Substantial triaxiality with γ between 15° and 45° is proved to be expected along horizontal and vertical stripes on the nuclear chart, covering the nucleon numbers 22–26, 34–48, 74–80, 116–124, 172–182. Empirical support for these stripes is found by collecting all even–even nuclei for which the first two excited 2⁺ states are known, along with the B(E2)s connecting them, as well as the second 2⁺ state to the ground state. The stripes are related to regions in which oblate SU(3) irreducible representations appear, bearing similarity to the appearance of triaxiality within the SU(3)* dynamical symmetry of the interacting boson model-2. Detailed comparisons of the proxy-SU(3) predictions to the data and to predictions by state-of-the-art Monte Carlo shell model calculations for deformed N = 94, 96, 98 isotones in the rare earth region show good overall agreement, with the exception of Z = 70 and N = 94, which correspond to fully symmetric proxy-SU(3) irreps, suggesting that the latter are an artifact of the method which can be amended by considering the influence of the neighboring irreps.

We employed the isobar model for investigating the $K^{+}\mathrm{\Lambda }$ photoproduction process. We paid special attention to the recent CLAS polarization data and enhanced the ${\chi }^2$ minimization by adding a penalty term. Without changing the set of included resonances used by the model, this technique known as Ridge regression leads to reduced couplings that in previous studies acquired unreasonably large values. As a result, we have arrived at a much more robust model with hyperon couplings which are reduced to more physical values. This model serves us to extract valuable information on the background to the $K^{+}\mathrm{\Lambda }$ photoproduction and particularly on the role of various hyperon resonances. The set of the nucleon resonances is the same with respect to previous fits but their role may have changed due to different couplings which they acquire in the present fit.

The proxy-SU(3) symmetry predicts, in a parameter-free way, the collective deformation variables $\beta$ and $\gamma$ in even–even atomic nuclei away from closed shells based on the highest weight irreducible representations (irreps) of SU(3) in the relevant proton and neutron shells, which are the most symmetric irreps allowed by the Pauli principle and the short-range nature of the nucleon–nucleon interactions. The special cases in which the use of the next-highest-weight irrep of SU(3) becomes necessary are pointed out, and numerical results are given for several regions of the nuclear chart, which can be used as input for irrep-mixing calculations.

The electroproduction of selected $p$- and $sd$-shell hypernuclei was studied within a many-body approach using realistic interactions between the constituent baryons. The cross sections were computed in the distorted-wave impulse approximation using two elementary amplitudes for the electroproduction of the $\mathrm{\Lambda }$ hyperon. The structure of the hypernuclei was investigated within the framework of the self-consistent $\mathrm{\Lambda }$-nucleon Tamm-Dancoff approach and its extension known as the $\mathrm{\Lambda }$-nucleon equation of motion phonon method. Use was made of the ${\mathrm{NNLO}}_{\mathrm{sat}}$ chiral potential plus the effective Nijmegen-F $YN$ interaction. The method was first implemented on light nuclei for studying the available experimental data and establishing a relation to other approaches. After this proof test, it was adopted for predicting the electroproduction cross section of the hypernuclei ${}_{\mathrm{\Lambda }}{}^{40}\mathrm{K}$ and ${}_{\mathrm{\Lambda }}{}^{48}\mathrm{K}$ in view of the E12-15-008 experiment in preparation at JLab. On the grounds of these predictions, appreciable effects on the spectra are expected to be induced by the $YN$ interaction.

Triaxial shapes in even–even nuclei have been considered since the early days of the nuclear collective model. Although many theoretical approaches have been used over the years for their description, no effort appears to have been made for grouping them together and identifying regions on the nuclear chart where the appearance of triaxiality might be favored. In addition, over the last few years, discussion has started on the appearance of small triaxiality in nuclei considered so far as purely axial rotors. In the present work, we collect the predictions made by various theoretical approaches and show that pronounced triaxiality appears to be favored within specific stripes on the nuclear chart, with low triaxiality being present in the regions between these stripes, in agreement with parameter-free predictions made by the proxy-SU(3) approximation to the shell model, based on the Pauli principle and the short-range nature of the nucleon–nucleon interaction. The robustness of triaxiality within these stripes is supported by global calculations made in the framework of the Finite-Range Droplet Model (FRDM), which is based on completely different assumptions and possesses parameters fitted in order to reproduce fundamental nuclear properties.