Spin–isospin properties of N=Z odd–odd nuclei from a core+ pn three-body model including core excitations

For N= Z odd–odd nuclei, a three-body model assuming two valence particles and an inert core can provide insight into pairing correlations in the ground state and spin–isospin excitations. However, since residual core–nucleon interactions can have a significant impact, the inclusion of core excitations in the model is essential for a detailed understanding of both the ground state and spin–isospin properties. To qualitatively understand the effect of core excitation on the ground state and spin–isospin excitations of N= Z odd–odd nuclei, we solve the three-body core–nucleon–nucleon problem including core vibrational states described by the random-phase approximation. We pay a particular attention to the magnetic dipole and Gamow–Teller transitions between 0 ⁺ and 1 ⁺ states of N= Z nuclei and discuss it in terms of the SU(4) multiplet. We also discuss the effect of coupling to the core vibration on low energy spectra of even–odd nuclei, the spatial distribution, core contributions to the ground state, and possible uncertainties in the present framework.