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For $N=Z$ odd-odd nuclei, a three-body model assuming two valence particlesand an inert core can provide an understanding of pairing correlations in theground state and spin-isospin excitations. However, since residual core-nucleoninteractions can have a significant impact on these quantities, the inclusionof core excitations in the model is essential for useful calculation to beperformed. The effect of core excitations must be included in order to gain adetailed understanding of both the ground state and spin-isospin properties ofthese systems. To this end, we include the vibrational excitation of the corenucleus in our model. We solve the three-body core-nucleon-nucleon problemincluding core vibrational states to obtain the nuclear ground state as well asspin-isospin excitations. The spin-isospin excitations are examined from thepoint of view of SU(4) multiplets. By including the effect of core excitation,several experimental quantities of $N=Z$ odd-odd nuclei are better described,and the root mean square distances between proton and neutron and that betweenthe center of mass of proton and neutron and core nucleus increase. Large$B$($M1$) and $B$(GT) observed for $^{18}$F and $^{40}$Ca were explained interms of the SU(4) symmetry. The core nucleus is meaningfully broken by theresidual core-nucleon interactions, and various quantities concerningspin-isospin excitations as well as the ground state become consistent withexperimental data. Including the core excitation in the three-body model isthus important for a more detailed understanding of nuclear structure.

Spin-Isospin Properties of $N=Z$ Odd-Odd Nuclei from a Core+$pn$ Three-Body Model including Core Excitations