Magnetic dipole moments as a strong signature for α-clustering in even-even self-conjugate nuclei

We investigate the magnetic dipole moments in even-even self-conjugate nuclei from ${}^{12}$C to ${}^{48}$Cr. For these nuclei, the measured gyromagnetic factors of excited states turn out to assume the same value of g ≈ +0.5 within statistical errors. This peculiar feature can be interpreted on the basis of collective excitations of α-clusters. Analogously, the behaviour of the same observable is studied for all isotopes obtained by adding one or two neutrons to the considered self-conjugate nuclei. It is found that for the N = Z + 1 isotopes the α-cluster structure hardly contributes to the observed negative g- factor value, corroborating molecular α-cluster models. The addition of a further neutron, however, restores the original α-cluster g-factors, except for the semi-magic isotopes, in which the deviations from g ≈ +0.5 can be associated with the relevant shell closures. Secondly, we analyze the same observable in the framework of a macroscopic α-cluster model on a finite lattice of side length L. We focus on the discretization effects induced in the magnetic dipole moments of the 2${}_1^{+}$ and the 3${}_1^{-}$ states of ${}^{12}$C at different values of the lattice spacing a.