Magnetic dipole moments as a strong signature for $$\alpha $$-clustering in even-even self-conjugate nuclei

Abstract

We investigate the magnetic dipole moments in even-even self-conjugate nuclei from $$^{12}$$ 12 C to $$^{48}$$ 48 Cr. For these nuclei, the measured gyromagnetic factors of excited states turn out to assume the same value of $$g \approx + 0.5$$ g ≈ + 0.5 within statistical errors. This peculiar feature can be interpreted on the basis of collective excitations of $$\alpha $$ 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 $$N = Z + 1$$ N = Z + 1 isotopes the $$\alpha $$ α -cluster structure hardly contributes to the observed negative g- factor value, corroborating molecular $$\alpha $$ α -cluster models. The addition of a further neutron, however, restores the original $$\alpha $$ α -cluster g-factors, except for the semi-magic isotopes, in which the deviations from $$g \approx + 0.5$$ g ≈ + 0.5 can be associated with the relevant shell closures. Secondly, we analyze the same observable in the framework of a macroscopic $$\alpha $$ 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 $$2_1^+$$ 2 1 + and the $$3_1^-$$ 3 1 - states of $$^{12}$$ 12 C at different values of the lattice spacing a.

Clusters in light nuclei: history and recent developments

“…An interesting re-investigation on the magnetic dipole moments in excited states of self-conjugate nuclei up to chromium was reported in Ref. [316]. The gyromagnetic factors of excited states obtained from experimental data are g ≈ +0.5, a value in close agreement (within statistical uncertainties) to simple quantum mechanical predictions for macroscopic α cluster model.…”

“…applied physics or cosmic-ray studies) because of its impact on accurate predictions of absolute cross sections in the intermediate to relativistic energy domains. From the experimental point of view, we believe that the suggestion for the occurrence of selection rules in α-transfer reactions due to group symmetry considerations [313] would deserve some further experimental deepening; improvements in the determination of quadrupole electric and dipole magnetic momenta of excited states of self-conjugate nuclei and their neutron-rich isotopes would also be useful to further benchmark cluster model predictions, according to the recent work of [316]. The surprising findings of [318] of broad resonances in a non-self-conjugate reaction system would urge for the measurements of fusion cross sections all along the oxygen isotopic chain, both stable and unstable; it could be also useful to populate the same fused system, 29 Si, with a different entrance channel, in order to have an independent benchmark of the reported results.…”