Effects of a Single-particle versus a Coulomb interaction in bubble nuclei.*

The detailed investigation of microscopic mechanisms leading to the formation of bubble structures in the nuclei has been performed in the framework of covariant density functional theory. The main emphasis of this study is on the role of single-particle degrees of freedom and Coulomb interaction. In general, the formation of bubbles lowers the Coulomb energy. However, in nuclei, this trend is counteracted by the quantum nature of the single-particle states: only specific single-particle states with specific density profiles can be occupied with increasing proton and neutron numbers. A significant role of the central classically forbidden region at the bottom of the wine bottle potentials in the formation of nuclear bubbles (via primarily the reduction of the densities of the s states at r = 0) has been revealed for the first time. Their formation also depends on the availability of low-l single-particle states for occupation since single-particle densities represent the basic building blocks of total densities. Nucleonic potentials disfavor the occupation of such states in hyperheavy nuclei and this contributes to the formation of bubbles in such nuclei. Existing bubble indicators are strongly affected by single-particle properties and thus they cannot be reliable measures of bulk properties (such as the Coulomb interaction). The additivity rule for densities has been proposed for the first time. It was shown that the differences in the densities of bubble and at-density nuclei follow this rule in the A 40 mass region and in superheavy nuclei with comparable accuracy. This strongly suggests the same mechanism of the formation of a central depression in bubble nuclei of these two mass regions. Nuclear saturation mechanisms and self-consistency effects also affect the formation of bubble structures. The detailed analysis of different aspects of bubble physics strongly suggests that the formation of bubble structures in superheavy nuclei is dominated by single-particle effects. The role of the Coulomb interaction increases in hyperheavy nuclei but even for such systems, we do not nd strong arguments that the formation of bubble structures is dominated by it.