Spin-orbit coupling rule in bound fermions systems

Spin-orbit coupling characterizes quantum systems such as atoms, nuclei, hypernuclei, quarkonia, etc., and is essential for understanding their spectroscopic properties. Depending on the system, the effect of spin-orbit coupling on shell structure is large in nuclei, small in quarkonia, perturbative in atoms. In the standard non-relativistic reduction of the single-particle Dirac equation, we derive a universal rule for the relative magnitude of the spin-orbit effect that applies to very different quantum systems, regardless of whether the spin-orbit coupling originates from the strong or electromagnetic interaction. It is shown that in nuclei the near equality of the mass of the nucleon and the difference between the large repulsive and attractive potentials explains the fact that spin-orbit splittings are comparable to the energy spacing between major shells. For a specific ratio between the particle mass and the effective potential whose gradient determines the spin-orbit force, we predict the occurrence of giant spin-orbit energy splittings that dominate the single-particle excitation spectrum.

Microscopic evaluation of the hypernuclear chart with $Lambda$-hyperons

A large number of hypernuclei, where a considerable fraction of nucleons is replaced by strange baryons, and even pure hyperonic species are expected to be bound. Though, the hypernuclear landscape remains largely unknown because of scarce constraints on the $NY$ and $YY$ interactions. We want to estimate the number of potentially bound hypernuclei. In order to evaluate realistic error bars within the theoretical uncertainties associated to the spherical mean-field approach, and the present information from already synthetized hypernuclei on the $N-Y$ and $Y-Y$ channels, we limit ourselves to purely $Lambda$-hypernuclei, to magic numbers of $Lambda$s (for Z $leq$ 120 and $Lambda leq$70), and to even-even-even systems. We consider a density functional approach adjusted to microscopic Bruckner-Hartree-Fock calculations, where the $LambdaLambda$ term is corrected in a phenomenological way, to reproduce present experimental constraints. The number of bound even-even-even $Lambda$-hypernuclei is estimated to 491680 $pm$ 34400. This relatively low uncertainty is due to the fact that the well constrained low density and highly unconstrained high density behavior of the energy functional turn out to be largely decoupled. Results in $Lambda$-hypernuclei appear to be almost independent of the choice for the high-density part of the $LambdaLambda$ interaction. The location of the $Lambda$-hyperdriplines is also evaluated. Significant deviations from Iron-Nickel elements can be found for $Lambda$-hypernuclei with the largest binding energy per baryon. Proton, neutron and $Lambda$-hyperon magicity evolution and triple magic $Lambda$-hypernuclei are studied. Possible bubbles and haloes effect in $Lambda$-hypernuclei are also discussed.

Density Functional Theory studies of cluster states in nuclei

The framework of nuclear energy density functionals is applied to a study of the formation and evolution of cluster states in nuclei. The relativistic functional DD-ME2 is used in triaxial and reflection-asymmetric relativistic Hartree-Bogoliubov calculations of relatively light $N = Z$ and neutron-rich nuclei. The role of deformation and degeneracy of single-nucleon states in the formation of clusters is analysed, and interesting cluster structures are predicted in excited configurations of Be, C, O, Ne, Mg, Si, S, Ar and Ca $N = Z$ nuclei. Cluster phenomena in neutron-rich nuclei are discussed, and it is shown that in neutron-rich Be and C nuclei cluster states occur as a result of molecular bonding of $alpha$-particles by the excess neutrons, and also that proton covalent bonding can occur in $^{10}$C.

Localization and clustering in the nuclear Fermi liquid

Using the framework of nuclear energy density functionals we examine the conditions for single-nucleon localization and formation of cluster structures in finite nuclei. We propose to characterize localization by the ratio of the dispersion of single-nucleon wave functions to the average inter-nucleon distance. This parameter generally increases with mass and describes the gradual transition from a hybrid phase in light nuclei, characterized by the spatial localization of individual nucleon states that leads to the formation of cluster structures, toward the Fermi liquid phase in heavier nuclei. Values of the localization parameter that correspond to a crystal phase cannot occur in finite nuclei. Typical length and energy scales in nuclei allow the formation of liquid drops, clusters, and halo structures.

Bubbles in $^{34}$Si and $^{22}$O?

Bubble nuclei are characterized by a depletion of their central density. Their existence is examined within three different theoretical frameworks: the shell model as well as non-relativistic and relativistic microscopic mean-field approaches. We propose $^{34}$Si and $^{22}$O as possible candidates for proton and neutron bubble nuclei, respectively. In the case of $^{22}$O, we observe a significant model dependence, thereby calling into question the bubble structure of $^{22}$O. In contrast, an overall agreement among the models is obtained for $^{34}$Si. Indeed, all models predict a central proton density depletion of about 40%. This result provides strong evidence in favor of a proton bubble in $^{34}$Si.