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.
A systematic study of the central depletion of proton density has been performed in the isotonic chains of nuclei with neutron numbers $N = 20$ and $28$ using different variants of the relativistic mean-field (RMF) models. These models include either the non-linear contributions from the mesons with the coupling constants being density independent or the non-linearity of the mesonic fields realized through the density dependent coupling strengths. The central depletion in deformed nuclei tends to disappear irrespective of the occupancy of $2s_{1/2}$ state in contrast to the spherical nuclei in…
The natural orbitals and natural occupation numbers of various N = Z, sp and sd shell nuclei are calculated by applying a correlated one-body density matrix. The correlated density matrix has been evaluated by considering central correlations of Jastrow type and an approximation named factor cluster expansion. The correlation effects on the natural orbitals, natural occupation numbers and the Fermi sea depletion are discussed and analysed. In addition, an approximate expression for the correlated one-body density matrix of the nuclear matter has been used for the evaluation of the relative mom…
We briefly review the significance of quantum corrections in the total energy of systems with voids: bubble nuclei, atomic clusters and the inhomogeneous phase of neutron stars.
The existence of bubble nuclei identified by the central depletion in nucleonic density is studied for the conventional magic N (Z) $=$ 8, 20, 28, 40, 50, 82, 126 isotones (isotopes) and recently speculated magic N $=$ 164, 184, 228 superheavy isotones. Many new bubble nuclei are predicted in all regions. Study of density profiles, form factor, single particle levels and depletion fraction (DF) across the periodic chart reveals that the central depletion is correlated to shell structure and occurs due to unoccupancy in s-orbit (2s, 3s, 4s) and inversion of (2s, 1d) and (3s, 1h) states in nucle…
The shape of a nucleus is one of fundamental nuclear properties. We perform a systematic investigation of bubble nuclei that also exhibit shape coexistence in Hf, W, Os, Pt and Hg even-even isotopes using the deformed relativistic Hartree-Bogoliubov theory in continuum. For a systematic study, we first consider nuclear bubble structures and shape coexistence separately. We confirm that deformations and pairing correlations hinder bubble structures by comparing our results with those from relativistic continuum Hartree-Bogoliubov theory that assumes spherical symmetry in nuclei. We then predict…
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 signific…
We calculate the ground state properties of recently synthesized superheavy nuclei starting from $Z$=105-120. The nonrelativistic and relativistic mean field formalisms is used to evaluate the binding energy, charge radius, quadrupole deformation parameter and the density distribution of nucleons. We analyzed the stability of the nuclei based on the binding energy and neutron to proton ratio. We also studied the bubble structure of the nucleus which reveals about the special features of the superheavy nucleus.
It is theoretically and experimentally argued that there may exist bubble or toroid-shaped configurations in some nucleus systems. Based on the nuclear transport model, it is shown that compared with the collision of normal nuclei, there is a depletion of central density of compression with bubble configurations in projectile and target nuclei. This depletion of central compression density may affect some observables in heavy-ion collisions.
We investigate the shell structure of bubble nuclei in simple phenomenological shell models and study their binding energy as a function of the radii and of the number of neutron and protons using Strutinsky's method. Shell effects come about, on the one hand, by the high degeneracy of levels with large angular momentum and, on the other, by the big energy gaps between states with a different number of radial nodes. Shell energies down to -40 MeV are shown to occur for certain magic nuclei. Estimates demonstrate that the calculated shell effects for certain magic numbers of constituents are pr…
In this work, we identify a unique and novel feature of central density depletion in both proton and neutron named as doubly bubble nuclei in 50$\leq$Z(N)$\leq$82 region. The major role of 2d-3s single-particle (s.p.) states in the existence of halo and bubble nuclei is probed. The occupancy in s.p. state 3s$_{1/2}$ leads to the extended neutron density distribution or halo while the unoccupancy results in the central density depletion. By employing the Relativistic Mean-Field (RMF) approach along with NL3* parameter, the separation energies, single-particle energies, pairing energies, proton,…
A unified classification-quantification framework for bubble-like nuclei within the extended quantum molecular dynamics model
Henan Normal University（河南师范大学）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）；Institute of Nuclear Science and Technology, Henan Academy of Sciences（河南省科学院核科学技术的研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委与复旦大学上海理论核物理研究中心）；Shanghai Institute of Applied Physics, Chinese Academy of Sciences（中国科学院上海应用物理研究所）
Temperature dependent relativistic mean-field (RMF) plus BCS approach has been used for the first time to investigate the anti-bubble effect of the temperature and deformation in the light, medium-heavy and superheavy nuclei. Influence of temperature is studied on density distribution, charge form-factor, single particle (s.p.) energies, occupancy, deformation and the depletion fraction (DF). At T $=$ 0, the quenching effect of deformation is predominant. DF is found usually less in oblate deformation than in prolate. DF decreases with increasing prolate deformation even though the 2s-orbit is…
The nonlinear effect of gluon depletion in the collision of large nuclei can be large. It is due to multiple scatterings among comoving partons initiated by primary scattering of partons in the colliding nuclei. The effect can give rise to substantial suppression of $J/ψ$ production in very large nuclei, even if the linear depletion effect is insignificant for the collisions of nuclei of smaller sizes. This mechanism offers a natural explanation of the enhanced suppression in the Pb-Pb data recently observed by NA50.
We investigate the possibility that some nuclei show density distributions with a depletion in the center, a semi-bubble structure, by using a Hartree-Fock plus Bardeen-Cooper-Schrieffer approach. We separately study the proton, neutron and matter distributions in 37 spherical nuclei mainly in the $s - d$ shell region. We found a relation between the semi-bubble structure and the energy splitting of spin-orbit partner single particle levels. The presence of semi-bubble structure reduces this splitting, and we study its consequences on the excitation spectrum of the nuclei under investigation b…
The positioning of a bubble inside a many fermion system does not affect the volume, surface or curvature terms in the liquid drop expansion of the total energy. Besides possible Coulomb effects, the only other contribution to the ground state energy of such a system arises from shell effects. We show that the potential energy surface is a rather shallow function of the displacement of the bubble from the center and in most cases the preferential position of a bubble is off center. Systems with bubbles are expected to have bands of extremely low lying collective states, corresponding to variou…
The occurrence of a bubble, due to an inversion of s$_{1/2}$ state with the state usually located above, is investigated. Proton bubbles in neutron-rich Argon isotopes are optimal candidates. Pairing effects which can play against the bubble formation are evaluated. They cannot prevent bubble formation in very neutron-rich argon isotopes such as $^{68}$Ar. This pleads for a measurement of the charge density of neutron-rich argon isotopes in the forthcoming years, with the advent of electron scattering experiments in next generation exotic beam facilities such as FAIR or RIBF.
We analyze the character of the shell effects/Casimir energy in inhomogeneous fermion systems. We estimate magnitude of the shell effects and discuss their dependence on a number of physical parameters (geometry, fermion density, temperature).
Deformation, halo, and bubble structure: A paradigm shift of exotic phenomena in light to medium mass nuclei
Indian Institute of Technology Roorkee（印度理工学院卢尔基）；RIKEN Nishina Center（理化学研究所仁科加速器中心）；Osaka Metropolitan University（大阪公立大学）；Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP)（南部阳一郎理论与实验物理研究所）；National Centre for Nuclear Research（国家核研究中心）；University of Manchester（曼彻斯特大学）；Akal University（阿卡尔大学）；Research Centre for Nuclear Physics (RCNP)（核物理研究中心）；Osaka University（大阪大学）；Dr. B. R. Ambedkar National Institute of Technology（B.R.安贝德卡尔国立理工学院）
The occurrence of the proton bubble-like structure has been studied within the relativistic Hartree-Fock-Bogoliubov (RHFB) and relativistic Hartree-Bogoliubov (RHB) theories by exploring the bulk properties, the charge density profiles and single proton spectra of argon isotopes and $N = 28$ isotones. It is found that the RHFB calculations with PKA1 effective interaction, which can properly reproduce the charge radii of argon isotopes and the $Z=16$ proton shell nearby, do not support the occurrence of the proton bubble-like structure in argon isotopes due to the prediction of deeper bound pro…
Applying the semi-realistic $NN$ interactions that include realistic tensor force to the Hartree-Fock calculations, we investigate tensor-force effects on the single-particle levels in the Ca isotopes. The semi-realistic interaction successfully describes the experimental difference between $\varepsilon(p1s_{1/2})$ and $\varepsilon(p0d_{3/2})$ (denoted by $\mathitΔ\varepsilon_{13}$) both at $^{40}$Ca and $^{48}$Ca, confirming importance of the tensor force. The tensor force plays a role in the $N$-dependence of $\mathitΔ\varepsilon_{13}$ also in neutron-rich Ca nuclei. While the $p1s_{1/2}$-$p…
We study the property of alpha-aggregates on a soap bubble shape within a microscopic framework, which takes full account of the Pauli principle. Our special attention is payed to the Coulomb energy for such an exotic shapes of nuclei, and we discuss the advantage of alpha-clusters with geometric configurations compared with the uniform density distributions in reducing the repulsive effect. We consider four kinds of configurations of alpha clusters on a soap bubble, which are dual polyhedra composed of a dodecahedron and an icosahedron, octacontahedron and two types of truncated icosahedrons,…
We investigate the shell structure of spherical nuclear bubbles in simple phenomenological shell model potentials. The shell correction energies for doubly magic bubbles may be as large as -40 MeV and probably imply a very long lifetime against spontaneous fission. Beta-stability occurs for ratios of the neutron number N to the proton number Z which differ markable from the beta-stability valley of ordinary compact nuclei. The alpha-decay probability is shown to be very small for proton rich bubbles with a moderately large outer radius. Metastable islands of nuclear bubbles are shown to exist …
Structural properties and the decay modes of the superheavy elements Z $=$ 122, 120, 118 are studied in a microscopic framework. We evaluate the binding energy, one- and two- proton and neutron separation energy, shell correction and density profile of even and odd isotopes of Z $=$ 122, 120, 118 (284 $\leq$ A $\leq$ 352) which show a reasonable match with FRDM results and the available experimental data. Equillibrium shape and deformation of the superheavy region are predicted. We investigate the possible decay modes of this region specifically $α$-decay, spontaneous fission (SF) and the $β$-…
In a decade-and-a-half old experiment, Raabe et al.(Nature 431 (2004) 823), had studied fusion of an incoming beam of halo nucleus $^{6}He$ with the target nucleus $^{238}U$. We extract a new interpretation of the experiment, different from the one that has been inferred so far. We show that their experiment is actually able to discriminate between the structures of the target nucleus (behaving as standard nucleus with density distribution described with canonical RMS radius r = $r_0 A^{\frac{1}{3}}$ with $r_0$ = 1.2 fm), and the {\bf "core"} of the halo nucleus, which surprisingly, does not f…
We employ Relativistic Mean Field (RMF) model with NL3 parametrization to investigate the ground state properties of superheavy nucleus, Z = 124. The nuclei selected (from among complete isotopic series) for detailed investigation show that the nucleon density at the center is very low and therefore, these nuclei can be treated as semi-bubble nuclei. The considerable shell gap appears at neutron numbers N = 172, 184 and 198 showing the magicity corresponding to these numbers. The results are compared with the macro-microscopic Finite Range Droplet Model (FRDM) wherever possible.
Central depression of nucleonic density, i.e., a reduction of density in the nuclear interior, has been attributed to many factors. E.g., bubble structures in superheavy (SH) nuclei are believed to be due to the electrostatic repulsion. In light nuclei, the mechanism has been discussed in terms of shell effects associated with occupations of s-orbits. The objective of this work is to reveal mechanisms behind the formation of central depression in nucleonic densities in light and heavy nuclei. We introduce several measures of the internal nucleonic density. Through the statistical analysis, we …
Background: The density of most nuclei is constant in the central region and is smoothly decreasing at the surface. A depletion in the central part of the nuclear density can have nuclear structure effects leading to the formation of "bubble" nuclei. However, probing the density profile of the nuclear interior is, in general, very challenging. Purpose: The aim of this paper is to investigate the nuclear bubble structure, with nucleon-nucleus scattering, and quantify the effect that has on the nuclear surface profile. Method: We employed high-energy nucleon-nucleus scattering under the aegis of…
A phenomenological method based on the natural orbital representation is applied to construct the ground state one-body density matrix which describes correctly both density and momentum distributions in $^{4}He$, $^{16}O$ and $^{40}Ca$ nuclei. The parameters of the matrix are fixed by a best fit to the experimental density distribution and to the correlated nucleon momentum distribution. The method allows the natural orbitals, the occupation probabilities and the depletion of the Fermi sea to be obtained. Ground-state characteristics of $^{4}He$, $^{16}O$ and $^{40}Ca$ nuclei, such as rms rad…
Collective-flow signatures of bubble nuclei in intermediate-energy projectile fragmentation reactions
Henan Normal University（河南师范大学）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）；Institute of Nuclear Science and Technology, Henan Academy of Sciences（河南省科学院核科学技术的研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委与复旦大学理论物理上海研究中心）；Shanghai Institute of Applied Physics, Chinese Academy of Sciences（中国科学院上海应用物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, nuclear bubble configuration in the hypothetical $^{48}$Si nucleus is studied by proton induced central reaction at an incident beam energy of 0.8 GeV/nucleon. It is found that along the beam direction more energetic protons are emitted with bubble configuration in the target. In the forward angles, compared with the case without bubble configuration, less scattered energetic protons are emitted with bubble configuration in the target. We thus provide a new way to probe the bubble configuration in nuclei.
The main characteristics of the ground and, in particular, the first excited monopole state in the $^{4}$He, $^{16}$O and $^{40}$Ca nuclei are studied within the generator coordinate method using Skyrme-type effective forces and three construction potentials, namely the harmonic-oscillator, the square-well and Woods-Saxon potentials. Calculations of density distributions, radii, nucleon momentum distributions, natural orbitals, occupation numbers and depletions of the Fermi sea, as well as of pair density and momentum distributions are carried out. A comparison of these quantities for both gro…
Recent self-consistent mean-field calculations predict a substantial depletion of the proton density in the interior of 34Si. In the present study, we investigate how correlations beyond the mean field modify this finding. The framework of the calculation is a particle-number and angular-momentum projected Generator Coordinate Method based on Hartree-Fock-Bogoliubov+Lipkin-Nogami states with axial quadrupole deformation. The parametrization SLy4 of the Skyrme energy density functional is used together with a density-dependent pairing energy functional. For the first time, the generator coordin…
A fully systematic study of even and odd isotopes (281 $\leq$ A $\leq$ 380) of Z = 121 superheavy nuclei is presented in theoretical frameworks of Relativistic mean-field plus state dependent BCS approach and Macroscopic-Microscopic approach with triaxially deformed Nilson Strutinsky prescription. The ground state properties namely shell correction, binding energy, two- and one- proton and neutron separation energy, shape, deformation, density profile and the radius are estimated that show strong evidence for magicity in N = 164, 228. Central depletion in the charge density due to large repuls…
We study the structural properties of some nuclei in the region of light mass using simple effective interaction in the frame work of microscopic non relativistic Hartree-Fock and relativistic mean field formalism. For the reaction dynamics, well known Glauber model is used with the conjunctions of the densities obtained from these formalism. We observe good agreement of results by both the formalism in comparison to the experimental values. These two different approaches seems to be equally capable to reproduce the ground state properties of nuclei in this region. A careful study of reaction …
Geometrical structure of matter at subnuclear densities is investigated in the presence of a degenerate gas of neutrinos as encountered in stellar collapse. The crystalline phases with spherical, cylindrical and planar nuclei as well as with spherical and cylindrical nuclear bubbles are considered by using a compressible liquid-drop model. This model allows for uncertainties in the lepton fraction $Y_{\rm L}$ in addition to those in the nuclear surface tension $E_{\rm surf}$ and in the proton chemical potential in bulk neutron matter $μ_{\rm p}^{(0)}$. The phase diagrams obtained at zero tempe…
The possibility that an unconventional depletion in the center of the charge density distribution of certain nuclei occurs due to a purely quantum mechanical effect has attracted theoretical and experimental attention in recent years. We report on ab initio self-consistent Green's function calculations of one of such candidates, $^{34}$Si, together with its Z+2 neighbour $^{36}$S. Binding energies, rms radii and density distributions of the two nuclei as well as low-lying spectroscopy of $^{35}$Si, $^{37}$S, $^{33}$Al and $^{35}$P are discussed. The interpretation of one-nucleon removal and ad…
Screening effects of electrons on inhomogeneous nuclear matter, which includes spherical, slablike, and rodlike nuclei as well as spherical and rodlike nuclear bubbles, are investigated in view of possible application to cold neutron star matter and supernova matter at subnuclear densities. Using a compressible liquid-drop model incorporating uncertainties in the surface tension, we find that the energy change due to the screening effects broadens the density region in which bubbles and nonspherical nuclei appear in the phase diagram delineating the energetically favorable shape of inhomogeneo…
We examine how the properties of inhomogeneous nuclear matter at subnuclear densities depend on the density dependence of the symmetry energy. Using a macroscopic nuclear model we calculate the size and shape of nuclei in neutron star matter at zero temperature in a way dependent on the density dependence of the symmetry energy. We find that for smaller symmetry energy at subnuclear densities, corresponding to larger density symmetry coefficient L, the charge number of nuclei is smaller, and the critical density at which matter with nuclei or bubbles becomes uniform is lower. The decrease in t…
The neutron-rich even-even nuclei $^{26-40}$Mg, $^{28-46}$Si, $^{30-48}$S, and $^{32-56}$Ar are calculated with the RMF model and the phase-shift electron scattering method. Results show that level inversion of the 2$s_{1/2}$ and 1$d_{3/2}$ proton states may occur for the magnesium, silicon, sulphur, and argon isotopes with more neutrons away from the stability line. Calculations show that the variation of the central charge densities for $^{30-48}$S, and $^{32-56}$Ar are very sensitive to the 2$s_{1/2}$ and 1$d_{3/2}$ proton state level inversion, and the level inversion can lead to a large m…
