Skin Thickness Of Heavy Nuclei Research Articles

Optimized chiral N2LO interactions in nuclear matter

We employ modern two- and three-nucleon interactions derived in chiral perturbation theory (ChPT) at next to-next-to leading order (N2LO), to calculate the energy per particle of symmetric nuclear matter and pure neutron matter in the framework of the microscopic Brueckner-Hartree-Fock approach. In particular, we present results concerning two optimized versions at N2LO of chiral potentials ( $ \mathrm{N2LO}_{opt}$ ), fitted to properties of light nuclei. We also employ the recently developed $\mathrm{N2LO}_{sat}$ interaction which has been calculated at the same order of ChPT but fitted in a very different way compared with the $\mathrm{N2LO}_{opt}$ interactions. We find that using these potentials, in general, it is not possible to reproduce all the saturation properties of nuclear matter. In particular the behaviour of the symmetry energy ( $E_{sym}$ predicted by the interactions considered is quite soft. This is shown comparing our results with the empirical constraints on $E_{sym}$ obtained from the data analysis of the excitation energies of isobaric analog states in nuclei and from experimental data of the neutron skin thickness of heavy nuclei. We finally confront our results with similar calculations performed by other research groups using nuclear chiral interactions at various order of ChPT and employing different many-body methods.

Nuclear matter properties from local chiral interactions with Δ isobar intermediate states

Using two-nucleon and three-nucleon interactions derived in the framework of chiral perturbation theory (ChPT) with and without the explicit $\Delta$ isobar contributions, we calculate the energy per particle of symmetric nuclear matter and pure neutron matter in the framework of the microscopic Brueckner-Hartree-Fock approach. In particular, we present for the first time nuclear matter calculations using the new fully local in coordinate-space two-nucleon interaction at the next-to-next-to-next-to-leading-order (N3LO) of ChPT with $\Delta$ isobar intermediate states (N3LO$\Delta$) recently developed by Piarulli et al. [arXiv:1606:06335]. We find that using this N3LO$\Delta$ potential, supplemented with a local N2LO three-nucleon interaction with explicit $\Delta$ isobar degrees of freedom, it is possible to obtain a satisfactory saturation point of symmetric nuclear matter. For this combination of two- and three-nucleon interactions we also calculate the nuclear symmetry energy and we compare our results with the empirical constraints on this quantity obtained using the excitation energies to isobaric analog states in nuclei and using experimental data on the neutron skin thickness of heavy nuclei, finding a very good agreement with these empirical constraints in all the considered nucleonic density range. In addition, we find that the explicit inclusion of $\Delta$ isobars diminishes the strength of the three-nucleon interactions needed the get a good saturation point of symmetric nuclear matter. We also compare the results of our calculations with those obtained by other research groups using chiral nuclear interactions with different many-body methods, finding in many cases a very satisfactory agreement.

Effects of differences between neutron and proton density distributions onα-decay half-lives

The neutron skin of heavy nuclei is one of the hot topics in contemporary nuclear physics. In this article, effects of differences between neutron and proton density distributions on $\ensuremath{\alpha}$ decay are investigated. $\ensuremath{\alpha}$-decay calculations are performed within the generalized density-dependent cluster model, where the $\ensuremath{\alpha}$-core potential is determined in the double-folding model using the neutron and proton density distributions of daughter nuclei. The proton and neutron density distributions, assumed to be of two-parameter Fermi form, are constrained by the experimental nuclear charge radii as well as the neutron skin thickness of heavy nuclei. The resulting distribution of daughter nuclei results in an improved $\ensuremath{\alpha}$-core potential which is important for $\ensuremath{\alpha}$-decay calculations. It is found that the neutron skin thickness plays an important role in reducing the calculated $\ensuremath{\alpha}$-decay half-lives, implying a smaller $\ensuremath{\alpha}$ preformation factor. The calculations with neutron skin thickness show good agreement with the available experimental data for even-even nuclei including the known heaviest nuclei.

Cluster correlations in dilute matter and equation of state

Cluster correlations are an important feature in strongly interacting matter at subsaturation densities. They modify the chemical composition of the system and the thermodynamic properties, which are encoded in the equation of state. The formation and dissolution of clusters can be described in a generalized relativistic density functional approach. Clusters are included as explicit degrees of freedom with medium-dependent properties. They are considered as quasiparticles with scalar and vector self-energies that represent the effective in-medium interaction. Essential ingredients in the self-energies are rearrangement contributions, which guarantee the thermodynamic consistency of the model, and mass shifts of composite particles, which take into account the effects of the Pauli exclusion principle. They cause the dissolution of clusters at high densities. The occurence of α-particle clusters on the surface of heavy nuclei can be considered by adapting the generalized relativistic density functional approach to nuclear structure calculations. A systematic variation of the α-particle abundance and neutron skin thickness with the neutron excess of the nucleus and the strength of the isovector contribution to the effective interaction is observed. The surface a clustering affects the correlation of the neutron skin thickness of heavy nuclei with the density dependence of the symmetry energy, which is relevant for calculations of neutron star structure.

Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei

Expressing explicitly the parameters of the standard Skyrme interaction in terms of the macroscopic properties of asymmetric nuclear matter, we show in the Skyrme-Hartree-Fock approach that unambiguous correlations exist between observables of finite nuclei and nuclear matter properties. We find that existing data on neutron skin thickness $\ensuremath{\Delta}{r}_{\mathit{np}}$ of Sn isotopes give an important constraint on the symmetry energy ${E}_{\mathrm{sym}}({\ensuremath{\rho}}_{0})$ and its density slope $L$ at saturation density ${\ensuremath{\rho}}_{0}$. Combining these constraints with those from recent analyses of isospin diffusion and the double neutron/proton ratio in heavy-ion collisions at intermediate energies leads to a more stringent limit on $L$ approximately independent of ${E}_{\mathrm{sym}}({\ensuremath{\rho}}_{0})$. The implication of these new constraints on the $\ensuremath{\Delta}{r}_{\mathit{np}}$ of $^{208}\mathrm{Pb}$ as well as the core-crust transition density and pressure in neutron stars is discussed.

Nuclear symmetry energy effects in finite nuclei and neutron star

Within a relativistic mean-field model with nonlinear isoscalar–isovector coupling, we explore the possibility of constraining the density dependence of nuclear symmetry energy from a systematic study of the neutron skin thickness of finite nuclei and neutron star properties. We find the present skin data supports a rather stiff symmetry energy at subsaturation densities that corresponds to a soft symmetry energy at supranormal densities. Correlation between the skin of 208Pb and the neutron star masses and radii with kaon condensation has been studied. We find that 208Pb skin estimate suggest star radii that reveals considerable model dependence. Thus precise measurements of neutron star radii in conjunction with skin thickness of heavy nuclei could provide significant constraint on the density dependence of symmetry energy.

DETERMINING THE DENSITY DEPENDENCE OF THE NUCLEAR SYMMETRY ENERGY USING HEAVY-ION REACTIONS

We review recent progress in the determination of the subsaturation density behavior of the nuclear symmetry energy from heavy-ion collisions as well as the theoretical progress in probing the high density behavior of the symmetry energy in heavy-ion reactions induced by high energy radioactive beams. We further discuss the implications of these results for the nuclear effective interactions and the neutron skin thickness of heavy nuclei.

Probing the nuclear symmetry energy with heavy-ion reactions induced by neutron-rich nuclei

Heavy-ion reactions induced by neutron-rich nuclei provide a unique means to investigate the equation of state of isospin-asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy. In particular, recent analyses of the isospin diffusion data in heavy-ion reactions have already put a stringent constraint on the nuclear symmetry energy around the nuclear matter saturation density. We review this exciting result and discuss its implications on nuclear effective interactions and the neutron skin thickness of heavy nuclei. In addition, we also review the theoretical progress on probing the high density behaviors of the nuclear symmetry energy in heavy-ion reactions induced by high energy radioactive beams.

CONSTRAINING THE SKYRME EFFECTIVE INTERACTIONS AND THE NEUTRON SKIN THICKNESS OF NUCLEI USING ISOSPIN DIFFUSION DATA FROM HEAVY ION COLLISIONS

Recent analysis of the isospin diffusion data from heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections has led to the extraction of a value of L = 88 ± 25 MeV for the slope of the nuclear symmetry energy at saturation density. This imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nuclei. Among the 21 sets of Skyrme interactions commonly used in nuclear structure studies, the 4 sets SIV, SV, Gσ, and Rσ are found to give L values that are consistent with the extracted one. Further study on the correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy in the Skyrme Hartree-Fock approach leads to predicted thickness of the neutron skin of 0.22 ± 0.04 fm for 208 Pb , 0.29 ± 0.04 fm for 132 Sn , and 0.22 ± 0.04 fm for 124 Sn .

Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei

Correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy are studied in the Skyrme Hartree-Fock model. From the most recent analysis of the isospin diffusion data in heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections, a value of $L=88\pm 25$ MeV for the slope of the nuclear symmetry energy at saturation density is extracted, and this imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nuclei. Predicted thickness of the neutron skin is $0.22\pm 0.04$ fm for $% ^{208}$Pb, $0.29\pm 0.04$ fm for $^{132}$Sn, and $0.22\pm 0.04$ fm for $% ^{124}$Sn.