Neutron Skin Of Nuclei Research Articles

Implications of parity-violating electron scattering experiments on 48Ca (CREX) and 208Pb (PREX-II) for nuclear energy density functionals

Recent precise parity-violating electron scattering experiments on 48Ca (CREX) and 208Pb (PREX-II) provide a new insight on the formation of neutron skin in nuclei. Within the energy density functional (EDF) framework, we investigate the implications of CREX and PREX-II data on nuclear matter symmetry energy and isovector properties of finite nuclei: neutron skin thickness and dipole polarizability. The weak-charge form factors from the CREX and PREX-II experiments are employed directly in constraining the relativistic density-dependent point coupling EDFs. The EDF established with the CREX data acquires considerably smaller values of the symmetry energy parameters, neutron skin thickness and dipole polarizability both for 48Ca and 208Pb, in comparison to the EDF obtained using the PREX-II data, and previously established EDFs. Presented analysis shows that CREX and PREX-II experiments could not provide consistent constraints for the isovector sector of the EDFs, and further theoretical and experimental studies are required.

Nuclear fragmentation reactions as a probe of neutron skins in nuclei

We investigate the contributions of various reaction channels to the interaction, reaction, charge-changing and neutron-changing cross sections. The goal is to investigate the relation between microscopic interactions and the symmetry energy component of the equation of state (EoS) of interest for the structure of neutron stars. We have made a comparison of the neutron skins extracted from diverse experimental techniques with those obtained with Hartree-Fock-Bogoliubov calculations with 23 Skyrme and with 8 density-dependent interactions used in the relativistic mean field method. We have shown that no particular conclusion can be drawn on the best EoS in view of the wide range of uncertainty in the experimental data. We have further investigated the prospects of using neutron-changing reactions to assess the isospin dependence of the neutron-skin in neutron-rich nuclei.

Neutron–proton interaction, bubble structure and neutron skin properties of Co in a Supernova

In the present paper, we investigated the neutron skin properties, central depletion effects, residual and average neutron–proton interactions for Co in a Type II Supernova 1987A. The neutron skin thicknesses performed by Skyrme–Hartree–Fock model for the isotopic chain of Co $$(17\le N\le 82)$$ are obtained with different methods to investigate the bulk and surface contributions to neutron skin thicknesses as a function of neutron number N and relative neutron excess I = (N-Z)/A. For this purpose, two-parameter Fermi (2pF) distributions for each nucleus are obtained by the proton and neutron density distributions. Since the neutron skin thickness demonstrates the dependency on the symmetry pressure of neutron matter and sensitive to the symmetry energy at the sub-saturation density, the neutron skin properties lead to the investigation on the formation and composition of the crusts in Supernova and neutron stars. For a proper understanding of surface effects of nuclei, the central depletion (or bubble structure) effects on neutron skin of nuclei in the Supernova are explained by calculating the bubble parameters b and b′. Furthermore, in order to illustrate accuracy of theoretical model used in the current work, the mass model approach is also analyzed by the calculating residual and average neutron–proton interactions, where the fluctuations in the mass model approaches have also been compared with the experimental and theoretical results in the literature. In order to evaluate more nuclear properties, we also analyzed the charge form factors and the single- particle energy levels for Co isotopes in the Supernova for providing nuclear data for electron-nucleus scattering experimental processes.

Proton and neutron skins and symmetry energy of mirror nuclei

The neutron skin of nuclei is an important fundamental property, but its accurate measurement faces many challenges. Inspired by charge symmetry of nuclear forces, the neutron skin of a neutron-rich nucleus is related to the difference between the charge radii of the corresponding mirror nuclei. We investigate this relation within the framework of the Hartree-Fock-Bogoliubov method with Skyrme interactions. Predictions for proton skins are also made for several mirror pairs in the middle mass range. For the first time the correlation between the thickness of the neutron skin and the characteristics related with the density dependence of the nuclear symmetry energy is investigated simultaneously for nuclei and their corresponding mirror partners. As an example, the Ni isotopic chain with mass number A=48−60 is considered. These quantities are calculated within the coherent density fluctuation model using Brueckner and Skyrme energy-density functionals for isospin asymmetric nuclear matter with two Skyrme-type effective interactions, SkM* and SLy4. Results are also presented for the symmetry energy as a function of A for a family of mirror pairs from selected chains of nuclei with Z=20, N=14, and N=50. The evolution curves show a similar behavior crossing at the N=Z nucleus in each chain and a smooth growing deviation when N≠Z starts. Comparison of our results for the radii and skins with those from the calculations based on high-precision chiral forces is made.

Neutron skins as laboratory constraints on properties of neutron stars and on what we can learn from heavy ion fragmentation reactions

The equation of state (EOS) of infinite nuclear matter with a small proton/neutron fraction is a crucial input to determine the properties of neutron stars and compare model predictions to astronomical observations. The so-called `symmetry energy' is the part of the EOS accounting for the difference in the number of neutrons and protons. Numerous experiments have been devised to assess the symmetry energy and constrain its functional dependence with the nucleon density. Further constraints follow from a stellar modeling using the EOS to reproduce astronomical observations such as neutron star masses and radii. The recent detection of gravitational waves emitted from neutron star mergers and the nucleosynthesis ensuing from these events caused a surge of interest for such studies. Several types of nuclear reactions have been proposed to study the symmetry energy part of the EOS. Some of them consist in determining the neutron skin in nuclei and exploit its correlation with the slope parameter of the symmetry energy. In this article we explore a particular set of reactions using high energy ($E_{lab} \sim 1$ GeV/nucleon) neutron-rich projectiles. We explore measurements of all reaction fragments (a) in the same isotopic chain, i.e., only by removal of neutrons, (b) in all charge-changing channels, and (c) total interaction cross sections. Using Hartree-Fock-Bogoliubov (HBF) predictions for neutron and proton densities with Skyrme interactions, we explore the sensitivity of these cross sections with the neutron skin in nuclei.

Mirror Charge Radii and the Neutron Equation of State.

The differences in the charge radii of mirror nuclei are shown to be proportional to the derivative of the neutron equation of state and the symmetry energy at nuclear matter saturation density. This derivative is important for constraining the neutron equation of state for use in astrophysics. The charge radii of several neutron-rich nuclei are already measured to the accuracy of about 0.005fm. Experiments at isotope-separator and radioactive-beam facilities are needed to measure the charge radii of the corresponding proton-rich mirror nuclei to a similar accuracy. It is also shown that neutron skins of nuclei with N=Z depend upon the value of the symmetry energy at a density of 0.10 nucleons/fm^{3}.

Systematics of nucleon density distributions and neutron skin of nuclei

Proton and neutron density profiles of 760 nuclei in the mass region of [Formula: see text] are analyzed using the Skyrme energy density for the parameter set SLy4. Simple formulae are obtained to fit the resulting radii and diffuseness data. These formulae are useful to estimate the values of the unmeasured radii and especially in extrapolating charge radii values for nuclei which are far from the valley of stability. Also, it provides an easy way to formulate the density profile for nuclear applications and to perform analytic calculations for bound and/or scattering problems. The obtained neutron and proton root-mean-square (rms) radii and the neutron skin thicknesses are in agreement with the available experimental data and previous Hartree–Fock (HF) calculations.

Recent Advances in Microscopic Approaches to Nuclear Matter and Symmetry Energy

Nuclear matter is a convenient theoretical laboratory to test many-body theories. When neutron and proton densities are different, the isospin dependence of the nuclear force gives rise to the symmetry energy term in the equation of state. This quantity is a crucial mechanism in the formation of the neutron skin in nuclei, as well as in other systems and phenomena involved in the dynamics of neutrons and protons in neutron-rich systems, such as isospin-asymmetric heavy-ion collisions. In this article, we will review phenomenological facts about the symmetry energy and recent experimental efforts to constrain its density dependence and related quantities. We will then review our microscopic approach to the equation of state of symmetric and asymmetric nuclear matter and present a corresponding set of predictions. Our calculations utilize the Dirac–Brueckner–Hartree–Fock method and realistic meson-theoretic nucleon-nucleon potentials. Chiral perturbation theory is an alternative approach, based on a well-defined scheme, which allows one to develop nuclear forces at each order of the chiral expansion. We will present and discuss predictions based on chiral perturbation theory, where we employ consistent two- and three-body chiral interactions. Throughout the article, one of the focal points is the importance of pursuing ab initio methods towards a deeper understanding of the many-body system.

Effect of temperature on the effective mass and the neutron skin of nuclei

We study the finite temperature Hartree-Fock-BCS approximation for selected stable Sn nuclei with zero-range Skyrme forces. Hartree Fock BCS approximation allows for a straightforward interpretation of the results since it involves u and v's which are not matrices as in HFB. Pairing transitions from superfluid to the normal state are studied with respect to the temperature. The temperature dependence of the nuclear radii and neutron skin are also analyzed. An increase of proton and neutron radii is obtained in neutron rich nuclei especially above the critical temperature. Using different Skyrme energy functionals, it is found that the correlation between the effective mass in symmetric nuclear matter and the critical temperature depends on the pairing prescription. The temperature dependence of the nucleon effective mass is also investigated, showing that proton and neutron effective masses display different behavior below and above the critical temperature, due to the small temperature dependence of the density.

Measurement of the Dipole Polarizability of the Unstable Neutron-Rich NucleusNi68

The E1 strength distribution in 68Ni has been investigated using Coulomb excitation in inverse kinematics at the R3B-LAND setup and by measuring the invariant mass in the one- and two-neutron decay channels. The giant dipole resonance and a low-lying peak (pygmy dipole resonance) have been observed at 17.1(2) and 9.55(17) MeV, respectively. The measured dipole polarizability is compared to relativistic random phase approximation calculations yielding a neutron-skin thickness of 0.17(2) fm. A method and analysis applicable to neutron-rich nuclei has been developed, allowing for a precise determination of neutron skins in nuclei as a function of neutron excess.

Anti-analog giant dipole resonances and the neutron skin of nuclei

We examine a method to determine the neutron-skin thickness of nuclei using data on the charge-exchange anti-analog giant dipole resonance (AGDR). Calculations performed using the relativistic proton–neutron quasiparticle random-phase approximation (pn-RQRPA) reproduce the isotopic trend of the excitation energies of the AGDR, as well as that of the spin-flip giant dipole resonances (IVSGDR), in comparison to available data for the even–even isotopes 112–124Sn. It is shown that the excitation energies of the AGDR, obtained using a set of density-dependent effective interactions which span a range of the symmetry energy at saturation density, supplemented with the experimental values, provide a stringent constraint on value of the neutron-skin thickness. For 124Sn, in particular, we determine the value ΔRpn=0.21±0.05 fm. The result of the present study shows that a measurement of the excitation energy of the AGDR in (p,n) reactions using rare-isotope beams in inverse kinematics, provides a valuable method for the determination of neutron-skin thickness in exotic nuclei.

Nucleon distribution in nuclei beyond theβ-stability line

The radii of nucleon distribution, bulk density, and neutron skin in nuclei beyond the \beta-stability line are studied within the direct variational method. We evaluate the partial equation of state of finite nuclei and demonstrate that the bulk density decreases beyond the beta stability line. We show that the growth of the neutron skin in unstable nuclei does not obey the saturation condition because of the polarization effect. The value of the neutron-skin thickness \Delta r_{np}=\sqrt{<r_n^2>}-\sqrt{<r_p^2>} is caused by the different radii (skin effect) and only slightly by the different shapes (halo effect) of neutron and proton distributions. The relative contribution of both effects depends on the competition between the symmetry energy, and the spin-orbit and Coulomb interactions. The calculations of the isovector shift of the nuclear radius \Delta r_{np} show its primarily linear dependence on the asymmetry parameter X=(N-Z)/A.

The Gamma Decay of the Pygmy Resonance and the Neutron Skin of Nuclei

The Coulomb excitation of the neutron rich 68Ni was measured using it as as secondary radioactive beam at 600 MeV/nucleon impinging on a 197Au target. The dipole strength in the region at around the nucleon binding energy was extracted from the gamma decay measurement. A sizable fraction of "pygmy" dipole strength, energetically located below the giant dipole resonance, is observed in this nucleus. The experimental data is discussed in connection with predictions obtained using different Random Phase Approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data for both 68Ni and 132Sn has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint.

Relativistic QRPA description of nuclear excitations

Self-consistent relativistic mean-field models have been applied to the description of a variety of nuclear structure phenomena, not only in stable nuclei but also in systems far from the valley of β stability. The relativistic quasiparticle random-phase approximation (RQRPA) has been used to study dynamical aspects of exotic nuclear structure. Interesting results have been obtained for the evolution of low-lying dipole strength in neutron-rich nuclei and the isotopic dependence of the pygmy dipole resonance, the relation between the neutron skin of nuclei and the excitation energies of Gamow–Teller resonances and isobaric analog states, the occurrence of pygmy dipole states in proton-rich nuclei and beta-decay rates of r-process nuclei.

Spin-isospin resonances and the neutron skin of nuclei.

The Gamow-Teller resonances (GTR) and isobaric analog states (IAS) of a sequence of even-even Sn target nuclei are calculated by using the framework of the relativistic Hartree-Bogoliubov model plus proton-neutron quasiparticle random-phase approximation. The calculation reproduces the experimental data on ground-state properties, as well as the excitation energies of the isovector excitations. It is shown that the isotopic dependence of the energy spacings between the GTR and IAS provides direct information on the evolution of neutron-skin thickness along the Sn isotopic chain. A new method is suggested for determining the difference between the radii of the neutron and proton density distributions along an isotopic chain, based on measurement of the excitation energies of the GTR relative to the IAS.

Excitation of Isovector Spin-Dipole Resonances and Neutron Skin of Nuclei

The cross sections of the isovector spin-dipole resonances (SDR) in the Sb isotopes excited by the ${(}^{3}\mathrm{He},t)$ charge-exchange reaction at 450 MeV for $0\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}{\ensuremath{\theta}}_{t}\ensuremath{\le}1.15\ifmmode^\circ\else\textdegree\fi{}$ have been measured. The results are compared with the predicted sum-rule strengths related to the difference of neutron and proton root-mean-square radii. Within the model used, the radii differences (neutron-skin thicknesses) deduced for ${}^{114}\mathrm{Sn}$, ${}^{116}\mathrm{Sn}$, ${}^{118}\mathrm{Sn}$, ${}^{122}\mathrm{Sn}$, and ${}^{124}\mathrm{Sn}$ are $\ensuremath{\le}0.09$, $0.12\ifmmode\pm\else\textpm\fi{}0.06$, $0.13\ifmmode\pm\else\textpm\fi{}0.06$, $0.22\ifmmode\pm\else\textpm\fi{}0.07$, and $0.19\ifmmode\pm\else\textpm\fi{}0.07\mathrm{fm}$, respectively. This result suggests a new method for the measurement of the neutron-skin thicknesses of unstable nuclei.

Neutron skin of nuclei near the neutron drip line.

Performing Skyrme-type deformed Hartree-Fock calculations, the possible presence of neutron skin in nuclei towards neutron drip line is studied. The thickness of the neutron skin is found to be nearly constant in all directions if it is measured perpendicular to the surface, and in a given nucleus the number of neutrons being inside of the neutron skin is almost independent of the deformation (namely, spherical shape or normal deformation or superdeformation). In the region of medium-heavy nuclei our calculation shows the presence of a series of neutron-rich nuclei, in which a neutron skin is present and yet the neutron one-particle spectra are far from those in a harmonic oscillator (plus spin-orbit) potential.

Rho meson coupling in the relativistic mean field theory and description of exotic nuclei

The role of the isovector rho-meson coupling on the symmetry energy in the relativistic mean-field theory has been investigated. In a multi-dimensional parameter search for an appropriate force within the framework of the non-linear σωϱ model the ϱ-meson coupling has been found to have a significant effect on the neutron skin of nuclei. It has been shown that a low value of ϱ-meson coupling strength remedies the defect of some of the existing parameter sets of providing a higher neutron skin thickness of nuclei. An extraordinarily good description of highly proton- as well as neutron-rich exotic nuclei has been found. It has been observed that the proper description of both proton-rich and neutron-rich nuclei is sensitive to the symmetry energy.

Revelation of thick neutron skins in nuclei

Thick neutron skins (∼ 0.9 fm) have been verified for the first time in 6He and 8He nuclei from a combined analysis of the interaction and the fragmentation cross sections of 4,6,8He incident reactions at 800 A MeV. A relativistic mean field (RMF) model was applied to 6He and 8He nuclei and shown to reproduce the neutron skin thicknesses very well. It is also shown that the RMF model predicts a gross linear dependence of the neutron skin thickness on the difference between the proton and the neutron Fermi energy in a wide range of nuclei. Possible observations of thick neutron skins in other nuclei, in particular in Na isotopes, are also discussed.

Excitation of the isovector giant dipole resonance by inelastic alpha scattering and the neutron skin of nuclei.

The cross section of the isovector giant dipole resonance (GDR) excited by inelastic scattering of 120-MeV \ensuremath{\alpha} particles for 0\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}\ensuremath{\Theta}\ensuremath{\alpha}'\ensuremath{\le}3\ifmmode^\circ\else\textdegree\fi{} has been measured using the $^{116,124}\mathrm{Sn}$(\ensuremath{\alpha},\ensuremath{\alpha}'${\ensuremath{\gamma}}_{0}$) and $^{208}\mathrm{Pb}$(\ensuremath{\alpha},\ensuremath{\alpha}'${\ensuremath{\gamma}}_{0}$) reactions. The results are compared with distorted-wave Born-approximation calculations with a GDR form factor depending on the relative difference of proton and neutron radii (\ensuremath{\Delta}${\mathit{R}}_{\mathit{p}\mathit{n}}$/${\mathit{R}}_{0}$). Within the model used, the \ensuremath{\Delta}${\mathit{R}}_{\mathit{p}\mathit{n}}$/${\mathit{R}}_{0}$ values for $^{116}\mathrm{Sn}$, $^{124}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ deduced from the comparison of measured and calculated cross sections are (0.${7}_{\mathrm{\ensuremath{-}}0.7}^{+2.3}$)%, (4.${1}_{\mathrm{\ensuremath{-}}2.5}^{+2.1}$)%, and (3.0\ifmmode\pm\else\textpm\fi{}1.3)%, respectively.