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.     

Links between heavy ion and astrophysics

Heavy-ion experiments provide important data to test astrophysical models. The high-density equation of state can be probed in HI collisions and applied to the hot protoneutron star formed in core collapse supernovae. The parity radius experiment (PREX) aims to accurately measure the neutron radius of ²⁰⁸Pb with parity-violating electron scattering. This determines the pressure of neutron-rich matter and the density dependence of the symmetry energy. Competition between nuclear attraction and Coulomb repulsion can form exotic shapes called nuclear pasta in neutron star crusts and supernovae. This competition can be probed with multifragmentation HI reactions. We use large-scale semiclassical simulations to study nonuniform neutron-rich matter in supernovae. We find that the Coulomb interactions in astrophysical systems suppress density fluctuations. As a result, there is no first-order liquid-vapor phase transition. Finally, the virial expansion for low-density matter shows that the nuclear vapor phase is complex with significant concentrations of alpha particles and other light nuclei in addition to free nucleons.     

Effective interactions for 208Pb + p reactions

RPA hole-particle wave functions for the lowest 2⁺ and 3^? states in ²⁰⁸Pb were used to test the validity of effective nucleon-nucleon interactions for (p, p') excitations. Excellent agreement with experiment was obtained for the long-range part of the Hamada-Johnston S-state potential. Equally good agreement was found for the elastic scattering from ²⁰⁸Pb and the (p, n) transition to the analog state. It was found to be important to include an imaginary part in the interaction. The transitions to the two excited states of ²⁰⁸Pb were found to be almost pure isoscalar, but the transitions are dominated by the neutron excitations.     

An analysis of some proton-nucleus scattering data at 1 GeV

The elastic and inelastic scattering data of 1 GeV protons on ¹²C, ³⁹K,^{40, 48}Ca, ⁵⁸Ni and ²⁰⁸Pb are analysed within the framework of Glauber theory. The collective excitations to one-phonon levels are treated using the Tassie model under the adiabatic approximation. Effects of both the coupling between the elastic and the inelastic channels and the two-body correlation in the intrinsic state are considered. The ground state and transition densities for the protons are taken from electron scattering experiments and appropriate assumptions for the neutron densities are made. In most of the cases, better agreement with the experimental data than reported in earlier analyses is obtained. The effects of the coupling and the pair correlation seem to be important only for ¹²C. The elastic data strongly indicate that the density distributions for protons and neutrons in ⁴⁸Ca and ²⁰⁸Pb are different. In ⁴⁸Ca, the surface envelope of the neutron distribution is found to be the same as for the proton distribution but is placed at a larger radius. On the other hand, the neutron distribution in ²⁰⁸Pb seems to be relatively much more diffuse.     

Volume form of coupling interaction in semi-direct (n, γ) and (p, γ) reactions

A coupling interaction between the nucleon and the nuclear E1 mode having a volume radial form instead of the usual surface one is used in the semi-direct nucleon radiative-capture theory. The calculated cross sections for the ²⁰⁸Pb(n,γ) and ¹⁴²Ce(p,γ) reactions in the giantresonance region reproduce the measured ones both in shape and magnitude. Satisfactory agreement is achieved in comparing the predicted and detected γ-ray spectra following neutron capture by ²⁰⁸Pb. A detailed analysis of the energy and angular-momentum dependence of the matrix elements when the volume and surface form factors are used, is performed.     

Timescale for isospin equilibration in projectile breakup

We discuss neutron matter calculations based on chiral effective field theory interactions and their predictions for the symmetry energy, the neutron skin of ²⁰⁸Pb , and for the radius of neutron stars.     

Neutron star structure and the neutron radius of 208Pb.

We study relationships between the neutron-rich skin of a heavy nucleus and the properties of neutron-star crusts. Relativistic effective field theories with a thicker neutron skin in 208Pb have a larger electron fraction and a lower liquid-to-solid transition density for neutron-rich matter. These properties are determined by the density dependence of the symmetry energy which we vary by adding nonlinear couplings between isoscalar and isovector mesons. An accurate measurement of the neutron radius in 208Pb-via parity violating electron scattering-may have important implications for the structure of the crust of neutron stars.     

Sub-Coulomb transfer reactions on 208Pb with carbon and oxygen projectiles

Single-neutron transfers induced by ^{12, 13}C and ^{16, 17, 18}O projectiles on ²⁰⁸Pb and the ¹²C(¹⁷O, ¹⁶O)¹³C reaction have been studied at energies close to the Coulomb barrier. These processes are well described by the distorted-wave Born approximation. Coupled-channels effects are found to be small. Normalization factors have been determined for all projectile and target transitions, and also for the triton-deuteron overlap by comparison with previous measurements of the ²⁰⁸Pb(d, t)²⁰⁷Pb reaction. The root-mean-square (rms) radii of single-particle neutron wave functions in ²⁰⁸Pb and ²⁰⁹Pb were calculated using known spectroscopic factors. The distribution of the point neutron excess density in the surface region of ²⁰⁸Pb has been derived and its rms radius determined to be 5.93 ± 0.13 fm with a local potential model. This is in good agreement with theoretical predictions, but is considerably larger than estimates based on Coulomb energy differences. The phenomena of core polarisation by the odd particle or hole outside ²⁰⁸Pb is discussed using the single-particle orbitals determined in this work.     

Neutron skin thickness and nuclear matter properties

Linear correlations are found among the isovector nuclear matter properties in both the Skyrme-Hartree-Fock (SHF) and the relativistic mean-field (RMF) models. In addition, we found a kind of correlation between the isovector nuclear matter properties and the incompressibility in the SHF model. The Skyrme parameters are related analytically to nuclear matter properties with the Thomas—Fermi approximation. By using a linear correlation between the neutron skin thickness and the pressure of the neutron matter in the SHF model, we show that the neutron skin thickness of ²⁰⁸Pb gives crucial information about not only the neutron equation of state but also the isovector nuclear matter properties and the parametrization of Skyrme interaction. The text was submitted by the authors in English.     

The single-particle characteristics of Pb isotopes near the drip lines calculated within the dispersive optical model

The neutron and proton dispersive optical potential for the ²⁰⁸Pb nucleus has been determined for the energy region from–70 to +60 MeV and used to calculate the differential elastic scattering, the total interaction and reaction cross sections, as well as the single-particle characteristics, the neutron and charge densities, rms radii, and the thickness of the nucleus skin. The calculated results are in good agreement with the experimental data. The proton dispersive optical model potential for the spherical and close to spherical Pb isotopes within the neutron and proton drip lines has been obtained by a similar method. The calculation predicts a trend towards the growth of the proton particle-hole gap, which corresponds to Z = 82 shell closure as Z approaches the proton drip line.     

Neutron scattering from 208Pb

Elastic scattering of 7, 9, 11, 20 and 26 MeV neutrons from ²⁰⁸Pb has been measured with the Ohio University Tandem Van de Graaff accelerator. Standard pulsed beam time-of-flight techniques were employed. Measurements of the incident flux at 0° were used to normalize the differential cross sections. The measured cross sections were corrected for dead time, detector efficiency, flux attenuation, multiple scattering, finite geometry, neutron source anisotropy and compound elastic contribution. Relative uncertainties are estimated to be between 5%–10% and the uncertainty in the normalization is estimated to be less than 5 %. The data were used to obtain neutron optical potential parameters. A comparison with proton optical parameters is presented, and the (p, n) quasi-elastic cross section is calculated and compared with available data. Deformation parameters for the 3^? state (Q = ?2.615 MeV) and 5ā (Q = ?3.198 MeV) in ²⁰⁸Pb were obtained at incident energies of 11 and 26 MeV.     

γ Spectroscopy of 209Pb with deep inelastic reactions

High spin states in nuclei around ²⁰⁸Pb were populated in deep inelastic collisions of ⁷⁶Ge, ¹³⁶Xe, and ²⁰⁸Pb projectiles with ²⁰⁸Pb targets at beam energies about 12% above the Coulomb barrier. New states in ²⁰⁹Pb were found by measuring γ-γ-coincidences. They are interpreted as the yrast states that originate from the coupling of one neutron to the lowest excitations of the ²⁰⁸Pb core. The results are discussed in the frame of the shell model. Received: 22 November 1997     

Cross sections and reaction mechanisms of (p,pxn) reactions on 208Pb in the 24–52 MeV range

The cross sections for the reactions ²⁰⁸Pb(p, pn)^207mPb, ²⁰⁸Pb(p, p2n)^206mPb have been measured for 24, 28, 36, 44 and 52 MeV incident protons. The experimental results are shown to be consistent with the clean knockout mechanism for the (p, pn) reaction and with knockout of one neutron followed by evaporation of another for the (p, p2n) reaction. We deduce a theoretical formula for the cross section for these reactions.     

A direct measurement of the total proton decay width of an isobaric analog state

Differential cross sections for the ²⁰⁸Pb (p, n) reaction populating the isobaric analog state (IAS) of the ²⁰⁸Pb ground state in ²⁰⁸Bi have been measured at a proton bombarding energy of 30.5 MeV. The experimental technique utilized the proton (p?) decay of the IAS to obtain neutron time-of-flight spectra. When these differential cross sections are compared to those obtained for the same reaction at 30.5 MeV using the pulsed-beam technique to obtain neutron time-of-flight spectra, the percentage of the IAS decay through p? channels is obtained. This comparison indicates that the p? decay of the IAS to the first three states of ²⁰⁷Pb accounts for almost all of the IAS width (0.97±0.28).     

核物质的对称能与中子皮厚度(英文)

在现有的平均场模型中引入同位旋相关的高阶修正项．研究了核物质对称能的密度依赖性和。^208Pb的中子皮厚度。采用新提出的PK1相互作用以及NL3．S271和Z271相互作用．得到核物质饱和点对称能的范围为29-38MeV以及相应的^208Pb中子皮厚度为0．17—0.28fm．在所有相互作用中，核物质饱和点的对称能与^208Pb的中子皮厚度近似呈线性关系。After adding isospin dependent high order correction terms to existing relativistic mean field models (RMF), the density dependence of symmetry energy and the neutron skin thickness S for 208Pb are studied. Using the new effective interaction PK1, together with NL3, S271 and Z271, a range of 29—38 MeV for the symmetry energy for nuclear matter at saturation point and the corresponding neutron skin thickness S = 0.14—0.28 fm for 208Pb are obtained. For all effective interactions, a linear relation between the symmetry energy at saturation point and the neutron skin thickness for 208Pb is observed.     

Shell model interaction between proton holes and between proton holes and neutron particles around 208Pb

An effective residual interaction between particles and holes for shell model calculations around ²⁰⁸Pb, derived from the interaction between free nucleons, is compared with the measured properties of proton-hole neutron states in ²⁰⁸Tl and the interaction between proton holes is adjusted to newly measured level energies in ²⁰⁶Hg. These interaction elements are particularly relevant for neutron-rich nuclei. The adjustment of two mixing elements reproduces the known γ-decay data in ²⁰⁸Tl. Received: 2 April 2002 / Accepted: 2 May 2002     

Yrast traps and high-spin states in 210Rn

Yrast and near-yrast states have been investigated in ²¹⁰Rn to high spin (J > 30) and high energy (E_x > 10 MeV). Three different (HI, xn) reactions were used to populate the states of interest and several different γ-ray spectroscopic techniques were utilized. Three high-spin yrast traps were discovered. Two de-excite by strong E3 transitions while the third decays mainly via an extremely inhibited E2 transition. The E3 decays are interpreted as allowed single-particle transitions between proton or neutron states above the ²⁰⁸Pb shell closure while the inhibited E2 transition is interpreted as indicating a substantial change in structure as the decay proceeds down the yrast line. The interpretation has been given in terms of shell-model calculations.     

Coulomb-nuclear interference at sub-Coulomb energies

The Coulomb-nuclear interference pattern in the low-energy heavy-ion excitation of nuclei near closed-shells can be used to investigate the nuclear mass density at large distances, the nature of the effective transition operator and the presence of higher-order direct processes. Semimicroscopic single-folding calculations are compared to low-energy data for ¹⁸O excitation by ²⁰⁸Pb. A strong effect of two-step transfer reactions is predicted in the sub-Coulomb excitation of ¹⁷O by ²⁰⁸Pb.