The lead nucleus as a miniature surrogate for a neutron star

The nucleus of ²⁰⁸Pb, a system 18 orders of magnitude smaller and 55 orders of magnitude lighter than a neutron star, may be used as a miniature surrogate to establish important correlations between its neutron skin and several neutron-star properties. Indeed, models with a thicker neutron skin in ²⁰⁸Pb generate larger neutron stars that have a lower liquid-to-solid transition density. Further, we illustrate how the correlation between the neutron skin in ²⁰⁸Pb and the radius of a 1.4 solar-mass neutron star may be used to place important constraints on the equation of state of neutron-rich matter and how it may help elucidate the existence of a phase transition at the core of the star.     

中子皮厚度测量探针对核物质状态方程的依赖性

利用同位旋相关的量子分子动力学模型模拟了 4He + 208 Pb的碰撞反应,发现中子质子产额比与 208 Pb的中子皮之间存在很好的线性关联,中子质子产额比可以作为中子皮厚度测量的一个探针。选取量子分子动力学模型中核物质状态方程的两套不同势参数进行模拟,通过对比发现,中子皮的厚度测量探针中子质子产额比对核物质状态方程中选择软势和硬势非常敏感,相同反应条件下,软势比硬势计算所得的中子质子产额比要低。无论选择何种状态方程参数,中子质子产额比与中子皮之间都存在线性关联。The reaction system of 4He + 208Pb has been simulated by Isospin-dependent Quantum Molecu-lar Dynamics (IQMD) mode and it was found that the neutron-to-proton yield ratio (Rnp) has a good linearrelationship with the neutron skin thickness of 208Pb. Therefore Rnp could be taken as a probe of neutron skin thickness of 208Pb. Using two sets of parameters for the nuclear equation of state (EOS) in IQMD model, it shows that Rnp is sensitive to nuclear equation of state. The calculation results of Rnp with the soft EOS is lower than the hard EOS. No matter which kind of EOS parameter has been chosen, however, Rnp holds a good linear correlation with the neutron skin thickness.     

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.     

中子皮厚度与中子星半径

在相对论平均场理论框架下在拉氏量密度中引入同位旋相关的高阶修正项, 研究了中子皮厚度和中子星半径的关系. 利用有效相互作用PK1得到208Pb的中子皮厚度最小可达0.17 fm, 这与近期Skyrme HF模型得到的结果一致. 随着同位旋相关的高阶修正项系数的变化, 208Pb的中子皮厚度和中子星半径的变化趋势相同. By adding isospin dependent high order correction ferms to existing relativistic mean field models．tlle thickness of neuron．skin in 208Pb and the radius of 1.4 solar mass neutron star are studied．The effecfive interaction PK1 would lead the thickness of neutron-skin to a minimum of 0.17 fm which agrees with the analysis from Skyrme‘HF models． The coupling constants of the isospin dependent high order corection terms tend to change，the thickness of neutron-skin and the radius of neutron stars chan ge simultaneously.     

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.     

在相对论平均场框架下研究同位旋依赖的高阶核子-ω-ρ介子耦合(英文)

在相对论平均场的框架下,对208Pb中子皮对新的同位旋依赖的高阶核子-ω-ρ介子耦合项的敏感性进行了研究。计算表明,高阶同位旋依赖的核子-ω-ρ介子耦合能够进一步软化对称能,因而能够在不影响其它基态可观测量的情况下,进一步减小208Pb的中子半径。The sensitivity of the neutron skin thickness S in ^208Pb to the new addition of the high order isospin-dependent nucleon-ω-ρ coupling term in the relativistic mean field model is studied. Calculations show that the high order isospin-dependent nucleon-ω-ρ coupling term can further soften the symmetry energy, and thus further decrease the neutron radius of ^208Pb without affecting other ground-state observables     

Theoretical study on neutron distribution of ~(208)Pb by parity-violating electron scattering

The precise determination of neutron distribution has important implications for both nuclear structure and nuclear astrophysics. The purpose of this paper is to study the characteristics of neutron distribution of~(208) Pb by parity-violating electron scattering(PVS). Parity-violating asymmetries of~(208) Pb with different types of neutron skins are systematically calculated and compared with the experimental data of PREx. The results indicate that the PVS experiments are very sensitive to the nuclear neutron distributions. From further PVS measurements, detailed information on nuclear neutron distributions can be extracted.     

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.     

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.     

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.     

Charge Density of ^23,24O with Isoscalar-Isovector Coupling Terms

The nonlinear isoscalar-isovector terms which are used to simulate the density dependence of the symmetry energy are considered in the relativistic mean field model. The charge density distributions of ^23,24O are investigated by considering the contribution from the isoscalar-isovector couplings. Contrarily to the uncertainty of the neutron radius of ^208Pb, a considerable uncertainty exists for the charge radii of ^23,24O. The data-to-data correlation between the neutron thickness of ^208Pb and that of ^23,24O is enhanced by the inclusion of the pNN tensor coupling. This enhancement is closely related to the structural factor, the 2s1/2 occupation of the out-layer neutrons.     

Parity violation,the neutron radius of lead,and neutron stars

The neutron radius of a heavy nucleus is a fundamental nuclear-structure observable that remains elusive. Progress in this arena has been limited by the exclusive use of hadronic probes that are hindered by large and controversial uncertainties in the reaction mechanism. The parity radius experiment at the Jefferson Laboratory offers an attractive electro-weak alternative to the hadronic program and promises to measure the neutron radius of ²⁰⁸Pb accurately and model independently via parity-violating electron scattering. In this contribution we examine the far-reaching implications that such a determination will have in areas as diverse as nuclear structure, atomic parity violation, and astrophysics.     

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.     

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).     

The (7Li, 8Li) reaction to the (h92)−1 state in 207Pb

Relative differential cross sections for the reaction ²⁰⁸ P(⁷Li, ⁸Li) leading to the predominantly single-hole states in ²⁰⁷Pb have been analysed using the DWBA to determine the rms radius of the 1h_{$\text{9}\text{2}$} neutron orbital in ²⁰⁸Pb by comparison with known sizes of the 3p_{$\text{1}\text{2}$} and 2f_{$\text{7}\text{2}$} orbits. The experiment was performed at a beam energy of 52 MeV. The insensitivity of the technique to unknown input parameters to the DWBA analysis is demonstrated and a value of 5.94±0.11 fm for the rms radius of the 1h_{$\text{9}\text{2}$} orbit obtained assuming 70% of the hole strength is concentrated on the $\text{9}\text{2}{}^{\mathrm{?}}$, 3.41 MeV state in ²⁰⁷Pb. Effects due to fragmentation of the different hole strengths are examined and a value of 6.00 ± 0.11 fm is extracted as the best value for the rms radius of the neutron excess in ²⁰⁸Pb. The relevance of these data to mean-field calculations of nuclei is discussed.     

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.     

利用非对称核物质状态方程对中子星的质量和半径的研究

在温度、密度及同位旋相关的核物质状态方程的基础上,通过求解Tol-man-Oppenheimer?Volkoff方程得到了中子星的质量与中心密度的关系,发现随着中心密度的变化,中子星存在一个最大质量.同时计算结果表明,中子星的最大质量与核物质状态方程的不可压缩系数、有效质量及对称能强度系数等密切相关.对中子星半径的研究表明,较硬的核物质状态方程给出的中子星半径较大,而且较大的对称能强度系数和较大的核子有效质量也会给出较大的中子星半径.     

Measurement of the neutron radius of 208Pb through parity violation in electron scattering

We report the first measurement of the parity-violating asymmetry A(PV) in the elastic scattering of polarized electrons from 208Pb. A(PV) is sensitive to the radius of the neutron distribution (R(n)). The result A(PV)=0.656±0.060(stat)±0.014(syst) ppm corresponds to a difference between the radii of the neutron and proton distributions R(n)-R(p)=0.33(-0.18)(+0.16) fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.     

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.