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Register a new userA Detailed Examination of Astrophysical Constraints on the Symmetry Energy and the Neutron Skin of $^{208}$Pb with Minimal Modeling Assumptions
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The symmetry energy and its density dependence are pivotal for many nuclear physics and astrophysics applications, as they determine properties ranging from the neutron-skin thickness of nuclei to the crust thickness and the radius of neutron stars. Recently, PREX-II reported a value of $0.283pm0.071$ fm for the neutron-skin thickness of $^{208}$Pb, $R_{rm skin}^{^{208}text{Pb}}$, implying a symmetry-energy slope parameter $L$ of $106pm37$ MeV, larger than most ranges obtained from microscopic calculations and other nuclear experiments. We use a nonparametric equation of state representation based on Gaussian processes to constrain the symmetry energy $S_0$, $L$, and $R_{rm skin}^{^{208}text{Pb}}$ directly from observations of neutron stars with minimal modeling assumptions. The resulting astrophysical constraints from heavy pulsar masses, LIGO/Virgo, and NICER favor smaller values of the neutron skin and $L$, as well as negative symmetry incompressibilities. Combining astrophysical data with chiral effective field theory ($chi$EFT) and PREX-II constraints yields $S_0 = 33.0^{+2.0}_{-1.8}$ MeV, $L=53^{+13}_{-15}$ MeV, and $R_{rm skin}^{^{208}text{Pb}} = 0.17^{+0.04}_{-0.04}$ fm. We also examine the consistency of several individual $chi$EFT calculations with astrophysical observations and terrestrial experiments. We find that there is only mild tension between $chi$EFT, astrophysical data, and PREX-IIs $R_mathrm{skin}^{^{208}mathrm{Pb}}$ measurement ($p$-value $= 12.3%$) and that there is excellent agreement between $chi$EFT, astrophysical data, and other nuclear experiments.
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We argue that the reaction mechanism for the coherent pion production is not known with sufficient accuracy to determine the neutron radius of 208Pb to the claimed precision of 0.03 fm.
We present and discuss numerical predictions for the neutron density distribution of $^{208}$Pb using various non-relativistic and relativistic mean-field models for the nuclear structure. Our results are compared with the very recent pion photoproduction data from Mainz. The parity-violating asymmetry parameter for elastic electron scattering at the kinematics of the PREX experiment at JLab and the neutron skin thickness are compared with the available data. We consider also the dependence between the neutron skin and the parameters of the expansion of the symmetry energy.
The $^{208}$Pb($p$,$ngammabar p$) $^{207}$Pb reaction at a beam energy of 30 MeV has been used to excite the anti-analog of the giant dipole resonance (AGDR) and to measure its $gamma$-decay to the isobaric analog state in coincidence with proton decay of IAS. The energy of the transition has also been calculated with the self-consistent relativistic random-phase approximation (RRPA), and found to be linearly correlated to the predicted value of the neutron-skin thickness ($Delta R_{pn}$). By comparing the theoretical results with the measured transition energy, the value of 0.190 $pm$ 0.028 fm has been determined for $Delta R_{pn}$ of $^{208}$Pb, in agreement with previous experimental results. The AGDR excitation energy has also been used to calculate the symmetry energy at saturation ($J=32.7 pm 0.6$ MeV) and the slope of the symmetry energy ($L=49.7 pm 4.4$ MeV), resulting in more stringent constraints than most of the previous studies.
The symmetry energy obtained with the effective Skyrme energy density functional is related to the values of isoscalar effective mass and isovector effective mass, which is also indirectly related to the incompressibility of symmetric nuclear matter. In this work, we analyze the values of symmetry energy and its related nuclear matter parameters in five-dimensional parameter space by describing the heavy ion collision data, such as isospin diffusion data at 35 MeV/u and 50 MeV/u, neutron skin of $^{208}$Pb, and tidal deformability and maximum mass of neutron star. We obtain the parameter sets which can describe the isospin diffusion, neutron skin, tidal deformability and maximum mass of neutron star, and give the incompressibility $K_0$=250.23$pm$20.16 MeV, symmetry energy coefficient $S_0$=31.35$pm$2.08 MeV, the slope of symmetry energy $L$=59.57$pm$10.06 MeV, isoscalar effective mass $m_s^*/m$=0.75$pm$0.05 and quantity related to effective mass splitting $f_I$=0.005$pm$0.170. At two times normal density, the symmetry energy we obtained is in 35-55 MeV. To reduce the large uncertainties of $f_I$, more critical works in heavy ion collisions at different beam energies are needed.
Information on the size and shape of the neutron skin on $^{208}$Pb has been extracted from coherent pion photoproduction cross sections measured using the Crystal Ball together with the Glasgow tagger at the MAMI electron beam facility. On exploitation of an interpolated fit of a theoretical model to the measured cross sections the half-height radius and diffuseness of the neutron distribution are found to be 6.70$pm 0.03(stat)$ fm and 0.55$pm 0.01(stat)$$^{+0.02}_{-0.03}(sys)$ fm respectively, corresponding to a neutron skin thickness $Delta r_{np}$=0.15$pm 0.03(stat)$$^{+0.01}_{-0.03}(sys)$ fm. The results give the first successful extraction of a neutron skin with an electromagnetic probe and indicate the skin of $^{208}$Pb has a halo character. The measurement provides valuable new constraints on both the structure of nuclei and the equation of state for neutron-rich matter.
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