Neutron Skin Thickness Of 208Pb Research Articles

Linkage among the neutron-skin thickness of 208Pb and nuclear symmetry energy using heavy particle radioactivity

The nuclear symmetry energy (NSE) is a linchpin in deciphering the behavior of matter in a wider domain extending from the characteristics of exotic nuclei to those of neutron stars in the cosmos. Therefore, it is crucial to utilize potential probes to constrain the NSE and its slope parameter L(ρ 0). In this work, we put forth the heavy particle radioactivity (HPR) as a probable bridge among the slope of NSE (L(ρ 0)) and neutron-skin thickness of 208Pb (R skin 208), which serves to put constrain on the L(ρ 0) value. The NSE and its slope parameter are determined from the single nucleon potential of asymmetric nuclear matter exploiting the analytical relationship between these quantities. The isovector/symmetry potential component of the single nucleon potential is derived through HPR for varying R skin 208 by employing the heavy particle/cluster densities and core densities from the relativistic mean field model in conjunction with M3Y nucleon–nucleon interaction. It facilitates in constraining the L(ρ 0) value and neutron skin of finite nuclei using HPR as a linkage, where heavy cluster and core densities of standard Fermi form are considered. The constrained value of L(ρ o ) is 45 ± 8 MeV, which aligns with other estimations derived from nuclear mass measurements, dipole polarizability measurements, and astrophysical data.

New equations of state for dense nuclear matter properties

In the present work, we investigate the bulk properties of nuclear matter and neutron stars with the newly proposed relativistic parametrizations HPUA, HPUB and HPUC which provides an opportunity to readjust the coupling parameters keeping in view the properties of finite nuclei, nuclear matter and astrophysical constraints. The HPUA, HPUB and HPUC are proposed by fitting both PREX-II + CREX results simultaneously, PREX-II and CREX results for neutron skin thickness of 208Pb and 48Ca respectively to assess their implications. The relativistic parameterizations have been generated by including non linear self-interactions of σ and ω- mesons and mixed interactions of ω, and ρ-meson up to the quartic order. The new equations of state (EoSs) composed of nucleons and leptons in β - equilibrium are constructed with the newly proposed parameter sets. The maximum mass of the neutron star by employing the EoSs computed with the HPU's parameter sets lies in the range 2.02±0.03 M⊙ - 2.04±0.03 M⊙ and the radius of canonical neutron star (R1.4) comes out to be equal to 12.89±0.08 Km - 13.27±0.30 Km (including BPS crust). The value of dimensionless tidal deformability, for canonical mass, is 590.83±22.58 - 631.52±78.13 which satisfies the constraints of waveform models analysis of GW170817. A covariance analysis is also performed to calculate the statistical uncertainties in the model parameters and nuclear matter observables along with their correlations.

Can the PREX-2 and CREX results be understood by relativistic mean-field models with the astrophysical constraints?

We construct new effective interactions using the relativistic mean-field models with the isoscalar- and isovector-meson mixing, σ2δ2 and ωμωμρνρν. Taking into account the particle flow data in heavy-ion collisions, the observed mass of PSR J0740+6620, and the tidal deformability of a neutron star from the binary merger event, GW170817, we study the ground-state properties of finite, closed-shell nuclei, and try to explain the recent results from the PREX-2 and CREX experiments. It is found that the σ–δ mixing is very powerful to understand the terrestrial experiments and astrophysical observations of neutron stars self-consistently. We can predict the large neutron skin thickness of 208Pb, Rskin208=0.243 fm, using the slope parameter of nuclear symmetry energy, L=70 MeV, which is consistent with the PREX-2 result. However, to explain the CREX data, it is preferable to adopt the small value of L=20 MeV. It is very difficult to understand the PREX-2 and CREX results simultaneously within relativistic mean-field models.

Theoretical uncertainties count: parity violating asymmetry and dipole polarizability in 208Pb

In this contribution, we overview a recent theoretical work [1] where a sound statistical and systematic analysis based on nuclear Energy Density Functionals of the parity violating asymmetry and dipole polarizability in 208Pb has been presented. Based on our results, we predict a neutron skin thickness in 208Pb which barely overlaps the lower-edge of the estimation presented in [2] and is consistent with much of the previous work.

Tension between implications from PREX-2 data and gravitational tidal response on dense matter equation of state

Recently an improved value of neutron skin thickness of 208Pb was reported in Lead Radius EXperiment-2 (PREX-2) to be Rskin = Rn Rp = (0.283 0.071) fm which corresponds to high estimations of nuclear symmetry energy (Esym) and its slope (Lsym). The updated values of Esym and Lsym commensurating to the neutron star observable estimations lie exterior to the astrophysical observed range. The higher values of Lsym at n0 deduced from recent PREX-2 data correlates to matter being easily deformable (yielding higher radius values) around intermediate matter densities leading to higher values of Λ̃ creating a tension between the terrestrial and astrophysical observations. In this study, we exploit this tension to constrain the Δ-scalar meson coupling parameter space.

ROLE OF ISOVECTOR-ISOSCALAR COUPLING ON CHARGE RADIUS OF HEAVY AND SUPERHEAVY NUCLEI

We have investigated the effect of the isovector-isoscalar coupling on the finite nuclei and nuclear matter properties, the neutron skin thickness of 208Pb, and the charge radius on heavy and superheavy nuclei calculated by the relativistic mean-field (RMF) model. In this work, we generates two parameter sets, i.e., PTE16 and PTE31. The numbers 16 and 31 denote the isovector-isoscalar coupling terms, while T and E denote the tensor coupling and electromagnetic exchange terms, respectively. We found that PTE16 and PTE31 are compatible with the constraints obtained by R. Essick, et al., arXiv: 2102.10074v1 [nucl-th] (2021). We also found that the increase of the isovector-isoscalar coupling terms gives a significant effect on the binding energy and the charge radius on heavy nuclei except for the charge radius of 208Pb. Increased of the isovector-isoscalar coupling terms make the values of charge radius prediction increase too, but vice versa for the neutron skin thickness and nuclear matter prediction. PTE31 yields symmetry energy J = 31.521 MeV, slope L = 57.643 MeV, and neutron skin thickness = 0.21419 fm. While the β2 correction (for deform nuclei) does not always give a significant effect on the charge radius.

The Hadron-quark Crossover in Neutron Star within Gaussian Process Regression Method

The equations of state of the neutron star at the hadron-quark crossover region are interpolated with the Gaussian process regression (GPR) method, which can reduce the randomness of present interpolation schemes. The relativistic mean-field (RMF) model and Nambu–Jona-Lasinio (NJL) model are employed to describe the hadronic phase and quark phase, respectively. In the RMF model, the coupling term between ω and ρ mesons is considered to control the density-dependent behaviors of symmetry energy, i.e., the slope of symmetry energy L. Furthermore, the vector interaction between quarks is included in the NJL model to obtain the additional repulsive contributions. Their coupling strengths and the crossover windows are discussed in the present framework under the constraints on the neutron star from gravitational-wave detections, massive neutron star measurements, mass–radius simultaneous observation of the NICER Collaboration, and the neutron skin thickness of 208Pb from PREX-II. It is found that the slope of symmetry energy, L, should be around 50−90 MeV and the crossover window is (0.3, 0.6) fm−3 with these observables. Furthermore, the uncertainties of neutron star masses and radii in the hadron-quark crossover regions are also predicted by the GPR method.

Effects of Isoscalar- and Isovector-scalar Meson Mixing on Neutron Star Structure

Based on the accurately calibrated interaction FSUGold, we show that including isovector-scalar δ meson and its coupling to isoscalar-scalar σ meson in the relativistic mean-field (RMF) model can soften the symmetry energy E sym(n) at intermediate densities while stiffening the E sym(n) at high densities. We find this new RMF model can be simultaneously compatible with (1) the constraints on the equation of state of symmetric nuclear matter at suprasaturation densities from flow data in heavy-ion collisions; (2) the neutron skin thickness of 208Pb from the PREX-II experiment; (3) the largest mass of a neutron star (NS) reported so far from PSR J0740+6620; (4) the limit of Λ1.4 ≤ 580 for the dimensionless tidal deformability of the canonical 1.4 M ⊙ NS from the gravitational-wave signal GW170817; (5) the mass–radius relation of PSR J0030+0451 and PSR J0740+6620 measured by NICER. The new model thus removes the tension between PREX-II and GW170817 observed in the conventional RMF model.

Impact of PREX-II and Combined Radio/NICER/XMM-Newton’s Mass–radius Measurement of PSR J0740+6620 on the Dense-matter Equation of State

Abstract In this paper, we discuss the impact of the following laboratory experiments and astrophysical observation of neutron stars (NSs) on their equation of state (EoS): (a) the new measurement of neutron skin thickness of 208Pb, R skin 208 = 0.29 ± 0.07 fm by the PREX-II experiment; (b) the mass measurement of PSR J0740+6620 has been slightly revised down by including additional ∼1.5 yr of pulsar timing data. As well as the radius measurement of PSR J0740+6620 by joint NICER/XMM-Newton collaboration, which has a similar size to PSR J0030+0451. We combine this information using Bayesian statistics along with the previous LIGO/Virgo and NICER observations of NS using a hybrid nuclear+piecewise-polytrope EoS parameterization. Our findings are as follows. (a). Adding PREX-II result yields the value of empirical parameter L = 69 − 19 + 21 MeV, R skin 208 = 0.20 − 0.05 + 0.05 fm, and radius of a 1.4 M ⊙ ( R 1.4 ) = 12.75 − 0.54 + 0.42 km at 1σ confidence interval. We find these inferred values are mostly dominated by the combined astrophysical observations as the measurement uncertainty in R skin 208 by PREX-II is much broader. Also, a better measurement of R skin 208 might have a small effect on the radius of low-mass NSs but, for the high masses, there will be almost no effect. (b) After adding the revised mass and radius measurement of PSR J0740+6620, we find the inferred radii of NSs are slightly pushed toward the larger values and the uncertainty on the radius of a 2.08 M ⊙ NS is moderately improved.

Implications of PREX-2 on the electric dipole polarizability of neutron-rich nuclei

The recent announcement by the PREX collaboration of an unanticipated thick neutron skin in 208Pb (Rskin208) has challenged our understanding of neutron rich matter in the vicinity of nuclear saturation density. Whereas earlier constraints indicate that the symmetry energy is relatively soft, the PREX-2 result seems to suggest the opposite. We confront constraints on the symmetry energy obtained from measurements of the electric dipole polarizability against those informed by the PREX-2 measurement of Rskin208 and by the correlations that it entails. Covariant energy density functionals informed by the properties of finite nuclei are used to compute the electric dipole response of 48Ca, 68Ni, 132Sn, and 208Pb. The set of functionals used in this work are consistent with experimental data, yet are flexible enough in that they span a wide range of values of Rskin208. It is found that theoretical predictions of the electric dipole polarizability that are consistent with the PREX-2 measurement systematically overestimate the corresponding values extracted from the direct measurements of the distribution of electric dipole strength. The neutron skin thickness of 208Pb extracted from parity violating electron scattering and the electric dipole polarizability measured in photoabsorption experiments are two of the cleanest experimental tools used to constrain the symmetry energy around nuclear saturation density. However, the recent value of Rskin208 that suggests a fairly stiff symmetry energy stands in stark contrast to the conclusions derived from the electric dipole polarizability. At present, we offer no solution to this dilemma.

Electric Dipole Polarizability of Neutron Rich Nuclei

AbstractInsights into the equation of state of neutron rich matter obtained from the neutron skin thickness of 208Pb are in sharp conflict with earlier measurements of the electric dipole polarizability. A set of accurately calibrated energy density functionals are used to highlight the tension and to articulate how a highly‐intense Gamma Factory may help resolve the present dilemma.

Nuclear symmetry energy parameters from neutron skin thickness in 208Pb and electric dipole polarizability in 68Ni , 120Sn and 208Pb

Observables like neutron skin thickness and electric dipole polarizability in heavy nuclei are considered as most effective probes for the density dependence of nuclear symmetry energy at subsaturation density region. In the present work, within the framework of droplet model, we use finite range effective interactions to calculate the neutron skin thickness in 208Pb and the electric dipole polarizability in 68Ni, 120Sn and 208Pb. We correlate these quantities with the parameters of nuclear symmetry energy. Available experimental data on the neutron skin thickness in 208Pb and electric dipole polarizability in 68Ni, 120Sn and 208Pb are used to deduce information on the density slope parameter of nuclear symmetry energy at saturation and at subsaturation densities. Constraints such as 35.2 ≤ L(ρ 0) ≤ 64.4 MeV and 43 ≤ L(ρ c ) ≤ 55 MeV are obtained using experimental values for neutron skin thickness.

Nuclear symmetry energy and neutron skin thickness of 208Pb using a finite range effective interaction

We use a finite range simple effective interaction to construct nuclear equations of state for the study of the density dependence of the nuclear symmetry energy. The EoSs provide good descriptions of the nuclear symmetry energy at a subsaturation density ρc = 0.11 fm−3 and at a density around two times the saturation density ρ0. We obtain a correlation between the neutron skin thickness in 208Pb and the density slope parameter at the subsaturation density. A linear relation is obtained between the neutron skin thickness and the parameter , where Es(ρ0) and L(ρc) are respectively the nuclear symmetry energy at saturation density and the density slope parameter at the subsaturation density.

Constraints on neutron skin thickness and symmetry energy of 208Pb through Skyrme forces and cluster model

We used the cluster structure properties of the 212Po to estimate the neutron skin thickness of 208Pb. For this purpose, we considered two important components: (a) alpha decay is a low energy phenomenon; therefore, one can expect that the mean-field, which can explain the ground state properties of 212Po, does not change during the alpha decay process. (b) 212Po has a high alpha cluster-like structure, two protons and two neutrons outside its core nucleus with a double magic closed-shell, and the cluster model is a powerful formalism for the estimation of alpha decay preformation factor of such nuclei. The slope of the symmetry energy of 208Pb is estimated to be MeV within the selected same mean-fields and Skyrme forces, which can simultaneously satisfy the ground-state properties of parent and daughter nuclei, as their neutron skin thicknesses are consistent with experimental data.

Electroweak probes of ground state densities

Elastic electron scattering has been used to paint the most accurate picture of the proton distribution in atomic nuclei. Spurred by new experimental developments, it is now possible to gain valuable insights into the neutron distribution using exclusively electroweak probes. Our goal is to assess the information content and complementarity of the following three electroweak experiments in constraining the neutron distribution of atomic nuclei: (a) parity violating elastic electron scattering, (b) coherent elastic neutrino nucleus scattering, and (c) elastic electron scattering of unstable nuclei. Relativistic mean-field models informed by the properties of finite nuclei and neutron stars are used to compute ground state densities and form factors of a variety of nuclei. All the models follow the same fitting protocol, except for the assumed and presently unknown value of the neutron skin thickness of 208Pb. This enables one to tune the density dependence of the symmetry energy without compromising the success in reproducing well known physical observables. We found that the ongoing PREX-II and upcoming CREX campaigns at Jefferson Lab will play a vital role in constraining the weak form factor of xenon and argon, liquid noble gases that are used for the detection of both neutrinos and dark matter particles. We concluded that remarkable new advances in experimental physics have opened a new window into ground state densities of atomic nuclei using solely electroweak probes. The diversity and versatility of these experiments reveal powerful correlations that impose important nuclear structure constraints. In turn, these constraints provide quantitative theoretical uncertainties that are instrumental in searches for new physics and insights into the behavior of dense matter.

Chiral Effective Field Theory for Nucleonic Matter

Predictions for the interaction part of the symmetry energy obtained from different microscopic approaches are reviewed and discussed in comparison with updated constraints recently obtained at GSI. The discussion is then extended to the neutron skin thickness in 208Pb and its relation to the density derivative of the symmetry energy. We highlight the importance of giving proper consideration to theoretical uncertainties of microscopic predictions in order to guide phenomenological analyses.

Searching for isovector signatures in the neutron-rich oxygen and calcium isotopes

We search for potential isovector signatures in the neutron-rich oxygen and calcium isotopes within the framework of a relativistic mean-field theory with an exact treatment of pairing correlations. To probe the isovector sector we calibrate a few relativistic density functionals using the same isoscalar constraints but with one differing isovector assumption. It is found that under certain conditions, the isotopic chain in oxygen can be made to terminate at the experimentally observed 24O isotope and in the case of the calcium isotopes at 60Ca. To produce such behavior, the resulting symmetry energy must be soft, with predicted values for the symmetry energy and its slope at saturation density being J=(30.92±0.47) MeV and L=(51.0±1.5) MeV, respectively. As a consequence, the neutron-skin thickness of 208Pb is rather small: Rskin208=(0.161±0.011) fm. This same model—labeled “FSUGarnet”—predicts R1.4=(13.0±0.1) km for the radius of a “canonical” 1.4M⊙ neutron star, yet is also able to support a two-solar-mass neutron star.

Symmetry energy at subsaturation densities and the neutron skin thickness of 208Pb

The mass-dependent symmetry energy coefficients $a_{sym}(A)$ has been extracted by analysing the heavy nuclear mass differences reducing the uncertainties as far as possible in our previous work. Taking advantage of the obtained symmetry energy coefficient $a_{sym}(A)$ and the density profiles obtained by switching off the Coulomb interaction in $^{208}\text{Pb}$, we calculated the slope parameter $L_{0.11}$ of the symmetry energy at the density of $0.11\text{fm}^{-3}$. The calculated $L_{0.11}$ ranges from 40.5 MeV to 60.3 MeV. The slope parameter $L_{0.11}$ of the symmetry energy at the density of $0.11\text{fm}^{-3}$ is also calculated directly with Skyrme interactions for nuclear matter and is found to have a fine linear relation with the neutron skin thickness of $^{208}\text{Pb}$, which is the difference of the neutron and proton rms radii of the nucleus. With the linear relation the neutron skin thickness $ \Delta R_{np} $ of $^{208}\text{Pb}$ is predicted to be 0.15 - 0.21 fm.

Form factor effects in the direct detection of isospin-violating dark matter

Isospin-violating dark matter (IVDM) provides a possible mechanism to ameliorate the tension among recent direct detection experiments. For IVDM, we demonstrate that the results of direct detection experiments based on neutron-rich target nuclei may depend strongly on the density dependence of the symmetry energy which is presently largely unknown and controls the neutron skin thickness that reflects the relative difference of neutron and proton form factors in the neutron-rich nuclei. In particular, using the neutron and proton form factors obtained from Skyrme-Hartree-Fock calculations by varying the symmetry energy within the uncertainty region set by the latest model-independent measurement of the neutron skin thickness of 208Pb from PREX experiment at JLab, we find that, for IVDM with neutron-to-proton coupling ratio fixed to fn/fp=-0.7, the form factor effect may enhance the sensitivity of Xe-based detectors (e.g., XENON100 and LUX) to the DM-proton cross section by a factor of 3 in the DM mass region constrained by CMDS-II(Si) and even by more than an order of magnitude for heavy DM with mass larger than 80 GeV, compared with the results using the empirical Helm form factor. Our results further indicate that the form factor effect can significantly modify the recoil spectrum of Xe-based detectors for heavy IVDM with fn/fp=-0.7.

Electric dipole response of 208Pb from proton inelastic scattering: Constraints on neutron skin thickness and symmetry energy

The electric dipole (E1) response of 208Pb has been precisely determined by measuring Coulomb excitation induced by proton scattering at very forward angles. The electric dipole polarizability, defined as inverse energy-weighted sum rule of the E1 strength, has been extracted as 20.1+-0.6 fm^3. The data can be used to constrain the neutron skin thickness of 208Pb to 0.168(+-0.009)_expt(+-0.013)_theo(+-0.021)_est fm, where the subscript "expt" refers to the experimental uncertainty, "theor" to the theoretical confidence band and "est" to the uncertainty associated with the estimation of the symmetry energy at the saturation density. In addition, a constraint band has been extracted in the plane of the symmetry energy (J) and its slope parameter (L) at the saturation density.