Search NASA⌕ Search

SEARCH · Search NASA

Results for “Symmetry energy”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The Symmetry Energy: Current Status of Ab Initio Predictions vs. Empirical Constraints

Infinite nuclear matter is a suitable laboratory to learn about nuclear forces in many-body systems. In particular, modern theoretical predictions of neutron-rich matter are timely because of recent and planned experiments aimed at constraining the equation of state of isospin-asymmetric matter. For these reasons, we have taken a broad look at the equation of state of neutron-rich matter and the closely related symmetry energy, which is the focal point of this article. Its density dependence is of paramount importance for a number of nuclear and astrophysical systems, ranging from neutron skins to the structure of neutron stars. We review and discuss ab initio predictions in relation to recent empirical constraints. We emphasize and demonstrate that free-space nucleon–nucleon data pose stringent constraints on the density dependence of the neutron matter equation of state, which essentially determines the slope of the symmetry energy at saturation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Rapidity distributions of Z = 1 isotopes and the nuclear symmetry energy from Sn+Sn collisions with radioactive beams at 270 MeV/nucleon

The rapidity distributions of hydrogen isotopes emitted from central collisions of neutron-rich 132 Sn+ 124 Sn and neutron-deficient 108 Sn+ 112 Sn systems at 270 MeV/nucleon were investigated at RIKEN-RIBF. The data are compared with antisymmetrized molecular dynamics (AMD) calculations and the rapidity distributions can be reproduced after adjusting the in-medium nucleon-nucleon cross sections. The double ratios between the two reaction systems taken for the relative yields of deuteron to proton (d/p) and triton to proton (t/p) are further examined in the midrapidity domain, where the adjustments in the AMD calculations do not affect much on them. The d/p and t/p double ratios at midrapidity agree well with the ratio of the system neutron numbers and its squared value, respectively, and the rapidity dependence of these double ratios is consistent with a picture of partial mixing of colliding nuclei. By comparing with the AMD model which shows a strong symmetry energy dependence of the t/p double ratio, the experimental result in the midrapidity domain favors the calculation with a symmetry-energy slope parameter around L = 46 MeV rather than L = 108 MeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Bayesian inference of nuclear symmetry energy from measured and imagined neutron skin thickness in Sn 116 , 118 , 120 , 122 , 124 , 130 , 132 , Pb 208 , and Ca 48

The neutron skin thickness Δr np in heavy nuclei has been known as one of the most sensitive terrestrial probes of the nuclear symmetry energy E sym (ρ) around $\frac{2}{3}$ of the saturation density ρ 0 of nuclear matter. Existing neutron skin data mostly from hadronic observables suffer from large uncertainties and their extraction from experiments are often strongly model dependent. While waiting eagerly for the promised model-independent and high-precision neutron skin data for 208 Pb and 48 Ca from the parity-violating electron scattering experiments (PREX-II and CREX at JLab as well as MREX at MESA), within the Bayesian statistical framework using the Skyrme-Hartree-Fock model we infer the posterior probability distribution functions (PDFs) of the slope parameter L of the nuclear symmetry energy at ρ 0 from imagined Δr np ( 208 Pb)=0.15, 0.20, and 0.30 fm with a 1σ error bar of 0.02, 0.04, and 0.06 fm, respectively, as well as Δr np ( 48 Ca)=0.12, 0.15, and 0.25 fm, with different 1σ error bar of 0.01 and 0.02 fm, respectively. The results are compared with the PDFs of L inferred using the same approach from the available Δr np data for 116, 118, 120, 122, 124, 130, 132 Sn from hadronic probes. They are also compared with results from a recent Bayesian analysis of the radius and tidal deformability data of canonical neutron stars from GW170817 and NICER. The neutron skin data for Sn isotopes gives L = 45.5 $^{+ 26.5}_{-21.6}$ MeV surrounding its mean value or L = 53 . 4 $^{+ 18.6}_{ -29.5}$ MeV surrounding its maximum a posteriori value, respectively, with the latter smaller than but consistent with the L = 66 $^{+ 12}_{-20}$ MeV from the neutron star data within their 68% confidence intervals. We found that Δr np = 0.17 –0.18 fm in 208 Pb with an error bar of about 0.02 fm leads to a PDF of L compatible with that from analyzing the Sn data. To provide additionally useful information on L extracted from the Δr np of Sn isotopes, the experimental error bar of Δr np in 208 Pb should be at least smaller than 0.06 fm aimed by some current experiments. In addition, the Δr np ( 48 Ca) needs to be larger than 0.15 fm but smaller than 0.25 fm to be compatible with the Sn and/or neutron star results. To further improve our current knowledge about L and distinguish its PDFs in the examples considered, even higher precisions leading to significantly less than ±20 MeV error bars for L at 68% confidence level are necessary.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Impact of NICER’s Radius Measurement of PSR J0740+6620 on Nuclear Symmetry Energy at Suprasaturation Densities

By directly inverting several neutron star observables in the three-dimensional parameter space for the Equation of State of super-dense neutron-rich nuclear matter, we show that the lower radius limit for PSR J0740 + 6620 of mass 2.08 ± 0.07 M ⊙ from Neutron Star Interior Composition Explorer (NICER)'s very recent observation sets a much tighter lower boundary than previously known for nuclear symmetry energy in the density range of (1.0 ~ 3.0) times the saturation density ρ 0 of nuclear matter. Furthermore, the super-soft symmetry energy leading to the formation of proton polarons in this density region of neutron stars is clearly disfavoured by the first radius measurement for the most massive neutron star observed reliably so far.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Investigating effects of relativistic kinematics, dimensionality, interactions, and short-range correlations on the ratio of quartic over quadratic nuclear symmetry energies

While ample evidence for the so-called empirical parabolic law of the Equation of State (EOS) of isospin asymmetric nuclear matter (ANM) has been obtained in many studies within both non-relativistic and relativistic nuclear many-body theories using various interactions, it has been unclear if there is any fundamental physics reason for the small quartic symmetry energy compared to the quadratic one even as the ANM approaches pure neutron matter. Within both relativistic and non-relativistic Free Fermi Gas (FFG) models in coordinate spaces of arbitrary dimension d with and without considering Short-Range Correlations (SRC) as well as non-linear Relativistic Mean Field (RMF) models, we study effects of relativistic kinematics, dimensionality, interactions and SRC on the ratio Ψ(ρ) of quartic over quadratic symmetry energies in ANM EOSs. We found that the ratio Ψ(ρ) in the FFG model depends strongly on the dimension d. While it is very small already in the normal 3D space, it could be even smaller in spaces with reduced dimensions for sub-systems of particles in heavy-ion reactions and/or whole neutron stars due to constraints, collectivities and/or symmetries. Here, we also found that the ratio Ψ(ρ) could theoretically become very large only at the ultra-relativistic limit far above the density reachable in neutron stars. On the other hand, nuclear interaction directly and/or indirectly through SRC-induced high-momentum nucleons affect significantly the density dependence of Ψ(ρ) compared to the relativistic FFG model prediction. The SRC affects significantly not only the kinetic energy of symmetric nuclear matter but also the ratio Ψ(ρ) while the relativistic corrections are found negligible. The results may help better understand the EOS of dense neutron-rich matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

How do mirror charge radii constrain density dependence of the symmetry energy?

It has recently been suggested that differences in the charge radii of mirror nuclei (Δ$R^{mirr}_{ch}$) are strongly correlated with the neutron-skin thickness ($R_{skin}$) of neutron-rich nuclei and with the slope of the symmetry energy ($L$). To test this assumption, we present ab initio calculations of $R_{skin}$ in 48 Ca and 208 Pb, Δ$R^{mirr}_{ch}$ in 36 Ca$-$ 36 S, 38 Ca$-$ 38 Ar, 41 Sc$-$ 41 Ca, 48 Ni$-$ 48 Ca, 52 Ni$-$ 52 Cr, and 54 Ni$-$ 54 Fe mirror pairs, and $L$. Employing the recently developed 34 chiral interaction samples, identified by the history matching approach, we conduct rigorous statistical analysis of correlations among Δ$R^{mirr}_{ch}$, $R_{skin}$ and $L$, accounting for quantified uncertainties from low-energy constants of chiral interaction, chiral effective field theory truncation and many-body method approximation. The ab initio results reveal an appreciable Δ$R^{mirr}_{ch}$ $-$ $L$ correlation in $fp$-shell mirror pairs. However, contrary to previous studies, the present calculation finds that the studied $sd$-shell mirror pairs do not exhibit any Δ$R^{mirr}_{ch}$ $-$ $L$ correlation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Charge Radius of Neutron-Deficient Ni 54 and Symmetry Energy Constraints Using the Difference in Mirror Pair Charge Radii

he nuclear root-mean-square charge radius of Ni 54 was determined with collinear laser spectroscopy to be R ( Ni 54 ) = 3.737 ( 3 ) fm . In conjunction with the known radius of the mirror nucleus Fe 54 , the difference of the charge radii was extracted as Δ R ch = 0.049 ( 4 ) fm . Based on the correlation between Δ R ch and the slope of the symmetry energy at nuclear saturation density ( L ), we deduced 21 ≤ L ≤ 88 MeV . The present result is consistent with the L from the binary neutron star merger GW170817, favoring a soft neutron matter EOS, and barely consistent with the PREX-2 result within 1 σ error bands. Our result indicates the neutron-skin thickness of Ca 48 as 0.15–0.21 fm.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Curvature-slope correlation of nuclear symmetry energy and its imprints on the crust-core transition, radius, and tidal deformability of canonical neutron stars

Background: The nuclear symmetry energy E sym (ρ) encodes information about the energy necessary to make nuclear systems more neutron-rich. While its slope parameter L at the saturation density ρ 0 of nuclear matter has been relatively well constrained by recent astrophysical observations and terrestrial nuclear experiments, its curvature K sym characterizing the E sym (ρ) around 2ρ 0 remains largely unconstrained. Over 520 calculations for E sym (ρ) using various nuclear theories and interactions in the literature have predicted several significantly different K sym –L correlations. Purpose: If a unique K sym –L correlation of E sym (ρ) can be firmly established, it will enable us to progressively better constrain the high-density behavior of E sym (ρ) using the available constraints on its slope parameter L. Here, we investigate if and by how much the different K sym –L correlations may affect neutron star observables. Method: A meta-model of nuclear Equation of States (EOSs) with three representative K sym –L correlation functions is used to generate multiple EOSs for neutron stars. We then examine effects of the K sym –L correlation on the crust-core transition density and pressure as well as the radius and tidal deformation of canonical neutron stars. Results: The K sym –L correlation affects significantly both the crust-core transition density and pressure. It also has strong imprints on the radius and tidal deformability of canonical neutron stars especially at small L values. The available data from LIGO/VIRGO and NICER set some useful limits for the slope L but can not distinguish the three representative K sym –L correlations considered.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Slope parameter of the symmetry energy and the structure of three-particle interactions in nuclear matter

In the first part of this paper, we present a study of the symmetry energy (a s ) and its slope parameter (L) for nuclear matter in the framework of the Fermi liquid theory of Landau and Migdal. We derive an exact relation between a s and L, which involves the nucleon effective masses and three-particle Landau-Migdal parameters. We present simple estimates which suggest that there are two main mechanisms to explain the empirical values of L: The proton-neutron effective mass difference in isospin asymmetric matter and the ℓ = 0 moment of the isovector in-medium three-particle scattering amplitude. In the second part of this paper, we discuss the general structure of three-particle interactions in nuclear matter in the framework of the Fermi liquid theory. The connections to the Bethe-Brueckner-Goldstone theory and other approaches are also discussed. Finally, we show explicitly how the first few terms in the Faddeev series, together with medium induced three-particle interactions, emerge naturally in the Fermi liquid theory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Beyond $\rho ^{2/3}$ scaling: microscopic origins and multimessengers of high-density nuclear symmetry energy

The nature and Equation of State (EOS) of dense neutron-rich matter are still very poorly known, while they have broad impacts on many interesting issues in both astrophysics and nuclear physics. In particular, the nuclear symmetry energy $E_{\textrm{sym}}(\rho )$ encoding the cost to make nuclear matter more neutron-rich has been the most uncertain component of the EOS of dense neutron-rich nucleonic matter. It significantly affects the radii, tidal deformations, cooling rates, and frequencies of various oscillation modes of isolated neutron stars as well as the strain amplitude and frequencies of gravitational waves from their mergers, besides its many effects on the structures of nuclei as well as the dynamics and observables of their collisions. Siemens (1970s) observed that $E_{\textrm{sym}}(\rho )$ scales as $(\rho /\rho _0)^{2/3}$ near the saturation density $\rho _0$ of nuclear matter, since both the kinetic part and the potential contribution (quadratic in momentum) exhibit this dependence. The scaling holds if: (1) the nucleon isoscalar potential is quadratic in momentum, and (2) the isovector interaction is weakly density-dependent. After examining many empirical evidences and understanding theoretical findings in the literature, we conclude that: (1) Siemens’ $\rho ^{2/3}$ scaling is robust and serves as a valuable benchmark for both nuclear theories and experiments up to $2\rho _0$ but breaks down at higher densities, (2) Experimental and theoretical findings about $E_{\textrm{sym}}(\rho )$ up to $2\rho _0$ are broadly consistent, but uncertainties remain large for its curvature $K_{\textrm{sym}}(\rho )$ and higher-order parameters, (3) Above $2\rho _0$ , uncertainties grow due to poorly constrained spin-isospin-dependent tensor and three-body forces as well as the resulting nucleon short-range correlations. Looking forward, combining signals from both observations of neutron stars and terrestrial heavy-ion reaction experiments is the most promising path to finally constraining the high-density $E_{\textrm{sym}}(\rho )$ and the EOS of supradense neutron-rich matter. Multiple examples of community efforts to further constrain the high-density $E_{\textrm{sym}}(\rho )$ using both real and mocked data of present and future high-precision observations of neutron stars, as well as heavy-ion collisions involving high-energy rare isotopes, are briefly reviewed.

Li, Bao-An [East Texas A & M Univ., Commerce, TX (↗
DOE OSTI2023

Impact of symmetry energy on sound speed and spinodal decomposition in dense neutron-rich matter

Using a meta model for nuclear Equation of State (EOS) with its parameters constrained by astrophysical observations and terrestrial nuclear experiments, we examine effects of nuclear EOS especially its symmetry energy $E$ sym ($ρ$) term on the speed of sound squared $C$ $^2_s$($ρ$) and the critical density ρt where $C$ $^2_s$($ρ_t$) vanishes (indicating the onset of spinodal decomposition) in both dense neutron-rich nucleonic matter relevant for relativistic heavy-ion collisions and the cold $n$ + $p$ + $e$ + $μ$ matter in neutron stars at $β$- equilibrium. Unlike in nucleonic matter with fixed values of the isospin asymmetry $δ$, in neutron stars with a density dependent isospin profile $δ$($ρ$) determined consistently by the $β$-equilibrium and charge neutrality conditions, the $C$ $^2_s$($ρ$) almost always show a peak and then vanishes at $ρ_t$. Furthermore, the latter strongly depends on the high-density behavior of $E$ sym ($ρ$) if the skewness parameter $J$ 0 characterizing the stiffness of high-density symmetric nuclear matter (SNM) EOS is not too far above its currently known most probable value of about -190 MeV inferred from recent Bayesian analyses of neutron star observables. Moreover, in the case of having a super-soft $E$ sym ($ρ$) that is decreasing with increasing density above about twice the saturation density of nuclear matter, the $ρ$ $t$ is significantly lower than the density where the $E$ sym ($ρ$) vanishes (indicating the onset of isospin-separation instability and pure neutron matter formation) in neutron star cores.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Analysis of the neutron matter equation of state and the symmetry energy up to fourth order of chiral effective field theory

We present predictions for the neutron matter equation of state, from leading to fourth order of chiral effective field theory, using recently developed, accurate chiral nucleon-nucleon potentials. For the many-body method, we employ the nonperturbative particle-particle ladder approximation, that is, we solve the G-matrix equation. Furthermore, we find the impact of subleading three-neutron forces to be mild and attractive. We also show order-by-order predictions for the symmetry energy, and discuss its density dependence in relation to empirical constraints. For the nuclear matter equation of state, in this work we adopt an empirical parametrization with good saturation properties. This is to highlight, specifically, the energy and pressure in neutron matter, particularly when comparing with empirical constraints.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Variational Quantum Circuits to Prepare Low Energy Symmetry States

We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally trained unitary that maps any vector output by ansatz A(α → ) from a defined subspace to a vector in the symmetry space. The parameters are trained varitionally to minimize the energy, thus keeping the output within the labelled symmetry value. The method was tested for a spin XXZ Hamiltonian using rotation and reflection symmetry and H 2 Hamiltonian within S z = 0 subspace using S 2 symmetry. We have found the variationally trained unitary gives good results with very low depth circuits and can thus be used to prepare symmetry states within near term quantum computers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗