Density dependence of the nuclear symmetry energy constrained by mean-field calculations

Within the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, the transverse-velocity dependence of the elliptic flow of free nucleons from 197 Au+ 197 Au collisions at the incident energy 400 MeV/nucleon is studied within different windows of the normalized c.m. rapidity y 0 . It is found that the elliptic flow difference v n 2 -v p 2 and ratio v n 2 /v p 2 of neutrons versus protons are sensitive to the density dependence of the symmetry energy, especially the ratio v n 2 /v p 2 at small transverse velocity in the intermediate rapidity intervals 0.4 < |y 0 | < 0.6. By comparing either transverse-momentum dependent or integrated FOPI/LAND elliptic flow data of nucleons and hydrogen isotopes with calculations using various Skyrme interactions, all exhibiting similar values of isoscalar incompressibility but very different density dependences of the symmetry energy, a moderately soft to linear symmetry energy is extracted, in good agreement with previous UrQMD or Tübingen QMD model calculations but contrasting results obtained with π − /π + yield ratios available in the literature.

Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Constraining the high-density nuclear symmetry energy with the transverse-momentum-dependent elliptic flow

Wang

Guo

et al. 2014

“…The binding energies of stable atomic nuclei are the most accurately known experimental entities in nuclear physics; these supplemented with knowledge of giant monopole and dipole resonances followed by theoretical analysis have yielded some of the EoS parameters such as the saturation density ρ 0 of symmetric nuclear matter and e(ρ 0 ), K(ρ 0 ), and e sym (ρ 0 ) in reasonably tight bounds [1][2][3][4][5][6]. The knowledge of the symmetry derivatives L(ρ 0 ) and K τ (ρ 0 ) is still not very certain [1,[7][8][9]. Analyses of the different nuclear observables do not help much in removing the uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Equation of state of nuclear matter from empirical constraints

Alam

Agrawal

et al. 2014

From empirically determined values of some of the characteristic constants associated with homogeneous nuclear matter at saturation and subsaturation densities, within the framework of a Skyrme-inspired energy density functional, we construct an equation of state (EoS) of nuclear matter.This EoS is then used to predict values of density slope parameters of symmetry energy L(ρ), isoscalar incompressibility K(ρ), and a few related quantities. The close consonance of our predicted values with the currently available ones for the density dependence of symmetry energy and incompressibility gleaned from diverse approaches offers the possibility that our method may help in settling their values in tighter bounds. Extrapolation of our EoS at supranormal densities shows that it is in good harmony with the one extracted from experimental data.

“…(6) (case I) has some limitations [39]. With this functional form, C v (ρ 0 ), L and K sym , when calculated from Eqs.…”

mentioning

confidence: 99%

“…In the present communication we use different functional forms for the C v (ρ), employed very recently in Ref. [39,40] in checking the validation of the relationship between C v (ρ 0 ), L and K sym using different effective interactions. Our calculations are performed for both the spherical and well deformed 208 Pb and 238 U nuclei, respectively.…”

mentioning

confidence: 99%

Constraining the density dependence of the symmetry energy from nuclear masses

Agrawal

Samaddar

et al. 2013

Empirically determined values of the nuclear volume and surface symmetry energy coefficients from nuclear masses are expressed in terms of density distributions of nucleons in heavy nuclei in the local density approximation. This is then used to extract the value of the symmetry energy slope parameter L. The density distributions in both spherical and well deformed nuclei calculated within microscopic framework with different energy density functionals give L = 59.0 ± 13.0 MeV. Application of the method also helps in a precision determination of the neutron skin thickness of nuclei that are difficult to measure accurately. The nuclear symmetry energy measures the energy transfer in converting symmetric nuclear matter to the asymmetric one. The density dependence gives information on the isospin-dependent part of the equation of state (EOS) of asymmetric nuclear matter. The density content of symmetry energy is mostly encoded in the symmetry energy coefficient C v , the symmetry slope parameter L and the symmetry incompressibility K sym , all evaluated at the nuclear saturation density ρ 0 . Here C v (ρ) is the volume symmetry energy per nucleon of homogeneous nuclear matter at density ρ,andIn Eq. (1), e is the energy per nucleon and X = (ρ n − ρ p )/(ρ n +ρ p ) is the isospin asymmetry of the system. The parameters C v (ρ 0 ), L and K sym deem to be of fundamental importance in both nuclear physics and astrophysics. The nuclear binding energies, the position of the nuclear drip lines, the neutron skin thickness or the neutron density distribution in neutron-rich nuclei, − all of these are known to have affectations from [1-8] the symmetry parameters so mentioned. Many astrophysical phenomena also depend sensitively on the symmetry slope parameter L. Most notable among them are the dynamical evolution of the core collapse of a massive star and the associated explosive nucleosynthesis [9, 10], the cooling of proto-neutron stars through neutrino convection [11] or the radii of cold neutron stars [11]. The nature and stability of phases within a neutron star, its crustal com-[12] also seem to be strongly influenced by the symmetry energy and its density dependence. A glimmer of their import could further be seen in relation to some issues of new physics beyond the standard model [13,14]. Attempts on estimates of L have been made in the last few years from analyses of diverse experimental data, uncertainties still linger, however. Pygmy dipole resonance [15] in 68 N i and 132 Sn predicts a weighted average in the range L=64.8 ± 15.7 MeV, but giant dipole resonance in 208 P b [16] points to a value of L ∼ 52 ±7 MeV. Nucleon emission ratios from heavy ion collisions [17] favor a value close to it, L ∼ 55 MeV, but isoscaling gives L ∼ 65 MeV [18] and isospin diffusion shifts the value further up, L = 88 ± 25 MeV [19,20]. Recently, analyzing nuclear energies within the standard Skyrme-Hartree-Fock approach, Chen [21] brought down L to 52.5 ± 20 MeV. However, from the fit [3] of the experimental nuclear masses to the calc...