Effect of Coulomb energy on the symmetry energy coefficients of finite nuclei

Abstract

The nuclear symmetry energy coefficients of finite nuclei are extracted by using the differences between the masses of isobaric nuclei. Based on the masses of more than 2400 nuclei with A = 9 − 270, we investigate the model dependence in the extraction of symmetry energy coefficient. We find that the extraction of the symmetry energy coefficients is strongly correlated with the forms of the Coulomb energy and the mass dependence of the symmetry energy coefficient adopted. The values of the extracted symmetry energy coefficients increase by about 2 MeV for heavy nuclei when the Coulomb correction term is involved. We obtain the bulk symmetry energy coefficient S 0 = 28.26 ± 1.3 MeV and the surface-to-volume ratio κ = 1.26 ± 0.25 MeV if assuming the mass dependence of symmetry energy coefficient a sym (A) = S 0 (1 − κ/A 1/3 ), and S 0 = 32.80 ± 1.7 MeV, κ = 2.82 ± 0.57 MeV when a sym (A) = S 0 (1 + κ/A 1/3 ) −1 is adopted.

Mass dependence of symmetry energy coefficients in the Skyrme force

“…In Refs. [17][18][19] all these different models give quite similar predictions a sym = 22.90 ± 0.15 MeV. With the ETF2 approach, the corresponding result from SkM* is a sym = 22.95 MeV, which is in good agreement with the results in Fig.…”

“…Although a great effort has been devoted in recent decades to investigate the symmetry energy [2][3][4][5][6][7][8], the density dependence of the symmetry energy, even at sub-saturation density region, is not very well constrained. One usually obtains the information of the symmetry energy from nuclear dynamical behavior in reactions [9][10][11] and the static properties of finite nuclei such as nuclear masses [12][13][14][15][16][17][18][19] and neutron skin thickness [20][21][22][23], or from the asymmetric nuclear matter based on various effective interactions [24][25][26], or from the observables in nuclear astrophysics. To understand the behavior of symmetry energy in nuclear masses and nuclear matter, it is crucial to establish a reliable connection between the mass dependence of the symmetry energy coefficient a sym (A) of finite nuclei and the density dependence of the symmetry energy E sym (ρ) of nuclear matter, with which the obtained symmetry energy coefficients from various macroscopic-microscopic or liquid-drop models could be used to constrain the behavior of E sym (ρ) at sub-saturation densities.…”

Effect of Wigner energy on the symmetry energy coefficient in nuclei

“…The Wigner energy can be extracted from the difference of e n (A, I) of isobaric nuclei. However the Wigner energy is not included in extracting the symmetry energy coefficient in our previous paper [24]. The nature of the symmetry and Wigner energy are intertwined in the nuclear mass formula and that one term cannot be reliably determined without knowledge of the other [25].…”

Density dependence of nuclear symmetry energy

“…From the values of L(ρ 0 ) and K asy (ρ 0 ) in table 1 as well as from Fig.2(a) it can be seen that the exponential form with V s (ρ 0 ) = 20M eV (Set-IIB) and the other form with V s (ρ 0 ) = 16M eV ( Set-IA) constitute the two extreme curves for V s (ρ). The density dependence of nuclear symmetry energy E s (ρ) obtained with these two extreme curves of V s (ρ) are given in Figure 2 (9) and (10). The corresponding values of nuclear symmetry energy E s (ρ 0 ), slope parameter L(ρ 0 ) and isospin part of isobaric incompressibility K asy (ρ 0 ) at saturation density are also listed.…”

“…Significant progress has been made to constrain the nuclear symmetry energy at low densities from dynamical behaviour [1,2], resonances and excitations [3][4][5][6][7], static properties of finite nuclei [8][9][10][11][12] and neutron skin thickness [13][14][15][16][17][18]. However, the high density behaviour of E s (ρ) is not yet well determined, particularly, at densities much above the saturation point ρ 0 and at densities that occur in neutron star core.…”