Temperature-dependent symmetry energy of neutron-rich thermally fissile nuclei

Background: The density-dependent symmetry energy coefficient plays a crucial role in understanding a variety of issues in nuclear physics as well as nuclear astrophysics. It is quite interesting and crucial to determine the symmetry energy coefficient and its related observables for neutron-rich thermally fissile nuclei at finite temperature.

Purpose: We evaluate the symmetry energy coefficient, neutron pressure, and symmetry energy curvature of a finite nucleus from the corresponding quantities of infinite nuclear matter. Moreover, we correlate an effective symmetry energy coefficient and its related observables with the neutron skin thickness of neutron-rich thermally fissile nuclei at a finite temperature.

Methods: The temperature-dependent relativistic mean field model (TRMF) is used to obtain the ground and excited state bulk properties of finite nuclei and the energy density, pressure, and the symmetry energy for infinite nuclear matter. The TRMF model with FSUGarnet, IOPB-I, and NL3 parameter sets is used for the present analysis. The effective nuclear matter properties are used to estimate the corresponding quantities of finite nuclei by using the local density approximation.

Results: Nuclear bulk properties such as binding energy, quadrupole deformation, root-mean-square charge radius of the nuclei, and the equation of state and symmetry energy for infinite symmetric nuclear matter are estimated within the TRMF model. The nuclear matter observables at the local density of the nuclei serve as an input to obtain the effective symmetry energy coefficient, neutron pressure, and the symmetry energy curvature of ${}^{234,236,250}\mathrm{U}$ and ${}^{240}\mathrm{Pu}$ nuclei. The influence of temperature and density on these properties for neutron-rich thermally fissile nuclei is observed. A correlation is established between the neutron skin thickness and the neutron pressure of the nuclei.

Conclusions: The studied properties of nuclei such as effective symmetry energy coefficient, neutron pressure and symmetry energy curvature can be used in the synthesis of neutron-rich thermally fissile nuclei. The method presented here (fully microscopic) can be used further to study the properties of exotic and superheavy nuclei from the corresponding quantities of nuclear matter and vice versa.

Figure 1

The energy density and pressure for SNM and PNM at zero temperature with FSUGarnet, IOPB-I, and NL3 parameter sets. The calculated results are compared with the results by Hebeler [75], the DBHF equation of state [76, 77], and the available experimental data [78].

Figure 2

(a) The symmetry energy ($S^{NM}$) of infinite SNM at zero temperature for the FSUGarnet, IOPB-I, and NL3 parameter sets. (b) The same quantity at finite temperature corresponding to IOPB-I. The zoomed part shows $S^{NM}$ at low density.

Figure 3

The densities of the nuclei ${}^{234}\mathrm{U}$ (left panel) and ${}^{250}\mathrm{U}$ (right panel) corresponding to the IOPB-I set at finite $T$. The zoomed part shows the effect of $T$ on the density at the surface of the nuclei.

Figure 4

The symmetry energy of nuclear matter $S^{NM}[\rho \left(r\right),T]$ at the local density of ${}^{250}\mathrm{U}$ (a) at $T=0$ MeV corresponding to the FSUGarnet, IOPB-I, and NL3 parameter sets, and (b) at finite $T$ corresponding to the IOPB-I set. The zoomed part of panel (b) shows the effect of $T$ at low density.

Figure 5

The effective symmetry energy coefficient ($S$) of ${}^{234,236,250}\mathrm{U}$ and ${}^{240}\mathrm{Pu}$ at finite $T$.

Figure 6

The effective neutron pressure ($P$) of the nuclei ${}^{234,236,250}\mathrm{U}$ and ${}^{240}\mathrm{Pu}$ at finite $T$ for the chosen parameter sets.

Figure 7

The symmetry energy curvature ($K_{\mathrm{sym}}$) of the nuclei ${}^{234,236,250}\mathrm{U}$ and ${}^{240}\mathrm{Pu}$ at finite $T$.

Figure 8

The variation of the symmetry energy coefficient with the neutron skin thickness for the FSUGarnet, IOPB-I, and NL3 parameter sets. The circle, square, triangle up, and triangle down symbols correspond to the values at temperature 0, 1, 2, and 3 MeV.

Figure 9

The effective neutron pressure $P$ for (a) ${}^{234}\mathrm{U}$, (b) ${}^{236}\mathrm{U}$, (c) ${}^{240}\mathrm{Pu}$, and (d) ${}^{250}\mathrm{U}$, as a function of the neutron skin thickness $\mathrm{\Delta }r$ for the three parameter sets FSUGarnet, IOPB-I, and NL3. The lines in all panels represent a linear fit.

Figure 10

The effective neutron pressure $P$ as a function of the neutron skin thickness $\mathrm{\Delta }r$ for ${}^{250}\mathrm{U}$ at temperatures $T=1,2,3$ MeV [panels (a), (b), and (c), respectively] for the three parameter sets FSUGarnet, IOPB-I, and NL3. The lines in all panels represent a linear fit.