Effect of nuclear matter incompressibility on the ${}^{16}\text{O}+{}^{208}\text{Pb}$ system

To analyze the property of nuclear matter in the ${}^{16}\text{O}+{}^{208}\text{Pb}$ collision system, the internuclear potential of the fusion reaction is calculated by using the Skyrme forces associated with an extensive nuclear matter incompressibility $K$ range in the semiclassical energy-density formalism. Comparison of the experimental fusion cross sections and those obtained by using potentials derived from different forces with various $K$ values shows that the incompressibility of nuclear matter changes during the fusion process at different bombarding energies. The results indicate that, as the energy increases, the nuclear matter becomes more incompressible.

Figure 1

The neutron and proton density distributions of (a) the ${}^{16}\text{O}$ and (b) ${}^{208}\text{Pb}$ nuclei obtained by using the SkSC4 and SI Skyrme interactions in the HFB approximation.

Figure 2

The percentage relative deviations, i.e., $\left|\right(\text{Theor.}-\text{Expt.})/\text{Expt.}|\times 100\%$ of (a) the theoretical binding energies and (b) root-mean-square charge radii from their experimental data for the ${}^{16}\text{O}$ and ${}^{208}\text{Pb}$ nuclei. The incompressibility values corresponding to the Skyrme forces are displayed on the top horizontal axis.

Figure 3

The calculated diffuseness parameters of the neutron and proton density distributions, $a_{n,p}$, for (a) the ${}^{16}\text{O}$ and (b) ${}^{208}\text{Pb}$ nuclei. The incompressibility values corresponding to the Skyrme forces are displayed on the top horizontal axis.

Figure 4

(a) The theoretical fusion barrier heights and (b) positions calculated from different Skyrme forces for the ${}^{16}\text{O}+{}^{208}\text{Pb}$ system. The incompressibility values corresponding to the Skyrme forces are displayed on the top horizontal axis.

Figure 5

The fusion cross sections of the ${}^{16}\text{O}+{}^{208}\text{Pb}$ system calculated with the potentials obtained from different Skyrme forces. The experimental data were taken from Ref. [40].

Figure 6

The fusion cross sections of the ${}^{16}\text{O}+{}^{208}\text{Pb}$ system calculated with the potentials derived from different Skyrme forces and the density parameters obtained from the SkP Skyrme force.

Figure 7

The fusion barrier distributions for the ${}^{16}\text{O}+{}^{208}\text{Pb}$ system calculated by using the cross sections derived from different Skyrme forces and their corresponding density distributions.

Figure 8

The predicted values of the nuclear matter incompressibility in the ${}^{16}\text{O}+{}^{208}\text{Pb}$ system at different bombarding energies. The temperature of the compound nucleus corresponding to each energy is displayed on the top horizontal axis.

Figure 9

The fusion cross sections of the ${}^{40}\text{Ca}+{}^{90}\text{Zr}$ system calculated with the potentials obtained from the SkT4, $\mathrm{SkT}{1}^{*}$, SK255, and SK272 Skyrme forces and their corresponding density distributions. The experimental data were taken from Ref. [46].