Probing surface diffuseness of nucleus-nucleus potential with quasielastic scattering at deep sub-barrier energies

We perform a systematic study on the surface property of nucleus-nucleus potential in heavy-ion reactions using large-angle quasielastic scattering at energies well below the Coulomb barrier. At these energies, the quasielastic scattering can be well described by a single-channel potential model. Exploiting this fact, we point out that systems which involve spherical nuclei require the diffuseness parameter of around 0.60 fm in order to fit the experimental data, while systems with a deformed target between 0.8 and 1.1 fm.

Figure 1

The ratio of the quasielastic to the Rutherford cross sections at ${\theta }_{\mathrm{lab}}={159}^{°}$ for the ${}^{32}\mathrm{S}+{}^{197}\mathrm{Au}$ (the upper panel) reaction and for the ${}^{34}\mathrm{S}+{}^{197}\mathrm{Au}$ (the lower panel) reaction. The experimental data are taken from Ref. 14. The solid line results from using a diffuseness parameter obtained by performing a least-square fit to the data. The dotted and the dot-dashed lines are obtained with the diffuseness parameter of $a=0.80$ fm and $a=1.00$ fm, respectively.

Figure 2

The ratio of the quasielastic to the Rutherford cross sections for the ${}^{32}\mathrm{S}+{}^{208}\mathrm{Pb}$ (the upper panel) reaction at ${\theta }_{\mathrm{lab}}={170}^{°}$ and for the ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$ (the lower panel) reaction at ${\theta }_{\mathrm{lab}}={159}^{°}$. The experimental data are taken from Ref. 14. The meaning of each line is the same as in Fig. 1.

Figure 3

The ratio of the quasielastic to the Rutherford cross sections for the ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ reaction at ${\theta }_{\mathrm{lab}}={170}^{°}$. The experimental data are taken from Ref. 15. The meaning of each line is the same as in Fig. 1.

Figure 4

Comparison of quasielastic cross sections obtained for three different values of the Coulomb barrier height for the ${}^{32}\mathrm{S}+{}^{208}\mathrm{Pb}$ reaction. The surface diffuseness parameter is determined for each barrier energy by fitting the experimental data.

Figure 5

The ratio of the quasielastic to the Rutherford cross sections for the ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ reaction at ${\theta }_{\mathrm{lab}}={170}^{°}$. The solid line is obtained using the best fitted value of the surface diffuseness parameter, $a=1.14$ fm. The dotted line denotes the cross sections obtained with the diffuseness parameter of $a=0.60$ fm. The experimental data are taken from Ref. 16.

Figure 6

The ratio of the quasielastic to the Rutherford cross sections for the ${}^{16}\mathrm{O}+{}^{186}\mathrm{W}$ reaction at ${\theta }_{\mathrm{lab}}={170}^{°}$. The meaning of each line is the same as in Fig. 5. The experimental data are taken from Ref. 16.

Figure 7

The best fitted values of the surface diffuseness parameter a as a function of the charge product of the projectile and target nuclei, $Z_P{Z}_T$. The filled circles and triangles are for the spherical and the deformed systems, respectively. The open circles and triangles are the surface diffuseness parameters deduced from the analyses of fusion cross sections [4].