Influence of vibrational excitation on surface diffuseness of the internuclear potential: Study through heavy-ion quasielastic scattering at deep sub-barrier energies

We discuss the role of channel coupling in the surface properties of an internuclear potential for heavy-ion reactions. To this end, we analyze the experimental quasielastic cross sections for the ${}^{12}\mathrm{C}+{}^{105,106}\mathrm{Pd}$ and ${}^{13}\mathrm{C}+{}^{105,106}\mathrm{Pd}$ systems using the coupled-channels approach by including the vibrational excitations in the target nuclei. While earlier studies have reported a negligible influence of vibrational excitation on the surface diffuseness parameter for spherical systems, we find a significant effect for the C + Pd systems. Our systematic study also reveals influence of transfer couplings on the surface diffuseness parameter.

Figure 1

Comparisons of the single-channel calculations for the quasielastic excitation function obtained with several values of the surface diffuseness parameter, $a_0$, in the nuclear potential. The panels (a), (b), (c), and (d) are for the ${}^{12}\mathrm{C}+{}^{105}\mathrm{Pd},{}^{12}\mathrm{C}+{}^{106}\mathrm{Pd},{}^{13}\mathrm{C}+{}^{105}\mathrm{Pd}$, and ${}^{13}\mathrm{C}+{}^{106}\mathrm{Pd}$ systems, respectively. The experimental data are taken from Ref. [20].

Figure 2

The ${\chi }^2$ for the ${}^{13}\mathrm{C}+{}^{106}\mathrm{Pd}$ system as a function of the surface diffuseness parameter, $a_0$. The open and filled symbols represent the results of the single-channel and coupled-channel calculations, respectively.

Figure 3

Same as Fig. 1, but with the coupled-channels calculations.

Figure 4

The extracted surface diffuseness parameter for the ${}^{12,13}\mathrm{C}+{}^{105,106}\mathrm{Pd}$ systems as a function of the product of masses of the projectile and target nuclei, $A_t{A}_p$. The open and filled symbols represent the results of the single-channel and the coupled-channel calculations, respectively.

Figure 5

Same as Fig. 4, but as a function of the $Q$ value for the neutron transfer channels. The lines are to guide the eye.