Investigating the nucleus-nucleus potential at very short distances

Recent progress in experimental techniques have made possible accurate measurements of fusion cross sections far below the Coulomb barrier, revealing an unexpected behavior of these quantities as a function of the bombarding energy. Besides providing a plausible cause for the observed energy dependence we profit from the nature of this explanation and the high sensitivity of the experimental data to show how one can use these measurements to investigate the radial dependence of the nuclear ion-ion potential at extremely close distances.

Figure 1

(Color online) The nucleus-nucleus potential for a head-on collision $\left(\ell =0\right)$ in the reaction ${}^{60}\mathrm{Ni}+{}^{89}\mathrm{Y}$. The nuclear part of the interaction is given by the Akyüz-Winther potential. Shown in the figure is also the profile of the parabolic approximation that results from approximating the potential near the top of the barrier, $V_B$, by a quadratic dependence in $r$. The inner pocket $V_P$ is in this case about $15\text{MeV}$ below the barrier, at an energy considerably larger than the value of $\approx 90\text{MeV}$ that sets the absolute lower limit for which the fusion process can energetically occur.

Figure 2

(Color online) (top) Three possible ion-ion potentials for the reaction ${}^{60}\mathrm{Ni}+{}^{89}\mathrm{Y}$ having an identical radial dependence for $r>11.01x\text{fm}$. This is a matching distance chosen somewhat inside the barrier radius and, consequently, the values of $V_B$, $r_B$, and $\hslash {\omega }_B$ are shared by all three potential functions. The matching is done with the purpose of generating different alternatives for the inner side of the potential barrier. The curves shown are for the partial wave $\ell =0$ but a similar prescription can also be implemented for the effective potentials corresponding to all the other low values of $\ell$ which are relevant for a calculation of sub-barrier fusion cross sections. Also shown in the frame is the parabolic approximation that is common to the three potentials. (Bottom) The fusion cross sections as a function of bombarding energy in the center of mass for the four potential profiles shown above. ${\sigma }_{par}\left(E\right)$ is the cross section within the parabolic approximation while ${\sigma }_{1,2,3}\left(E\right)$ correspond to each of the potential functions as identified in the upper frame.