Hindrance of Heavy-Ion Fusion due to Nuclear Incompressibility

We propose a new mechanism to explain the unexpected steep falloff of fusion cross sections at energies far below the Coulomb barrier. The saturation properties of nuclear matter are causing a hindrance to large overlap of the reacting nuclei and consequently a sensitive change of the nuclear potential inside the barrier. We report in this Letter a good agreement with the data of coupled-channels calculation for the ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ combination using the double-folding potential with Michigan-3-Yukawa-Reid effective $N-N$ forces supplemented with a repulsive core that reproduces the nuclear incompressibility for total overlap.

Figure 1

Various spherical ion-ion potentials for ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$. The solid curve is the potential employed in the present work. The curve with small dashes is the Winther-Akyüz potential used in 1, 2, 3, 4, 5. The dashed strip corresponds to experimental boundaries of the threshold energy $E_s$.

Figure 2

Experimental fusion excitation function for the system ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ [3] is compared to various calculations described in the text.

Figure 3

The experimental $S$ factor of ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ [3] (solid points) is compared to the coupled-channels calculations performed with the $\mathrm{M}3\mathrm{Y}+\mathrm{\text{repulsion}}$ (solid curve) and the Winther-Akyüz (dashed curve) potential.