Structures in the heavy-ion fusion excitation function at and above the Coulomb barrier

Contrary to descriptions from coupled-channels or other model calculations, heavy-ion fusion excitation functions are not smooth near and above the Coulomb barrier. There appear to be weak but noticeable oscillations or structures within the excitation functions that can be observed clearly in representation $d\left(\sigma E\right)/dE$ and in the comparison with theoretical calculations $\sigma \left(E\right)-{\sigma }_{\mathrm{th}}\left(E\right)$. A rather similar phenomenon has been studied before and can be explained in light symmetric systems as the influence of the centrifugal barrier penetration only on even angular momentum, but it cannot be extended to heavier, more asymmetric fusion systems. A more thorough investigation may be required to investigate this newly indicated behavior.

Figure 1

Various representations vs $E$ plots of the fusion cross sections for system ${}^{40}\mathrm{Ca}+{}^{90}\mathrm{Zr}$ [16]. (a) Barrier distribution $B\left(E\right)$, (b) $d\left(\sigma E\right)/dE$, (c) $\sigma E$, and (d) ${\sigma }_{exp}-{\sigma }_{\mathrm{th}}$. Curves are calculations from the three-Gaussian barrier distribution recipe.

Figure 2

Various representations vs $E$ plots of fusion cross sections for system ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ [17]. Others are the same as in Fig. 1.

Figure 3

$d\left(\sigma E\right)/dE$ and $\sigma -{\sigma }_{\mathrm{th}}$ spectra for fusion systems ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ [22] in upper part, ${}^{34}\mathrm{S}+{}^{168}\mathrm{Er}$ [26] in middle part, and ${}^{40}\mathrm{Ca}+{}^{192}\mathrm{Os}$ [19] in lower part, respectively. DN is the step number used in the differentiation process.

Figure 4

$d\left(\sigma E\right)/dE$ and $\sigma -{\sigma }_{\mathrm{th}}$ spectra for fusion systems ${}^{40}\mathrm{Ca}+{}^{90}\mathrm{Zr}$ [16] in upper part, ${}^{40}\mathrm{Ca}+{}^{94}\mathrm{Zr}$ [20] in middle part, and ${}^{40}\mathrm{Ca}+{}^{96}\mathrm{Zr}$ [21] in lower part, respectively. DN is the step number used in the differentiation process.

Figure 5

Excitation functions of fusions and transfer reactions for some systems of Ni $+$ Mo. Data come from Refs. [35, 36, 37], respectively.