Hindrance of heavy-ion fusion at extreme sub-barrier energies in open-shell colliding systems

The excitation function for the fusion-evaporation reaction ${}^{64}\mathrm{Ni}+{}^{100}\mathrm{Mo}$ has been measured down to a cross section of ∼5 nb. Extensive coupled-channels calculations have been performed, which cannot reproduce the steep falloff of the excitation function at extreme sub-barrier energies. Thus, this system exhibits a hindrance for fusion, a phenomenon that has been discovered only recently. In the S-factor representation introduced to quantify the hindrance, a maximum is observed at $E_s=120.6\mathrm{MeV}$, which corresponds to 90% of the reference energy $E_s^{\mathrm{ref}}$, a value expected from systematics of closed-shell systems. A systematic analysis of Ni-induced fusion reactions leading to compound nuclei with mass $A=100\text{−}200$ is presented in order to explore a possible dependence of fusion hindrance on nuclear structure.

Figure 1

Two-dimensional plots of $\Delta E_6$ vs $t_3$ for the new focal-plane detector system at the FMA, obtained at two sub-barrier incident energies. (a) At 198.8 MeV, the isolated group in (open circles) originates from evaporation residues, whereas the other events are caused by background. (b) At 196.0 MeV, 23 events (open circles) fall inside the acceptance window for fusion evaporation.

Figure 2

Same as Fig. 1, but for $\Delta E_5$ vs $t_3$. At 196.0 MeV, only one of the candidate evaporation residue events falls within the $\Delta E_5$ range. See text for details.

Figure 3

Position ($m/q$) spectra obtained at energies of 198.8 MeV (a) and 196.0 MeV (b). These events fall inside the windows in Fig. 1a or 1b, respectively. The event that also satisfies the $\Delta E_5$ condition is marked solid grey in panels (b) and (c).

Figure 4

Fusion excitation function for the system ${}^{64}\mathrm{Ni}+{}^{100}\mathrm{Mo}$ (solid circles). Statistical errors are smaller than the symbol size. For the two lowest energies, no residue events have been observed. The upper limits correspond to one count. Included in the figure are two previous measurements from Refs. [15, 16].

Figure 5

Fusion excitation function for ${}^{64}\mathrm{Ni}+{}^{100}\mathrm{Mo}$ compared with several calculations described in the text.

Figure 6

(a) Logarithmic derivative representation of the ${}^{64}\mathrm{Ni}+{}^{100}\mathrm{Mo}$ fusion excitation function. The circles were obtained from two successive data points, and stars were derived from least-squares fits to three neighboring data points. Included are the data from Ref. [15] (open circles) and Ref. [16] (open squares). (b) S factor representation of the same data. Calculations are shown by curves in both panels. The extrapolation curve (dotted) shown in (b) was obtained from a straight-line extrapolation of the logarithmic derivative representation in (a). A value of ${\eta }_0=105.74$ was used.

Figure 7

Logarithmic derivative representations of the fusion data for the systems ${}^{58}\mathrm{Ni}+{}^{74}\mathrm{Ge}$ (a) and ${}^{64}\mathrm{Ni}+{}^{74}\mathrm{Ge}$ (b). The circles represent a simple two-point estimate of the slope, whereas the stars were obtained by a three-point least-squares fit to the data. The data are from Ref. [13].

Figure 8

Plot of $E_s$ vs $Z_1{Z}_2\sqrt{\mu }$ for Ni bombarding different targets (see Table ). Solid symbols correspond to systems for which the S-factor maximum is well determined: ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$, ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$, ${}^{60}\mathrm{Ni}+{}^{89}\mathrm{Y}$, and ${}^{64}\mathrm{Ni}+{}^{100}\mathrm{Mo}$. Open symbols are associated with the extrapolations for the systems ${}^{58}\mathrm{Ni}+{}^{60}\mathrm{Ni}$, ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$, ${}^{58}\mathrm{Ni}+{}^{74}\mathrm{Ge}$, and ${}^{64}\mathrm{Ni}+{}^{74}\mathrm{Ge}$. The triangles represent Ni + Ni, diamonds Ni + Ge, a square ${}^{60}\mathrm{Ni}+{}^{89}\mathrm{Y}$, and a circle ${}^{64}\mathrm{Ni}+{}^{100}\mathrm{Mo}$.

Figure 9

Plot of $E_s/E_s^{\mathrm{ref}}$ vs $N_{\mathrm{ph}}$, where $N_{\mathrm{ph}}$ is the total number of “valence nucleons” outside closed shells in the entrance channel. Symbols are defined in Fig. 8.