Fusion hindrance at deep sub-barrier energies for the ${}^{11}\mathbf{B}+{}^{197}\mathbf{Au}$ system

Fusion cross sections for the ${}^{11}\mathrm{B}+{}^{197}\mathrm{Au}$ system have been measured at energies around and deep below the Coulomb barrier, to probe the occurrence of fusion hindrance in case of asymmetric systems. A deviation with respect to the standard coupled channels calculations has been observed at the lowest energy. The results have been compared with an adiabatic model calculation that considers a damping of the coupling strength for a gradual transition from sudden to adiabatic regime at very low energies. The data could be explained without inclusion of the damping factor. This implies that the influence of fusion hindrance is not significant within the measured energy range for this system. The present result is consistent with the observed trend between the degree of fusion hindrance and the charge product that reveals a weaker influence of hindrance on fusion involving lighter projectiles on heavy targets.

Figure 1

Activation $\gamma$-ray spectra for the ${}^{11}\mathrm{B}+{}^{197}\mathrm{Au}$ system (a) inclusive spectrum at $E_{\mathrm{lab}}$ of 61.6 MeV. The dominant $\gamma$ rays arising from the evaporation residues, ${}^{203,204}\mathrm{Po}$ are labeled. (b) $\gamma$-ray spectrum in coincidence with the $K_{\alpha }x$ rays detected in the second detector (shown in the inset) at $E_{\mathrm{lab}}=46.4$ and 41.2 MeV. Photopeaks at 437.8 and 449.8 keV, corresponding to the residue ${}^{205}\mathrm{Po}$ are marked.

Figure 2

Evaporation residue and fission cross sections for the ${}^{11}\mathrm{B}+{}^{197}\mathrm{Au}$ system. Fission cross sections are from Ref. [22]. Dashed curves are results of statistical model calculations (see text).

Figure 3

(a) Fusion excitation function and its (b) logarithmic derivative $\left[L\right(E\left)\right]$, along with CC calculations for the ${}^{11}\mathrm{B}+{}^{197}\mathrm{Au}$ system. The $S$-factor values are shown in the inset of (a). The $L\left(E\right)$ values fitted to an expression and those corresponding to a constant $S$ factor ($L_{cs}$) are shown as dot-dashed and dashed curves, respectively. Position of the Coulomb barrier is indicated with an arrow.

Figure 4

(a) Results from the adiabatic model calculation for the ${}^{11}\mathrm{B}+{}^{197}\mathrm{Au}$ system compared with the experimental (a) fusion cross sections along with $S$-factor (inset) (b) logarithmic derivative. Calculations using with and without a damping factor for the coupling strength are shown as solid and dashed-dot curves respectively.

Figure 5

Ratio of the slopes of $L\left(E\right)$ and $L_{cs}\left(E\right)$ calculated at their crossing point, as a function of the charge product of the reactants, for data from the present measurement and literature [1, 2, 3, 9, 11, 12, 13, 18, 19, 20,26]. Filled and open circles represent the data and extrapolated values obtained from the fit to $L\left(E\right)$, respectively. The data from the present work are shown as a filled diamond. The dashed line is obtained by fitting the data (filled circles) to an exponential function.