Fusion of ${}^{16}\mathrm{O}+{}^{165}\mathrm{Ho}$ at deep sub-barrier energies

Fusion cross sections have been measured for the asymmetric system ${}^{16}\mathrm{O}+{}^{165}\mathrm{Ho}$ at energies near and deep below the Coulomb barrier with an aim to investigate the occurrence of fusion hindrance for the system. Cross sections down to $\approx 700$ nb have been measured using the off-beam $\gamma$-ray technique. The fusion cross sections have been compared with the coupled channel calculations. The energy onset of fusion hindrance appears to occur at $E_{\mathrm{c}.\mathrm{m}.}=57\pm 0.85$ MeV, where a deviation in the slope of the experimental logarithmic derivative compared to that of coupled channel calculations has been observed. This is in agreement with the value obtained from the touching point configuration of the adiabatic model.

Figure 1

$\gamma$-ray spectrum of the evaporation residues arising from the complete fusion (CF) of ${}^{16}\mathrm{O}+{}^{165}\mathrm{Ho}$ system at 84-MeV beam energy. The red line is the background estimated by root data analysis package [29].

Figure 2

Activity of the ${}^{178}\mathrm{Re}$ evaporation residue as a function of progressing time at $E_{\text{lab}}=70$ MeV. The dotted line corresponds to the activity obtained by fitting the data. The half-life from the fit is mentioned in the graph, which is consistent with the known value.

Figure 3

The cross-sections of different evaporation residues of compound nucleus for ${}^{16}\mathrm{O}+{}^{165}\mathrm{Ho}$ system. The dotted lines are the statistical model calculation (PACE4) results.

Figure 4

Complete fusion excitation function measured in this experiment and the previous measurement (Kumar 2013: [27]) has been compared with coupled channel (CC) calculations using Woods-Saxon potential form. The solid lines are the results obtained from the CC calculations. The arrow corresponds to the Coulomb barrier for this system. The dashed curve shows the fusion cross sections obtained from the pace4 calculations. (Inset) Fusion cross section at above barrier energies are fitted with Wong formula to obtain the optical model potential parameters of the system. The solid line shows the fitted results. The x-axis corresponds to Ec.m. (MeV) and the y-axis corresponds to fusion cross-section (mb).

Figure 5

(a) Astrophysical $S$ factor for ${}^{16}\mathrm{O}+{}^{165}\mathrm{Ho}$ system compared with $S$ factor obtained from CC calculation. (b) Logarithmic derivative $L\left(E\right)$ of the experimental fusion excitation function compared with CC calculations (dash-dotted lines).

Figure 6

Systematic representation of $E_s$ as a function of system parameter $\zeta$. The solid circles are the values of $E_s$, obtained from the slope change in experimental log derivative with respect to CC calculations for the systems in Refs. [9, 14, 16, 45, 46, 47]. The solid square represents the $E_s$ value obtained in this work. The hollow squares correspond to Refs. [10, 48] where the value of $E_s$ cannot be obtained either by extrapolation or direct measurements and an upper bound has been mentioned in Ref. [4].

Figure 7

Comparison of normalized fusion excitation function between ${}^{16}\mathrm{O}+{}^{165}\mathrm{Ho}$ (in this work and Kumar 2013 [27]), ${}^{19}\mathrm{F}+{}^{165}\mathrm{Ho}$ (Navin 1996 [49]), and ${}^7\mathrm{Li}+{}^{165}\mathrm{Ho}$ (Tripathi 2002 [50]) systems.