Measurements of evaporation residue cross sections for the fusion reactions ${}^{86}\mathrm{Kr}+{}^{134}\mathrm{Ba}$ and ${}^{86}\mathrm{Kr}+{}^{138}\mathrm{Ba}$

We measured evaporation residue (ER) cross sections of the fusion reactions ${}^{86}\mathrm{Kr}+{}^{134,138}\mathrm{Ba}$ to investigate the effect of the shell structure of the interacting nuclei on the fusion process. The measured ER cross sections for the reaction ${}^{86}\mathrm{Kr}+{}^{138}\mathrm{Ba}$ have a sizable component, 37 nb, at the excitation energy ($E_{\mathrm{ex}}$) of 12.1 MeV. However, there is no evaporation residue for the reaction ${}^{86}\mathrm{Kr}+{}^{134}\mathrm{Ba}$ below the energy $E_{\mathrm{ex}}=24.7$ MeV. This result suggests that the neutron shell closure ($N=82$) of ${}^{138}\mathrm{Ba}$ plays a crucial role in the formation of the compound nucleus.

Figure 1

Reduced cross sections obtained from the measured ER cross sections for the reaction ${}^{86}\mathrm{Kr}+{}^{138}\mathrm{Ba}$ and from the theoretical calculations (see text). The dashed lines are the theoretical calculations using the Bass barrier, whereas the dot-dot-dash and solid lines are those using the Gaussian-shaped fusion barrier with the fitting parameters of ($E_{\mathrm{xx}},{\sigma }_B)=$ (27 MeV, 10 MeV) and (17 MeV, 7.2 MeV), respectively. Reduced cross sections produced in 5n and 6n channels of the reaction ${}^{27}\mathrm{Al}+{}^{197}\mathrm{Au}$ are also shown, as open circles and open squares, respectively. The error bars express not only statistical error but also systematic error, totaling 40% for the present reaction ${}^{86}\mathrm{Kr}+{}^{138}\mathrm{Ba}$. The downward arrows show the Bass barrier of the reaction ${}^{86}\mathrm{Kr}+{}^{138}\mathrm{Ba}$.

Figure 2

(Color online) The sum of reduced cross sections produced in each channel of the present reactions ${}^{86}\mathrm{Kr}+{}^{134,138}\mathrm{Ba}$. These for others reactions ${}^{82}\mathrm{Se}+{}^{140}\mathrm{Ce}$, ${}^{76}\mathrm{Ge}+{}^{150}\mathrm{Nd}$, ${}^{28}\mathrm{Si}$${+}^{198}$Pt, and ${}^{20}\mathrm{Ne}+{}^{208}\mathrm{Pb}$ are also shown. The upward-arrows show the position of Bass barrier and the downward arrows show the upper limit for the reactions ${}^{82}\mathrm{Se}+{}^{140}\mathrm{Ce}$ and ${}^{86}\mathrm{Kr}+{}^{134}\mathrm{Ba}$.

Figure 3

(a) Neutron binding energy $B_n$ and fission barrier height $B_f$ for several uranium isotopes. (b) Calculated ${\Gamma }_n$/${\Gamma }_f$ values for the nuclei ${}^{220}\mathrm{U}$, ${}^{224}\mathrm{U}$, and ${}^{228}\mathrm{U}$ using Eq. (2).