Complete fusion of ${}^9\mathrm{Be}$ with spherical targets

The complete fusion of ${}^9\mathrm{Be}$ with ${}^{144}\mathrm{Sm}$ and ${}^{208}\mathrm{Pb}$ targets is calculated in the coupled-channels approach. The calculations include couplings among the 3/$2^{-}$, 5/$2^{-}$, and 7/$2^{-}$ states in the $K=3/2$ ground-state rotational band of ${}^9\mathrm{Be}$. It is shown that the $B(E2)$ values for the excitation of these states are accurately described in the rotor model. The interaction of the strongly deformed ${}^9\mathrm{Be}$ nucleus with a spherical target is calculated using the double-folding technique and the effective M3Y interaction, which is supplemented with a repulsive term that is adjusted to optimize the fit to the data for the ${}^{144}\mathrm{Sm}$ target. The complete fusion is described by ingoing-wave boundary conditions. The decay of the unbound excited states in ${}^9\mathrm{Be}$ is considered explicitly in the calculations by using complex excitation energies. The model gives an excellent account of the complete fusion (CF) data for ${}^9\mathrm{Be}+{}^{144}\mathrm{Sm}$, and the cross sections for the decay of the excited states are in surprisingly good agreement with the incomplete fusion (ICF) data. Similar calculations for ${}^9\mathrm{Be}+{}^{208}\mathrm{Pb}$ explain the total fusion data at high energies but fail to explain the CF data, which are suppressed by 20%, and the calculated cross section for the decay of excited states is a factor of 3 smaller than the ICF data at high energies. Possible reasons for these discrepancies are discussed.

Figure 1

Correlation between the intrinsic quadrupole moment and the rms charge radius of ${}^9\mathrm{Be}$. Curves were obtained by varying ${\beta }_2$ for the fixed radius parameter $R=2.08$ and the three values of diffuseness indicated.

Figure 2

The shape of ${}^9\mathrm{Be}$, Eq. (3), derived by calibrating the density to reproduce the measured intrinsic quadrupole moment $Q_0$ and rms charge radius.

Figure 3

Entrance channel potentials for ${}^9\mathrm{Be}+{}^{144}\mathrm{Sm}$ and ${}^9\mathrm{Be}+{}^{208}\mathrm{Pb}$, respectively, obtained for the repulsive strength $v_r=410$ MeV fm${}^3$. The solid (red) curve is the monopole potential; the dotted (blue and black) curves are the entrance channel potentials for the magnetic quantum numbers $m=1/2$ and 3/2. Ground-state energies of the two compound nuclei, ${}^{153}\mathrm{Dy}$ and ${}^{217}\mathrm{Rn}$, are indicated.

Figure 4

Measured cross sections for the complete fusion of ${}^9\mathrm{Be}+{}^{144}\mathrm{Sm}$ [3] are compared to calculations for $m=1/2$ and 3/2 and the average cross section [solid (red) curve]. The strength of the repulsive interaction was set to $v_r=410$ MeV fm${}^3$.

Figure 5

(A) Measured complete (CF) and incomplete (ICF) fusion cross sections for ${}^9\mathrm{Be}+{}^{144}\mathrm{Sm}$ [3] are compared to calculated cross sections for CF [solid (red) curve] and absorption [dotted (blue) curve]. (B) This linear plot also shows the total fusion (TF) cross section.

Figure 6

The ${\chi }^2$ values per data point for complete (CF) and total (TF) fusion of ${}^9\mathrm{Be}+{}^{144}\mathrm{Sm}$ are shown as functions of the strength $v_r$ of the repulsive interaction, Eq. (17).

Figure 7

(A) Measured cross sections for complete (CF) and incomplete (ICF) fusion of ${}^9\mathrm{Be}+{}^{208}\mathrm{Pb}$ [2] are compared to calculated cross sections for CF [solid (red) curve] and absorption [dotted (blue) curve]. (B) This linear plot also shows the total fusion (TF) cross sections.

Figure 8

Similar to Fig. 7. Calculations include, in addition to the decay of the excited states of ${}^9\mathrm{Be}$, a weak imaginary potential with strength $W_0=-2.5$ MeV.