Pairing Effects at the Fission Saddle Point ofPo210andPo211

The fission-fragment angular distributions were measured for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$-induced fission of ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ targets. The compound nuclei ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$ and ${}_{}{}^{211}{}_{}{}^{}\mathrm{Po}$ were obtained at excitation energies ranging from 3 to 20 MeV above the fission barriers. The experimental data were fitted by a theoretical expression relating the angular distribution of fission fragments to the distribution of the total angular momentum $I$ and of the angular momentum projection $K$ on the nuclear symmetry axis at the saddle point. By a least-squares fitting procedure, the variance $K_0^{}{}_{}{}^2$ of the $K$ distribution was obtained. In the case of the even-even nucleus ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$, the $K_0^{}{}_{}{}^2$ value approaches zero at about 3 MeV above the barrier, while in the case of the odd-$A$ nucleus ${}_{}{}^{211}{}_{}{}^{}\mathrm{Po}$, $K_0^{}{}_{}{}^2$ remains rather large: This indicates the presence of the pairing gap in ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$ and of the residual quasiparticle in ${}_{}{}^{211}{}_{}{}^{}\mathrm{Po}$. Furthermore, the approximately constant difference in $K_0^{}{}_{}{}^2$ between the even-even and odd-$A$ nucleus at corresponding energies is consistent with the expected contribution of a single quasiparticle to $K_0^{}{}_{}{}^2$. From the analysis of the data, the value of the pairing gap $2\Delta$ at the saddle point of ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$ is estimated to be about 4 MeV, about two to three times larger than in the ground state. The odd-even differences of saddle-point masses are also analyzed and the dependence of pairing on the nuclear surface is discussed.