Isospin effect on probing nuclear dissipation with fission cross sections

Nuclear dissipation retards fission. Using the stochastic Langevin model, we calculate the drop of fission cross section caused by friction over its standard statistical-model value, ${\sigma }_f^{\mathrm{drop}}$, as a function of the presaddle friction strength for fissioning nuclei ${}^{195}\mathrm{Bi}, {}^{202}\mathrm{Bi}$, and ${}^{209}\mathrm{Bi}$ as well as for different angular momenta. We find that friction effects on ${\sigma }_f^{\mathrm{drop}}$ are substantially enhanced with increasing isospin of the Bi system and become greater with decreasing angular momentum. Our findings suggest that in experiments, to better constrain the strength of presaddle dissipation through the measurement of fission excitation functions, it is optimal to yield those compound systems with a high isospin and a low spin. Furthermore, we analyze the data of fission excitation functions of ${}^{210}\mathrm{Po}$ and ${}^{209}\mathrm{Bi}$ systems, which are populated in $p+{}^{209}\mathrm{Bi}$ and $p+{}^{208}\mathrm{Pb}$ reactions and which have a high isospin and a low spin, and find that Langevin calculations with a presaddle friction strength of (3–5) $\times {10}^{-21}$ ${\mathrm{s}}^{-1}$ describe these experimental fission data very well.

Figure 1

Comparison of the dynamical drop of fission cross sections [Eq. (8)] of ${}^{195}\mathrm{Bi}, {}^{202}\mathrm{Bi}$, and ${}^{209}\mathrm{Bi}$ systems at angular momentum (a) ${\ell }_c=15\hslash$ and (b) ${\ell }_c=50\hslash$ and at the friction strength $\beta =4$ ${\mathrm{zs}}^{-1}$ for different excitation energies $E^{*}$.

Figure 2

(a) Fission barrier as a function of mass number of element Bi at angular momentum of 15 $\hslash$. (b) Fission barrier of nuclei ${}^{195}\mathrm{Bi}$ as a function of angular momentum.

Figure 3

Dynamical drop of the fission cross section of ${}^{195}\mathrm{Bi}$ relative to that predicted by SMs as a function of the presaddle dissipation strength $\beta$ at excitation energy $E^{*}=80$ MeV and at three critical angular momenta ${\ell }_c=15$, 40, and 60 $\hslash$.

Figure 4

Fits to measured excitation function data of fission cross sections in the $p+{}^{209}\mathrm{Bi}$ system [34]. SM predictions are compared to Langevin model calculations carried out at friction strengths $\beta$ = 3, 3.5, 5, and 6 ${\mathrm{zs}}^{-1}$.

Figure 5

Same as Fig. 4, but for the $p+{}^{208}\mathrm{Pb}$ system [34].