Constraining presaddle dissipation with fission cross sections of light nuclear systems

Nuclear fission is hindered by dissipation. Based on the stochastic Langevin model, we calculate the drop of fission cross section caused by friction with respect to its standard statistical-model value, ${\sigma }_f^{\mathrm{drop}}$, as a function of the presaddle friction strength ($\beta$) for fissioning nuclei ${}^{205}\mathrm{Bi}$, ${}^{215}\mathrm{Fr}$, ${}^{225}\mathrm{Pa}$, and ${}^{230}\mathrm{Np}$ at different angular momenta and excitation energies. It is found that with increasing the size of fissioning systems, the sensitivity of ${\sigma }_f^{\mathrm{drop}}$ to $\beta$ is reduced substantially, and it disappears for the ${}^{230}\mathrm{Np}$ system. Our findings suggest that on the experimental side, to more stringently constrain the presaddle dissipation strength by measuring fission excitation functions, it is optimal to yield those fissioning systems with a small size.

Figure 1

Comparison of the dynamical drop of fission cross sections [Eq. (6)] of ${}^{205}\mathrm{Bi}$, ${}^{215}\mathrm{Fr}$, ${}^{225}\mathrm{Pa}$, and ${}^{230}\mathrm{Np}$ systems as a function of the presaddle friction strength $\beta$ at excitation energy $E^{*}=100$ MeV and at angular momentum (a) ${\ell }_c=30\hslash$ and (b) ${\ell }_c=50\hslash$.

Figure 2

Left: Fission barriers of nuclei ${}^{205}\mathrm{Bi}$, ${}^{215}\mathrm{Fr}$, ${}^{225}\mathrm{Pa}$, and ${}^{230}\mathrm{Np}$ at different angular momenta calculated with the method in Refs. [49, 53]. Right: The potential $V$ of systems ${}^{205}\mathrm{Bi}$, ${}^{215}\mathrm{Fr}$, ${}^{225}\mathrm{Pa}$, and ${}^{230}\mathrm{Np}$ at angular momentum of $30\hslash$ as a function of deformation coordinate $q$. The vertical lines denote the location of the barrier. Note that the upper and lower lines refer to nuclei ${}^{205}\mathrm{Bi}$ and ${}^{230}\mathrm{Np}$, respectively.

Figure 3

Same as in Fig. 1 but at $E^{*}=50$ MeV.