Fission barrier, damping of shell correction, and neutron emission in the fission of $A\sim 200$

Decay of ${}^{210}\mathrm{Po}$ compound nucleus formed in light- and heavy-ion induced fusion reactions has been analyzed simultaneously using a consistent prescription for fission barrier and nuclear level density incorporating shell correction and its damping with excitation energy. Good descriptions of all the excitation functions have been achieved with a fission barrier of $21.9\pm 0.2$ MeV, indicating no significant shell correction at the saddle point. For this barrier height, the predicted statistical prefission neutrons in heavy-ion fusion-fission are much smaller than the experimental values, implying the presence of dynamical neutrons due to dissipation even at these low excitation energies $\left(\sim 50\mathrm{MeV}\right)$ in the mass region $A\sim 200$. When only heavy-ion induced fission excitation functions and the prefission neutron multiplicities are included in the fits, the deduced best-fit fission barrier depends on the assumed fission delay time, during which dynamical neutrons can be emitted. A fission delay of $(0.8\pm 0.1)\times {10}^{-19}$ s has been estimated corresponding to the above fission barrier height, assuming that the entire excess neutrons over and above the statistical model predictions are due to the dynamics. The present observation has implication on the study of fission time scale and nuclear viscosity using neutron emission as a probe.

Figure 1

A schematic representation of the potential energy as a function of deformation in mass $A\sim 200$. For large $E$*, shell effects are washed out and the available thermal energy ($U$) is measured with respect to liquid drop surface.

Figure 2

Experimental fission probabilities of ${}^{210}\mathrm{Po}$ are compared with the statistical model calculations. The (black) continuous, (green online) dashed, (blue online) dot-dashed, and the (pink online) dot-dot-dashed lines are the statistical model predictions with $B_f\left(0\right)=21.9$ MeV, $\widetilde{a_f}/\widetilde{a_n}=1.027$ for fusion of $p$, $\alpha$, ${}^{12}\mathrm{C}$, and ${}^{18}\mathrm{O}$ projectiles, respectively. The black and green (gray) dotted lines are the predictions of the statistical model with $B_f=13.4$ MeV [14] for fusion of $p$ and $\alpha$ particles, respectively.

Figure 3

Experimental prefission neutron multiplicity data (open triangles) [30] are compared with the statistical model calculations (blue online, dotted line) with $B_f\left(0\right)=21.9$ MeV for fusion of ${}^{12}\mathrm{C}$ projectile. The (blue online) continuous line is obtained by adding the estimated dynamical neutrons corresponding to a fission delay of $0.8\times {10}^{-19}$ to the statistical model calculation (see text).

Figure 4

Correlation between the fission barrier height and the dynamical delay required to account for the excess neutrons as compared to the prediction of the statistical model. The hatched region corresponds to the uncertainty in the measured prefission neutron multiplicity data. The shaded region indicates the uncertainty in the fission barrier obtained from the analysis of all the fission excitation functions and the corresponding dynamical delay.