We demonstrate the damping of quantum octupole vibrations near the touching point when two colliding nuclei approach each other in the mass-asymmetric $^{208}$Pb + $^{16}$O system, for which the strong fusion hindrance was clearly observed. We, for t
he first time, apply the random-phase approximation method to the heavy-mass asymmetric di-nuclear system to calculate the transition strength $B$(E3) as a function of the center-of-mass distance. The obtained $B$(E3) strengths are substantially damped near the touching point, because the single-particle wave functions of the two nuclei strongly mix with each other and a neck is formed. The energy-weighted sums of $B$(E3) are also strongly correlated with the damping factor which is phenomenologically introduced in the standard coupled-channel calculations to reproduce the fusion hindrance. This strongly indicates that the damping of the quantum vibrations universally occurs in the deep sub-barrier fusion reactions.
The double-humped structure of many actinide fission barriers is well established both experimentally and theoretically. There is also evidence, both experimental and theoretical, that some actinide nuclei have barriers with a third minimum, outside
the second, fission-isomeric minimum. We perform a large-scale, systematic calculation of actinide fission barriers to identify which actinide nuclei exhibit third minima. We find that only a relatively few nuclei accessible to experiment exhibit third minima in their barriers, approximately nuclei with proton number $Z$ in the range $88 leq Z leq 94$ and nucleon number $A$ in the range $230 leq A leq 236 $. We find that the third minimum is less than 1 MeV deep for light Th and U isotopes. This is consistent with some previous experimental and theoretical results, but differs from some others. We discuss possible origins of these incompatible results and what are the most realistic predictions of where third minima are observable.
We demonstrate that when two colliding nuclei approach each other, their quantum vibrations are damped near the touching point. We show that this damping is responsible for the fusion hindrance phenomena measured in the deep sub-barrier fusion reacti
ons. To show those, we for the first time apply the random-phase-approximation (RPA) method to the two-body $^{16}$O + $^{16}$O and $^{40}$Ca + $^{40}$Ca systems. We calculate the octupole transition strengths for the two nuclei adiabatically approaching each other. The calculated transition strength drastically decreases near the touching point, strongly suggesting the vanishing of the quantum couplings between the relative motion and the vibrational intrinsic degrees of freedom of each nucleus. Based on this picture, we also calculate the fusion cross section for the $^{40}$Ca + $^{40}$Ca system using the coupled-channel method with the damping factor simulating the vanishing of the couplings. The calculated results reproduce well the experimental data, indicating that the smooth transition from the sudden to adiabatic processes indeed occurs in the deep sub-barrier fusion reactions.
Fission-fragment mass distributions are asymmetric in fission of typical actinide nuclei for nucleon number $A$ in the range $228 lnsim A lnsim 258$ and proton number $Z$ in the range $90lnsim Z lnsim 100$. For somewhat lighter systems it has been ob
served that fission mass distributions are usually symmetric. However, a recent experiment showed that fission of $^{180}$Hg following electron capture on $^{180}$Tl is asymmetric. We calculate potential-energy surfaces for a typical actinide nucleus and for 12 even isotopes in the range $^{178}$Hg--$^{200}$Hg, to investigate the similarities and differences of actinide compared to mercury potential surfaces and to what extent fission-fragment properties, in particular shell structure, relate to the structure of the static potential-energy surfaces. Potential-energy surfaces are calculated in the macroscopic-microscopic approach as functions of fiveshape coordinates for more than five million shapes. The structure of the surfaces are investigated by use of an immersion technique. We determine properties of minima, saddle points, valleys, and ridges between valleys in the 5D shape-coordinate space. Along the mercury isotope chain the barrier heights and the ridge heights and persistence with elongation vary significantly and show no obvious connection to possible fragment shell structure, in contrast to the actinide region, where there is a deep asymmetric valley extending from the saddle point to scission. The mechanism of asymmetric fission must be very different in the lighter proton-rich mercury isotopes compared to the actinide region and is apparently unrelated to fragment shell structure. Isotopes lighter than $^{192}$Hg have the saddle point blocked from a deep symmetric valley by a significant ridge. The ridge vanishes for the heavier Hg isotopes, for which we would expect a qualitatively different asymmetry of the fragments.
