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.
We systematically investigate the existence of exotic torus isomers and their precession motions for a series of $N=Z$ even-even nuclei from $^{28}$Si to $^{56}$Ni. We analyze the microscopic shell structure of the torus isomer and discuss why the to
rus shape is generated beyond the limit of large oblate deformation. We use the cranked three-dimensional Hartree-Fock (HF) method with various Skyrme interactions in a systematic search for high-spin torus isomers. We use the three-dimensional time-dependent Hartree-Fock (TDHF) method for describing the precession motion of the torus isomer. We obtain high-spin torus isomers in $^{36}$Ar, $^{40}$Ca, $^{44}$Ti, $^{48}$Cr, and $^{52}$Fe. The emergence of the torus isomers is associated with the alignments of single-particle angular momenta, which is the same mechanism as found in $^{40}$Ca. It is found that all the obtained torus isomers execute the precession motion at least two rotational periods. The moment of inertia about a perpendicular axis, which characterizes the precession motion, is found to be close to the classical rigid-body value. The high-spin torus isomer of $^{40}$Ca is not an exceptional case. Similar torus isomers exist widely in nuclei from $^{36}$Ar to $^{52}$Fe and they execute the precession motion. The torus shape is generated beyond the limit of large oblate deformation by eliminating the $0s$ components from all the deformed single-particle wave functions to maximize their mutual overlaps.
We investigate the precession motion of the exotic torus configuration in high-spin excited states of $^{40}$Ca. For this aim, we use the three-dimensional time-dependent Hartree-Fock (TDHF) method. Although the high-spin torus isomer is a unique qua
ntum object characterized by the alignment of angular momenta of independent single-particle motions, we find that the obtained moment of inertia for rotations about an axis perpendicular to the symmetry axis is close to the rigid-body value. We also analyze the microscopic structure of the precession motion using the random-phase approximation (RPA) method for high-spin states. In the RPA calculation, the precession motion of the torus isomer is generated by coherent superposition of many one-particle-one-hole excitations across the sloping Fermi surface that strongly violates the time-reversal symmetry. By comparing results of the TDHF and the RPA calculations, we find that the precession motion obtained by the TDHF calculation is a pure collective motion well decoupled from other collective modes.
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.
We investigate the possibility of the existence of the exotic torus configuration in the high-spin excited states of $^{40}$Ca. We here consider the spin alignments about the symmetry axis. To this end, we use a three-dimensional cranked Skyrme Hartr
ee-Fock method and search for stable single-particle configurations. We find one stable state with the torus configuration at the total angular momentum $J=$ 60 $hbar$ and an excitation energy of about 170 MeV in all calculations using various Skyrme interactions. The total angular momentum J=60 $hbar$ consists of aligned 12 nucleons with the orbital angular momenta $Lambda=+4$, +5, and +6 for spin up-down neutrons and protons. The obtained results strongly suggest that a macroscopic amount of circulating current breaking the time-reversal symmetry emerges in the high-spin excited state of $^{40}$Ca.
We investigate the existence of weakly coupled gas-like states comprised of three $alpha$ particles around an $^{16}$O core in $^{28}$Si. We calculate the excited states in $^{28}$Si using the multi-configuration mixing method based on the $^{16}$O +
3$alpha$ cluster model. We also include the $^{16}$O + $^{12}$C and $^{24}$Mg + $alpha$ basis wave functions prepared by the generator coordinate method. To identify the gas-like states, we calculate the isoscalar monopole transition strengths and the overlap of the obtained states with the geometrical cluster wave function and the Tohsaki-Horiuchi-Schuck-R{o}pke (THSR) wave function. The results show that the obtained fourth and twelfth states significantly overlap with the THSR wave function. These two states clearly coexist with the $^{16}$O + $^{12}$C cluster states, emerging at similar energies. The calculated isoscalar monopole strengths between those two states are significantly large, indicating that the states are members of the excitation mode. Furthermore, the calculated root-mean-squared (RMS) radii for these states also suggest that a layer of gas-like three $alpha$ particles could exist around the surface of the $^{16}$O core, which can be described as a two-dimensional gas in the intermediate state before the Hoyle-like three $alpha$ states emerge.
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.
We investigate the linear-chain configurations of four-$alpha$ clusters in $^{16}$O using a Skyrme cranked Hartree-Fock method and discuss the relationship between the stability of such states and angular momentum. We show the existence of a region o
f angular momentum (13-18 $hbar$) where the linear chain configuration is stabilized. For the first time we demonstrate that stable exotic states with a large moment of inertia ($hbar^2/2Theta$ $sim$ 0.06-0.08 MeV) can exist.
