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Register a new userDamping of Quantum Vibrations Revealed in Deep Sub-barrier Fusion
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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 reactions. 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.
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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 the 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.
To describe fusion hindrance observed in fusion reactions at extremely low incident energies, I propose a novel extension of the standard CC model by introducing a damping factor that describes a smooth transition from sudden to adiabatic processes. I demonstrate the performance of this model by systematically investigating various deep sub-barrier fusion reactions. I extend the standard CC model by introducing a damping factor into the coupling matrix elements in the standard CC model. I adopt the Yukawa-plus-exponential (YPE) model as a basic heavy ion-ion potential, which is advantageous for a unified description of the one- and two-body potentials. For the purpose of these systematic investigations, I approximate the one-body potential with a third-order polynomial function based on the YPE model. Calculated fusion cross sections for the medium-heavy mass systems of $^{64}$Ni + $^{64}$Ni, $^{58}$Ni + $^{58}$Ni, and $^{58}$Ni + $^{54}$Fe, the medium-light mass systems of $^{40}$Ca + $^{40}$Ca, $^{48}$Ca + $^{48}$Ca, and $^{24}$Mg + $^{30}$Si, and the mass-asymmetric systems of $^{48}$Ca + $^{96}$Zr and $^{16}$O + $^{208}$Pb are consistent with the experimental data. The astrophysical S factor and logarithmic derivative representations of these are also in good agreement with the experimental data. Since the results calculated with the damping factor are in excellent agreement with the experimental data in all systems, I conclude that the smooth transition from the sudden to adiabatic processes occurs and that a coordinate-dependent coupling strength is responsible for the fusion hindrance. In all systems, the potential energies at the touching point $V_{rm Touch}$ strongly correlate with the incident threshold energies for which the fusion hindrance starts to emerge, except for the medium-light mass systems.
Fusion cross-sections have been measured for the asymmetric system 16O+165Ho at energies near and deep below the Coulomb barrier with an aim to investigate the occurrence of fusion hindrance for the system. Fusion cross sections down to ~ 700 nb have been measured using the off-beam gamma-ray technique. The fusion cross sections have been compared with the coupled channel calculations. Although the onset of fusion hindrance could not be observed experimentally, an indication of a small deviation of the experimental fusion cross-sections with respect to the calculated cross-sections could be observed at the lowest energy measured. However, the energy onset of fusion hindrance has been obtained from the extrapolation technique and is found to be about 2 MeV below the lowest energy of the present measurement.
The tunneling of composite systems, where breakup may occur during the barrier penetration process is considered in connection with the fusion of halo-like radioactive, neutron- and proton-rich nuclei on heavy targets. The large amount of recent and new data clearly indicates that breakup hinders the fusion at near and below the Coulomb barrier energies. However, clear evidence for the halo enhancements, seems to over ride the breakup hindrance at lower energies, owing, to a large extent, to the extended matter density distribution. In particular we report here that at sub-barrier energies the fusion cross section of the Borromean two-neutron halo nucleus $^{6}$He with the actinide nucleus $^{238}$U is significantly enhanced compared to the fusion of a no-halo $^{6}$He. This conclusion differs from that of the original work, where it was claimed that no such enhancement ensues. This sub-barrier fusion enhancement was also observed in the $^{6}$He + $^{209}$% Bi system. The role of the corresponding easily excitable low lying dipole pygmy resonance in these systems is therefore significant. The consequence of this overall enhanced fusion of halo nuclei at sub-barrier energies, on stellar evolution and nucleosynthesis is evident.
Fusion excitation function of $^{35}$Cl + $^{130}$Te system is measured in the energy range around the Coulomb barrier and analyzed in the framework of the coupled-channels approach. The role of projectile deformation, nuclear structure, and the couplings of inelastic excitations and positive Q$-$value neutron transfer channels in sub-barrier fusion are investigated through the comparison of reduced fusion excitation functions of $^{35,37}$Cl +$^{130}$Te systems. The reduced fusion excitation function of $^{35}$Cl + $^{130}$Te system shows substantial enhancement over $^{37}$Cl + $^{130}$Te system in sub-barrier energy region which is attributed to the presence of positive Q-value neutron transfer channels in $^{35}$Cl + $^{130}$Te system. Findings of this work strongly suggest the importance of +2$n$ - transfer coupling in sub-barrier fusion apart from the simple inclusion of inelastic excitations of interacting partners, and are in stark contrast with the results presented by Kohley textit{et al.}, [Phys. Rev. Lett. 107, 202701 (2011)].
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