Since its beginnings, fission theory has assumed that low-energy induced fission takes place through transition-state channels at the barrier tops. Nevertheless, up to now there is no microscopic ...theory applicable to those conditions. We suggest that modern reaction theory is suitable for this purpose, and propose a methodology based on a configuration-interaction framework using the generator coordinate method (GCM). Simple reaction-theoretic models are constructed with the Gaussian overlap approximation to parametrize both the dynamics within the channels and their incoherent couplings to states outside the barrier. The physical characteristics of the channels examined here are their effective bandwidths and the quality of the coupling to compound-nucleus states as measured by the transmission factor T. We also investigate the spacing of GCM states with respect to their degree of overlap. We find that a rather coarse mesh provides an acceptable accuracy for estimating the bandwidths and transmission factors. The common numerical stability problem in using the GCM is avoided due to the choice of meshes and the finite bandwidths of the channels. Here, the bandwidths of the channels are largely controlled by the zero-point energy with respect to the collective coordinate in the GCM configurations.
Abstract
Low-energy heavy-ion fusion reactions are governed by quantum tunneling through the Coulomb barrier formed by the strong cancellation of the repulsive Coulomb force with the attractive ...nuclear interaction between the colliding nuclei. Extensive experimental as well as theoretical studies have revealed that fusion reactions are strongly influenced by couplings of the relative motion of the colliding nuclei to several nuclear intrinsic motions. Heavy-ion subbarrier fusion reactions thus provide a good opportunity to address the general problem of quantum tunneling in the presence of couplings, which has been a popular subject in recent decades in many branches of physics and chemistry. Here, we review theoretical aspects of heavy-ion subbarrier fusion reactions from the viewpoint of quantum tunneling in systems with many degrees of freedom. Particular emphases are put on the coupled-channels approach to fusion reactions and the barrier distribution representation for multichannel penetrability. We also discuss an application of the barrier distribution method to elucidate the mechanism of the dissociative adsorption of H2 molecules in surface science.
The study of fusion reactions at extreme sub-barrier energies has seen an increased interest in recent years, although difficult to measure due to their very small cross sections. Such reactions are ...extremely important for our understanding of the production of heavy elements in various environments. In this article, the status of the field is reviewed covering the experimental techniques, the available data, and the theoretical approaches used to describe such reactions. The fusion hindrance effect, first discovered in medium-mass systems, has been found to be relevant also for lighter systems. In some light systems, resonance structures are found to be important, while for heavy systems, the fission process plays an important role. In the near barrier region, couplings to collective excitations in the fusion participants and transfer reactions have been found to give a good description of the measured fusion cross sections and it results in a distribution of fusion barrier heights. New physics ingredients, related to the overlap process of the two projectiles, have to be introduced to describe the hindrance behavior. In addition, it has recently been found that the fusion cross section in both near-barrier and sub-barrier regions can be described very well in many cases using simple, analytical forms of the barrier-height distributions or a modified version of the classic Wong formula.
Differential cross sections of nuclear reactions often exhibit characteristic oscillations in the angular distribution originated from an interference of two indistinguishable processes. Here we ...propose a novel method to visualize origins of such oscillations. This is achieved by taking Fourier transform of scattering amplitudes, following the idea in wave optics. We apply this method to elastic scattering of 16O+16O and 18O+18O at energies above the Coulomb barrier. The former system shows strong oscillations in the angular distribution due to the nearside-farside interferences, while the oscillations are largely suppressed in the latter system due to a stronger absorption. We show that the images of the former and the latter systems correspond to a double-slit and a single-slit problems in quantum mechanics, respectively.
It has been known that the time-dependent Hartree-Fock (TDHF) method, or the time-dependent density functional theory (TDDFT), fails to describe many-body quantum tunneling. We overcome this problem ...by superposing a few time-dependent Slater determinants with the time-dependent generator coordinate method (TDGCM). We apply this method to scattering of two α particles in one dimension, and demonstrate that the TDGCM method yields a finite tunneling probability even at energies below the Coulomb barrier, at which the tunneling probability is exactly zero in the TDHF. This is the first case in which a many-particle tunneling is simulated with a microscopic real-time approach.
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