Fission life-time calculation using a complex absorbing potential

A comparison between the semi-classical approximation and the full quantum calculation with a complex absorbing potential is made with a model of the fission of 258Fm. The potential barrier is obtained with the constrained Skyrme HF+BCS theory. The life-time obtained by the two calculations agree with each other the difference being only by 25%.Comment: 5 pages, 2 figures, Conference proceedings of CNR*15 workshop, Tokyo, October 2015 to be published in EPJ Web of Conference

Hot fusion reactions with deformed nuclei for synthesis of superheavy nuclei: An extension of the fusion-by-diffusion model

The fusion-by-diffusion model proposed by Swiatecki {\it et al.} [Phys. Rev. C71, 014602 (2005)] has provided a simple and convenient tool to estimate evaporation residue cross sections for superheavy nuclei. I extend this model by taking into account deformation of the target nucleus, and discuss the role of orientation of deformed target in hot fusion reactions at energies around the Coulomb barrier. To this end, I introduce an injection point for the diffusion process over an inner barrier which depends on the orientation angle. I apply this model to the $^{48}$Ca+$^{248}$Cm reaction and show that the maximum of evaporation residue cross section appears at an energy slightly above the height of the capture barrier for the side collision, for which the effective inner barrier is considerably lower than that for the tip collision, thus enhancing the diffusion probability. I also discuss the energy dependence of the injection point, and show that a large part of the energy dependence found in the previous analyses can be attributed to the deformation effect of a target nucleus.Comment: 12 pages, 6 figure

Signature of smooth transition from diabatic to adiabatic states in heavy-ion fusion reactions at deep subbarrier energies

We propose a novel extension of the standard coupled-channels framework for heavy-ion reactions in order to analyze fusion reactions at deep subbarrier incident energies. This extension simulates a smooth transition between the diabatic two-body and the adiabatic one-body states. To this end, we damp gradually the off-diagonal part of the coupling potential, for which the position of the onset of the damping varies for each eigen channel. We show that this model accounts well for the steep falloff of the fusion cross sections for the $^{16}$O+$^{208}$Pb, $^{64}$Ni+$^{64}$Ni, and $^{58}$Ni+$^{58}$Ni reactions.Comment: 4 pages, 4 figure

Exotic Structure of Carbon Isotopes

We studied firstly the ground state properties of C-isotopes using a deformed Hartree-Fock (HF)+ BCS model with Skyrme interactions. Shallow deformation minima are found in several neutron$-$rich C-isotopes. It is shown also that the deformation minima appear in both the oblate and the prolate sides in $^{17}$C and $^{19}$C having almost the same binding energies. Secondly, we carried out shell model calculations to study electromagnetic moments and electric dipole transitions of the C-isotopes. We point out the clear configuration dependence of the quadrupole and magnetic moments in the odd C-isotopes, which will be useful to find out the deformations and the spin-parities of the ground states of these nuclei. We studied electric dipole states of C-isotopes focusing on the interplay between low energy Pigmy strength and giant dipole resonances. Reasonable agreement is obtained with available experimental data for the photoreaction cross sections both in the low energy region below $\hbar \omega$=14 MeV and in the high energy giant resonance region (14 MeV $<\hbar \omega \leq$30 MeV). The calculated transition strength below dipole giant resonance ($\hbar \omega \leq$14 MeV) in heavier C-isotopes than $^{15}$C is found to exhaust about $12\sim16$ of the classical Thomas-Reiche-Kuhn sum rule value and $50\sim80$ of the cluster sum rule value.Comment: 31 pages, 19 eps figure

Orbital-free Density Functional Theory: differences and similarities between electronic and nuclear systems

Orbital-free Density Functional Theory (OF-DFT) has been used when studying atoms, molecules and solids. In nuclear physics, there has been basically no application of OF-DFT so far, as the Density Functional Theory (DFT) has been widely applied to the study of many nuclear properties mostly within the Kohn-Sham (KS) scheme. There are many realizations of nuclear KS-DFT, but computations become very demanding for heavy systems, such as superheavy nuclei and the inner crust of neutron stars, and it is hard to describe exotic nuclear shapes using a finite basis made with a limited number of orbitals. These bottlenecks could, in principle, be overcome by an orbital-free formulation of DFT. This work is a first step towards the application of OF-DFT to nuclei. In particular, we have implemented possible choices for an orbital-free kinetic energy and solved the associated Schr\"odinger equation either with simple potentials or with simplified nuclear density functionals. While the former choice sheds light on the differences between electronic and nuclear systems, the latter choice allows us discussing the practical applications to nuclei and the open questions.Comment: Submitted for publicatio

Existence of One-Body Barrier Revealed in Deep Sub-Barrier Fusion

Based on the adiabatic picture for heavy-ion reactions, in which the neck formation in the one-body system is taken into account, we propose a two-step model for fusion cross sections at deep subbarrier energies. This model consists of the capture process in the two-body potential pocket, which is followed by the penetration of the adiabatic one-body potential to reach a compound state after the touching configuration. We describe the former process with the coupled-channels framework, while the latter with the WKB approximation by taking into account the coordinate dependent inertia mass. The effect of the one-body barrier is important at incident energies below the potential energy at the touching configuration. We show that this model well accounts for the steep fall-off phenomenon of fusion cross sections at deep subbarrier energies for the $^{64}$Ni+$^{64}$Ni and $^{58}$Ni+$^{58}$Ni reactions.Comment: 4 pages, 3 figure

Three related topics on the periodic tables of elements

A large variety of periodic tables of the chemical elements have been proposed. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. The periodic table currently used worldwide is of a long form pioneered by Werner in 1905. As the first topic, we describe the work of Pfeiffer (Naturwiss. 8:984–991, 1920), who refined Werner’s work and rearranged the rare-earth elements in a separate table below the main table for convenience. Today’s widely used periodic table essentially inherits Pfeiffer’s arrangements. Although long-form tables more precisely represent electron orbitals around a nucleus, they lose some of the features of Mendeleev’s short-form table to express similarities of chemical properties of elements when forming compounds. As the second topic, we compare various three-dimensional (3D) helical periodic tables that resolve some of the shortcomings of the long-form periodic tables in this respect. In particular, we explain how the 3D periodic table “Elementouch” (Maeno in Periodic-table-of-the-elements stationery. Design No. 1149493, Japan Patent Office. https://www.j-platpat.inpit.go.jp/d0000, 2001), which combines the s- and p-blocks into one tube, can recover features of Mendeleev’s periodic law. Finally we introduce a topic on the recently proposed nuclear periodic table based on the proton magic numbers (Hagino and Maeno in Found Chem 22:267–273, 2020). Here, the nuclear shell structure leads to a new arrangement of the elements with the proton magic-number nuclei treated like noble-gas atoms. We show that the resulting alignments of the elements in both the atomic and nuclear periodic tables are common over about two thirds of the tables because of a fortuitous coincidence in their magic numbers