T. Wada

Multi-dimensional Langevin approach to fission dynamics

Abstract Multi-dimensional Langevin approach to nuclear dissipative phenomena is presented. We solve two-dimensional Langevin equation numerically without any approximations for the study of induced fission dynamics. Transient time of the symmetric fission of 213At is calculated and discussed in comparison with empirically deduced value. Fragment kinetic energy distribution is calculated and compared with experiments.

Diffusion over a saddle with a Langevin equation

The diffusion problem over a saddle is studied using a multidimensional Langevin equation. An analytical solution is derived for a quadratic potential and the probability to pass over the barrier deduced. A very simple solution is given for the one-dimensional problem and a general scheme is shown for higher dimensions.

Study of 16O-16O Potential by the Resonating Group Method. I

Since the knowledge of the inter-nucleus optical potential is important for the understanding of nuclear reaction induced by heavy ions, it is necessary to study the inter-nucleus potential from a microscopic basis. Recently we proposed to study the optical potential by equivalent local potential (ELP) to the non-local potential of the resonating group method (RGM). The derivaxad tion of the ELP is made by applying the WKB approximation to the RGM equation. This method was applied to many systems and various kinds of knowledge about the inter-nucleus potential were obtained.!),2) The systems so far studied are Z + a, 16 0 and 4DCa (where Z denotes any Os-shell nucleus) and 16 0+

A new mechanism for synthesis of superheavy elements

A dynamical theory is proposed for nuclear reactions leading to residues of superheavy elements. Fusion and fission processes are treated consistently by a diffusion equation which describes a time-dependent probability distribution in the collective coordinate or deformation space. The potential energy in the equation is time-dependent, because cooling due to particle evaporation gradually restores the shell correction energy which gives rise to a potential pocket essential for the stabilization of the superheavy elements around Z = 114 and N = 184. It is shown that there is an optimum initial excitation energy or incident energy of reactions as the result of a compromise between two conflicting requirements; higher energies which favour larger fusion probabilities and lower energies which favour larger residue probabilities or a quicker restoration of the shell-correction energy. A promising experimental direction is suggested.

Fusion Dynamics of Massive Heavy-Ion Systems

A two-step model is proposed for the fusion mechanism of massive heavy-ion systems which is the most unknown part in the reaction theory for the synthesis of the superheavy elements. It consists of the approaching phase of incident ions and the dynamical shape evolution of the amalgamated system toward the spherical compound nucleus. Preliminary results are presented.

Radiative Capture Cross Section for 16O(n, γ)17O and 16O(p, γ)17F below Astrophysical Energies

In this paper we aim to construct a reliable theoretical framework to analyze nuclear reaction cross sections concerning the nucleosyntheses of light nuclei. To explain the reaction cross sections of O(n, γ)O and O(p, γ)F, we propose a theoretical procedure combining an O+N model and the complex scaling method with the Lippmann-Schwinger solution for the complex-scaled Green’s operator. We demonstrate that this procedure is a powerful tool in the analysis of the reactions observed in the lower-energy region including astrophysical energies.

Fusion Cross Section of Massive Nuclei by Fluctuation-Dissipation Dynamics

Fluctuation-dissipation dynamics is applied to the nearly mass-symmetric fusion reactions forming nuclei of Z> 80. We take into account the angular momentum of the system. The fusion cross section is calculated, and the hindrance of fusion is discussed. We estimate the amount of extra energy above the Coulomb barrier needed for fusion. In a fusion reaction with nearly symmetric projectile-target combination forming a compound nucleus with Z> 80 (or fissility larger than 0.65), additional kinetic energy above the incident Coulomb barrier is needed to realize the formation of a spherical compound nucleus. This supplementary energy was defined as the extraextra push energy EXX by Swiatecki 1) and systematic studies of this phenomenon, the so-called fusion hindrance, have been reported. 2) - 4) The origin of the necessity of the extra-extra push energy lies in the characteristics of the potential energy landscape in nuclear deformation parameter space. 5),6) As the system becomes heavier than Z around 80, the contact configuration comes to be located outside the ridge curve of the potential energy surface. Note that the fission saddle point is located on the ridge curve; it divides the deformation space into the mono-nucleus (fusion) region and di-nucleus (fission) region. This implies that the colliding nuclei must overcome the ridge to attain compact shapes, such as a sphere. Fusion hindrance has been investigated in the framework of the classical trajectory method 7) which describes fusion-fission dynamics in terms of the time evolution of the nuclear shape initially located at the contact configuration in the deformation space with a certain collective kinetic energy. To obtain information on EXX, the classical trajectory in a multi-dimensional deformation space has been calculated by Blocki et al. 7) taking into account the dissipative force stemming from the coupling between the collective and the single particle degrees of freedom. In their framework, the critical energy of the fusion reaction was obtained. There is no fusion event below the critical energy, while the trajectory always reaches the spherical region above the energy. The fluctuation of the trajectory which appears as the counterpart of the dissipative force was taken into account by Aguiar et al. 8) By the inclusion of fluctuations, it becomes possible to calculate the fusion probability; the trajectory becomes that of a Brownian particle and can thus be calculated using the Langevin equation. The aim of the present paper is to confirm the validity of the application of fluctuation-dissipation dynamics to the study of fusion of massive nuclei in the mass

Whack-A- Mole Model: Towards a Unified Description of Biological Effects Caused by Radiation Exposure

We present a novel model to estimate biological effects caused by artificial radiation exposure, Whack-a-mole (WAM) model. It is important to take account of the recovery effects during the time course of the cellular reactions. The inclusion of the dose-rate dependence is essential in the risk estimation of low dose radiation, while nearly all the existing theoretical models relies on the total dose dependence only. By analyzing the experimental data of the relation between the radiation dose and the induced mutation frequency of 5 organisms, mouse, drosophila, chrysanthemum, maize and tradescantia, we found that all the data can be reproduced by WAM model. Most remarkably, a scaling function, which is derived from WAM model, consistently accounts for the observed mutation frequencies of 5 organisms. This is the first rationale to account for the dose rate dependence as well as to give a unified understanding of a general feature of organisms.

Energy dependence of a local equivalent potential for RGM phase shifts for 16O + 16O

Abstract We have found, using the IP inversion method, the local representation of a potential that is S ( l ) equivalent to the RGM nonlocal potential of Wada and Horiuchi. Phase shifts corresponding to RGM calculations at laboratory energies 30, 41, 49, 59, 150, 350 and 500 MeV were inverted and the resulting local potentials compared with the local (but l -dependent) potentials obtained previously in the WKB-RGM scheme. The present l -independent potentials exhibit a smooth radial variation and show marked differences from previous results. The energy dependence arises from that of the exchange term and from the conversion of the l -dependence into an additional energy dependence. In particular, we show that the energy dependence of the volume integrals in this energy region is different from earlier WKB-RGM predictions.

Dynamics of the superheavy element synthesis with a diffusion model

Abstract A diffusion model is proposed for the dynamical treatment of the synthesis of superheavy elements. Fusion-fission process is analyzed by one-dimensional Smoluchowski equation with liquid drop model potential of no pocket and the temperature dependent shell correction energy which generates the pocket around the spherical shape. Competition between fission and neutron evaporation is taken into account in terms of the continuous cooling by neutron evaporation. The evaporation residue cross sections of superheavy elements have been shown to have an optimum value at a certain temperature, due to the balance between the diffusibility for fusion at high temperature and the restoration of the shell correction energy against fission at low temperature. The isotope dependence of the evaporation residue cross section is found to be very strong. Neutron rich compound system with small neutron separation energy is favorable for larger cross section because of the quick restoration of the shell correction energy.