Fission dynamics of excited nuclei within the liquid-drop model

We evaluate the temperature T_scis at the scission point and the saddle-to-scission time τ_scis for the fission of heated nuclei. We use classical Lagrange-like equations of motion within the liquid-drop model. The nuclear surface is parameterized by a two-parameter family of the Lawrence shapes. Conservative forces are defined through the free energy of the nucleus at finite temperatures. We use the friction tensor that is derived from the Navier-Stokes momentum-flux tensor and which takes into account the boundary conditions at the nuclear surface. The scission line is determined from the instability condition of the nuclear shape with respect to variations of the neck radius. A numerical solution to the dynamical equations is obtained for the ²³⁶U nucleus. The viscosity coefficient μ is deduced from a comparison of experimental data on the kinetic energy of fission fragments with the computed one. It is found that μ obtained by using our approach deviates significantly from μ of the standard hydrodynamic model.     

Evaporation and fission of hot metallic clusters and hot nuclei

Evaporation and fission of metallic clusters are described by models developed in nuclear physics which are appropriately modified. Results of calculations for evaporation rates, appearance sizes and fission times (with and without viscosity) are presented. Presented at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

New method for calculating the potential energy of deformed nuclei within the liquid-drop model

The method that we previously developed for going over from double volume integrals to double surface integrals in calculating the Coulomb energy of nuclei that have a sharp surface is generalized to the case of nuclei where the range of nuclear forces is finite and where the nuclear surface is diffuse. New formulas for calculating the Coulomb and the nuclear energy of deformed nuclei are obtained within this approach. For a spherically symmetric nucleus, in which case there is an analytic solution to the problem in question, the results are compared with those that are quoted in the literature, and it is shown that the respective results coincide identically. A differential formulation of the method developed previously by Krappe, Nix, and Sierk for going over from double volume integrals to double surface integrals is proposed here on the basis of the present approach.     

Large amplitude collective motion in nuclei and metallic clusters — Applicability of adiabatic theory for a pairing model

A model Hamiltonian describing a two-level system with a crossing plus a pairing force is investigated using the technique of large-amplitude collective motion. The collective path, which is determined by the decoupling conditions, is found to be almost identical to the one in the Born-Oppenheimer approximation for the case of a strong pairing force. For the weak pairing case, the obtained path describes a diabatic dynamics of the system. Presented by T. Nakatsukasa at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997. This work is supported by EPSRC (UK).     

Charge vibrations in the liquid-drop model of fission

The two-spheroid liquid-drop model of fission developed by Nix and Swiatecki has been extended to include charge vibrations. Using the Myers-Swiatecki mass formula, the appropriate stiffness constants have been obtained in analytic form. The effective mass, M_Δ, associated with charge vibrations for fission shapes was deduced from eigenenergies for the giant dipole resonance calculated by Updegraff and Onley, assuming that the eigenenergy is given by

$\text{h}\text{?}\text{ω}{}_{\mathrm{dipole}}\text{=}\text{h}\text{?}\text{K}{}_{\mathrm{\Delta \Delta }}\text{M}{}_{\mathrm{\Delta }}$

,where K_ΔΔ is the stiffness for charge vibrations. To account for the experimental charge dispersion widths a highly constricted fission shape was chosen. The dependence of fragment deformation energy on mass increases more rapidly than in the Nix and Swiatecki treatment when the eigenvalues of two new normal modes have similar values; it is concluded that this, together with spherical closed-shell effects, may explain the discrepancy between the Nix and Swiatecki values and experimental data. Various other aspects of the effect of charge vibrations are discussed.     

Similarities and differences for light-induced surface plasmons in one- and two-dimensional symmetrical metallic nanostructures

Two types of double-sided nanostructure, one possessing a slit aperture with parallel grooves and the other possessing a circular aperture with concentric grooves, were fabricated to examine the similarities and differences of their diffraction behavior in one-dimensional (1-D) and two-dimensional (2-D) nanostructures. Based on the projection-slice theory, we conjecture that the surface plasmons in these two different nano-scale grooves possess similar modes. A localized surface plasmon (LSP) was used to examine the transmission characteristics induced by the apertures. The transmission characteristics of the slitted nanostructure and the circular nanostructure aperture were then measured. We coupled the transmission spectra measured from these two apertures with a 1-D parallel groove transmission curve simulated by a 1-D rigorous coupled wave analysis. Measured spectra results show reasonable agreement with the simulated data. We propose that the apparent blueshift observed in the peak frequency of a 2-D nanostructure is due to the difference in the shape of the aperture and the spot transmission characteristics of 1-D and 2-D systems as induced by a LSP.     

Limits of the nuclear viscosity coefficient in the liquid-drop model

We estimate the upper and lower limits of the nuclear viscosity coefficient within the framework of the liquid-drop model. In addition, we find that there is a critical fissility parameter above which all quadrupole vibrations are overdamped even at T≈0     

Breathing cluster model for nuclei of two s-wave clusters

A microscopic cluster model with a pair of breathing clusters and an interaction that reproduces the correct energies and radii of the separate clusters is applied to the nuclei with 5⩽A⩽8. The energies are well reproduced, and, as shown by the charge form factor and αd fragmentation strength of ⁶Li, the low-momentum behaviour of the wave functions is also realistic.     

New formula for calculating coulomb energies in the liquid-drop model

A new transformation of double volume integrals into double surface integrals is presented. A simple regular method for deriving integrands in a surface integral is proposed. This method is used to calculate the Coulomb energy of a nucleus within the model of a liquid drop with a sharp boundary. Numerical results obtained on the basis of the new formula are compared with those calculated by one of the formulas employed previously.     

Energy model for the Zr-based metallic glass alloy melt with clusters

An energy model for the melt of bulk metallic glass (BMG) with clusters was established, the Gibbs free energy and interfacial energy for the Zr-Al-Ni ternary alloy melt with Zr2Ni clusters were calculated, and the effects of the clusters on the Gibbs free energy, interfacial energy and nucleation rate were analyzed. The results showed that the existence of the clusters in the Zr-Al-Ni ternary alloy melt enables the Gibbs free energy to decrease in the composition range where bulk metallic glass forms easily, makes the interfacial energy increase and changes the distribution of the interfacial energy with the alloy composition. Because of the clusters in the melt, the Gibbs free energy of the Zr66Al8Ni26 alloy melt decreases about 0.3-1 kJ/mol and the interfacial energy between the melt and crystal nucleus increases about 0.016 J/m2. The nucleation rate of the undercooled Zr66Al8Ni26 alloy melt decreases evidently under the influence of the clusters on Gibbs free energy and the interfacial energy, and the maximum of the nucleation rate in the melt with the Zr2Ni clusters is only about 107 mol-1·s-1.     

RPA in nuclei and metal clusters

We discuss and compare the gross features of resonance excitations in nuclei and metal clusters. We point out the phenomenon of ”jellium scaling” which means that different materials for metal clusters all give similar resonance spectra and we discuss the various effects which determine the exact position of the resonance.     

Polarizability effect in metallic clusters

Langevin approach implemented in the inelastic cross-sections measured for the low-energy electrons colliding with metallic clusters points out that statical form of the polarizability dominate at energies less than 1.25 eV. The dynamical form comes into play at energies around 1.3 eV. The form of the polarizabilities indicates that polarizability of the metallic clusters is energy-dependent.     

Preferred clusters in metallic glasses

In this work,we present a feasible scheme based on framework of the sophisticated Voronoi tessellation method in order to evaluate what clusters should be preferred for building blocks in any given metallic glass,by analysing the fivefold-symmetry axes as well as the degree of structural regularity in various clusters.This scheme is well proved by a group of experiments and calculations,which may have broad implications for exploration of obtaining explicit and proper structural pictures,and understanding the structural origin of the unique properties and glass forming ability in these novel amorphous alloys.     

Forces between heavy nuclei in the independent-particle model

We use the linear response theory to study the force on a heavy nucleus moving near the symmetry axis of ²³⁸U, in an independent-particle model. We present the first detailed microscopic computation showing relaxation of the single-particle motion due to incoherence, and find a relaxation time of about $\text{0.3}\text{MeV}\text{≈ 2 × 10}{}^{\mathrm{?22}}\text{sec}$. We consider three stages of the reaction. While the nuclei approach each other, the induced force is very weak, and is computed as a function of the position, velocity and acceleration of the other nucleus; it involves excitons of 10 to 20 MeV. The computed force agrees well with phenomenological values. The second stage of the reaction is the formation of a neck, which we argue will begin already when the nuclear half-density surfaces are more than 4 fm from each other. For slow collective motion, thought to occur after the neck forms, we show how to represent the incoherent excitation of low-frequency excitons by a friction force, and present a method suitable for numerical computations of the friction coefficient.     

判定金属玻璃微观结构中的二十面体类团簇

基于Voronoi几何分形法, 分析了理想二十面体团簇和ZrCu二元金属玻璃中各种团簇的结构特点, 提出了一种判定金属玻璃原子结构中二十面体类团簇的方法. 并选取三个ZrCu 非晶成分作为研究对象, 基于Voronoi团簇, 利用该方法提取了各种构型团簇, 证实其中四种构型团簇的基本几何结构与理想二十面体相似, 并具有同样近似于理想二十面体的高致密度、高规则度和高五次对称性, 因此可称之为二十面体类团簇. 此类二十面体类团簇可作为金属玻璃的主要结构单元, 普遍存在于非晶结构中; 二十面体类团簇及其连接能包含几乎所有的原子, 从而形成非晶结构. 研究结果提供了一种新的团簇判定方法, 有助于从微观结构层面分析合金中的非晶形成机理.     

Released energy formula for proton radioactivity based on the liquid-drop model

In this work, based on the liquid-drop model and considering the shell correction, we propose a simple formula to calculate the released energy of proton radioactivity(Q_p). The parameters of this formula are obtained by fitting the experimental data of 29 nuclei with proton radioactivity from ground state. The standard deviation between the theoretical values and experimental ones is only 0.157 Me V. In addition, we extend this formula to calculate 51 proton radioactivity candidates in region 51≤Z≤83 taken from the latest evaluated atomic mass table AME2016 and compared with the Q_p calculated by WS4 and HFB-29. The calculated results indicate that the evaluation ability of this formula for Q_p is inferior to WS4 while better than HFB-29.