An analysis of nuclear fissility for intermediate-energy proton induced reactions

In the framework of cascade-evaporation model for nuclear reactions and the liquid-drop model for fission the experimental data on nuclear fissility by protons with energy ≦ 1 GeV was analysed. The authors studied the influence on the value of fissility of the shell effects, pre-equilibrium particle emission from the excited nuclei and the dependence of the height of the fission barriers on the energy of the excited nucleus.     

Multidimensional dynamical-statistical model for describing the fission of excited nuclei

A multidimensional stochastic model for describing the decay of excited nuclei is presented. The model takes into account the dynamics of thermal fluctuations of collective variables, the dissipation of the kinetic energy of collective motion, and the emission of light particles from excited nuclei. The potential energy of a deformed nucleus is calculated within the liquid-drop model with a sharp surface and within the finiterange-interaction model. The friction parameters are calculated on the basis of the one-body-dissipation model. The inertia parameters are found in the Werner-Wheeler approximation. The drift components of forces are determined in terms of the entropy of an excited nucleus. The latter in turn is computed within the Fermi gas approximation with allowance for the deformation dependence of the density-level parameter. The fission probability, the mean multiplicity of neutrons emitted prior to scission (prescission neutrons), and the variances of the mass distributions of fission fragments at the most probable kinetic-energy value are calculated on the basis of the model developed here and are compared with experimental data. The dependences of these quantities on the model parameters are considered in detail.     

Multiply charged neon clusters: failure of the liquid drop model?

We have analyzed the stability and fission dynamics of multiply charged neon cluster ions. The critical sizes for the observation of long-lived ions are n2=284 and n3=656 for charge states 2 and 3, respectively, a factor 3 to 4 below the predictions of a previously successful liquid-drop model. The preferred fragment ions of fission reactions are surprisingly small (2相似文献   

Étude de la dissipation d'énergie dans la fission de 234u à l'aide de la réaction 233U(d,pf)

The energy balance in the fission of ²³⁴U has been investigated on the basis of experimental results from the ²³³U(d, pf) reaction. Taking into account the neutron evaporation we have deduced the total kinetic energy and excitation energy distributions of the primary fragments as functions of the excitation energy of the fissioning nucleus. The neutron evaporation temperatures have been adjusted so as to reproduce the average value and width of the measured kinetic energy distributions for each fragmentation. Excitation energy distributions of the fragments have been deduced. The data are discussed in the framework of the liquid-drop model with shell corrections. Evidence for energy dissipation in the fission of ²³⁴U, involving drastic changes in the scission configuration, is shown for some fragmentation modes.     

Nuclear interface energy at finite temperatures

The thermodynamic properties at finite temperatures of the plane interface between two phases of nuclear matter in equilibrium are examined theoretically, and explored numerically. The microscopic hamiltonian, the Skyrme I′ interaction, is used in the Thomas-Fermi approximation to obtain the finite-temperature extensions of earlier zero-temperature results which used the Hartree-Fock and Thomas-Fermi methods. Approximate analytic fits are given to the χ_i (proton fraction on the dense-matter side) dependence of the critical temperature, and to the T and χ_i dependences of the surface thermodynamic potentials, the density of surface neutrons, the surface entropy and the neutron and proton chemical potentials at phase equilibrium. These fits are an ingredient in a compressible liquid-drop nuclear model, the basis of an equation of state for hot, dense matter needed in certain astrophysical applications.The liquid-drop model is used here to construct an isolated, low-T nucleus, whose properties are compared with the original zero-T Hartree-Fock calculations which lead to the Skyrme I interaction, and with other mass formulae. The low-temperature expansion of the surface energy is compared with that obtained in other calculations. The nuclear level density at the Fermi surface, related to the low-T expansion of the entropy of the whole nucleus, is also discussed.     

Potential energy surfaces in the two-center shell model

The two-center shell model of two equal overlapping spheroids is combined with Lawrence's liquid-drop shapes. Within this framework, potential energy surfaces for nuclei from different mass regions are calculated. In particular, the transition of the ground state deformation from spherical to deformed is investigated for a sequence of ruthenium isotopes.     

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.     

Semiempirical atomic mass formula

An atomic mass formula based on the liquid-drop model with shell and deformation energies determined from the Nilsson model and BCS pairing energy has been adjusted simultaneously to ground-state binding energies and to fission barrier heights. A short table of calculated values is included, and additional calculations are available.     

A universal relation for the cohesive energy of nanoparticles

A universal relation between the cohesive energy and the particle size has been predicted based on the liquid-drop model. The universal relation is well supported by other theoretical models and the available experimental data. The universal relations for intermediate size range as well as for particles with very few atoms are discussed. A comparison of onset temperature of evaporation also establishes a universal relation.     

Liquid-drop model for the surface energy of nanoparticles

Based on the liquid-drop model, we have evaluated the Tolman length and surface energy of nanoparticles for different elements and compared with other theoretical models as well as the available simulated data. The predictions of the model show good agreement with the simulated results. Like the cohesive energy and melting temperature, the size-dependency of surface energy is also shape-dependent.     

Fusion Barrier of Super-heavy Elements in a Generalized Liquid Drop Model

The macroscopic deformed potential energies for super-heavy elements Z = 110,112,114,116,118 arc determined within a generalized liquid drop model (GLDM). A quasi-molecular mechanism is introduced to describe the deformation of a nucleus in the GLDM and the shell model simultaneously. The macroscopic energy of a twocenter nuclear system in the GLDM includes the volume-, surface-, and Coulomb-energies, the proximity effect at each mass asymmetry, and accurate nuclear radius. The shell correction is calculated by the Strutinsky method and the microscopic single particle energies are derived from a shell model in an axially deformed Woods-Saxon potential with the quasi-molecular shape. The total potential energy of a nucleus can be calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is applied to predict the fusion barriers of the cold reactions ^64Ni ^208 spb → ^272 110*, ^70Zn ^208pb → ^278 112*, ^76Ge ^208seb → ^284 114*,^82Se ^208pb → ^29 116*, ^86Kr ^208pb → ^294 118*. It is found that the neck in the quasi-molecular shape is responsible for the deep valley of the fusion barrier. In the cold fusion path, double-hump fusion barriers could be predicted by the shell corrections and complete fusion events may occur.     

Spheroidal cap configurations of atomic clusters on planar surfaces

Deposited atomic cluster configurations are investigated under the hypothesis of spheroidal cap shapes being a stable geometry. The macroscopic-microscopic method is employed to calculate the deformation energy. A new specialized single-particle model is developed in order to account for the quantum effects, and the liquid-drop approach is used to calculate the macroscopic part of the energy. The minima within the total deformation energy are interpreted as equilibrium states of atomic clusters on surfaces. Calculations have been performed for the metallic clusters of Na with atom numbers N = 20, 70 and 200.     

Temperature dependence of volume and surface symmetry energy coefficients of nuclei

The thermal evolution of the energies and free energies of a set of spherical and near-spherical nuclei spanning the whole periodic table are calculated in the subtracted finite-temperature Thomas–Fermi framework with the zero-range Skyrme-type KDE0 and the finite-range modified Seyler–Blanchard interaction. The calculated energies are subjected to a global fit in the spirit of the liquid-drop model. The extracted parameters in this model reflect the temperature dependence of the volume symmetry and surface symmetry coefficients of finite nuclei, in addition to that of the volume and surface energy coefficients. The temperature dependence of the surface symmetry energy is found to be very substantial whereas that of the volume symmetry energy turns out to be comparatively mild.     

Investigation of fragment yields from <Superscript>239</Superscript>U fission at anomalously high values of the total kinetic energy

The yields of fragments originating from ²³⁸U fission induced by 5-MeV neutrons are investigated. Accumulated statistics—2.5×10⁶ events of binary fission—make it possible to study fission-fragment yields at anomalously high values of the total kinetic energy. The spectra of the cold fragmentation of ²³⁹U are obtained. Events characterized by the total kinetic energy that is equal to the total reaction energy are found for some fragment masses. Methods of digital signal processing permit a highly reliable identification of these rare events. An interpretation of this phenomenon on the basis of the liquid-drop model of the fission process is proposed.     

三分裂中的级联裂变模式

用统计模型分析级联裂变，假设复合核首先分裂为两裂变碎片，其质量分布与实验分布一致，跟踪所有质量上可能的裂变碎片和所有能量上可能的衰变过程，统计裂变碎片再次裂变的几率，证明级联裂变模式基本上与三分裂的实验相符，复合核系统的激发能越高，裂片的质量越大，再裂的几率也就越大．     

Isomorphic shell model for closed-shell nuclei

The classical part of the isomorphic model for closed-shell nuclei is presented based on two physical assumptions, namely (a) the nucleons of a closed shell nucleus, considered at their most probable positions, are in an instantaneous dynamic equilibrium on spherical shells, and (b) the dimensions of the shells are determined by their close packing given that a neutron and a proton are represented by hard spheres of definite sizes. The first assumption leads to the instantaneous angular structure, and the second to the instantaneous radial structure of closed-shell nuclei. Applications of the model coming from this classical part alone and presented here are structural justification of all magic numbers, neutron (proton) and charge rms radii, nuclear densities of closed-shell nuclei, and Coulomb, kinetic, and binding energies. All the predictions are in good agreement with experimental data. A characteristic novelty of the isomphic model is that assumption (a) is related to the independent particle model, and assumption (b) to the liquid-drop model. The isomorphic model may provide a link between these two basic nuclear physics models since it incorporates features of both.     

Liquid-drop effects in sub-barrier fusion reactions

We introduce an operational measure for the enhancement of the fusion cross section at sub-barrier energies in terms of an asymptotic energy shift ΔE. It is shown that ΔE has a continuously growing trend with the size of the system. This trend is explained in terms of neck formation using the liquid-drop model. Deviations from this trend are attributed to strong coupling to specific channels.     

Superdeformed states in rotating152Dy

The recently observed gamma-spectrum of¹⁵²Dy at angular momenta 25>~I>~60 is interpreted in terms of a strongly deformed shape isomer. A pronounced minimum is found for these angular momenta in the sum of liquid-drop energy (including rotational part) and shell-correction (calculated in the Nilsson model) of¹⁵²Dy. The general criteria for stability of this minimum against rotation are discussed.     

Phase transitions in cold and warm dense matter

We consider the phase transitions, in dense matter, from nuclei to bubbles and from bubbles to uniform matter. A simplified version of the compressible liquid-drop model allows us to discuss analytically the densities at which the free energies of the different phases are equal, and the density discontinuities of the phases in equilibrium. A reasonable agreement with detailed numerical calculations is obtained only if the compressibility of the matter inside nuclei, and particularly outside bubbles, is taken into account. The dependence of the bubbles-uniform matter transition on the various elements of the Coulomb energy is discussed in detail: the transition is actually a first-order one, but it becomes of second order if the lattice Coulomb energy is turned off.The insight into the effect on the transition of the ratio of surface-plus-Coulomb energy to compression modulus allows us to understand the dependence of the transition densities on temperature and on the microscopic model employed.     

The spectrum of nuclear energy levels during the fission process

Despite great success in explaining the fission process qualitatively, the liquid-drop model has failed to explain a number of important aspects of nuclear fission. Thus there has appeared a tendency to interpret experimental data by considering shell [1] and single-particle [2] effects. However, the authors of these and other works have confined themselves to a qualitative examination of the problem. In the fission process, the nucleus passes through various states of deformation. In the adiabatic approximation, each of these corresponds to a definite single-particle energy-level spectrum. In the present article we find the single-particle nucleon states during the fission process using specific assumptions about the mechanism of this process.