Nucleon-nucleon interactions in the double folding model for fusion reactions

Nucleus-nucleus potentials are determined in the framework of double folding model for M3Y-Reid and M3Y- Paris effective nucleon-nucleon （NN） interactions. Both zero-range and finite-range exchange parts of NN interactions are considered in the folding procedure. In this paper the spherical projectile-spherical target system 16O＋^2008Pb is selected for calculating the barrier energies, fusion cross sections and barrier distributions with the density-independent and density-dependent NN interactions on the basis of M3Y-Reid and M3Y Paris NN interactions. The barrier energies become lower for Paris NN interactions in comparison with Reid NN interactions, and also for finite-range exchange part in comparison with zero-range exchange part. The density-dependent NN interactions give similar fusion cross sections and barrier distributions, and the density-independent NN interaction causes the barrier distribution moving to a higher position. However, the density-independent Reid NN interaction with zero-range exchange part gives the lowest fusion cross sections. We find that the calculated fusion cross sections and the barrier distributions are in agreement with the experimental data after renormalization of the nuclear potential due to coupled-channel effect.

Simplification of Double Folding Model Calculations in Study of Interaction Between Two Deformed Nuclei

The Double Folding （DF） model calculation of the internuclear potential in heavy-ion interactions when the participant nuclei are deformed in their ground states involves a six-dimensional integral. Using the multipole expansion in these calculations, the DF six-dimensional integral reduce to the sum of the products of three single-dimensional integrals. In this paper we have presented a procedure for the calculation of the radius dependent functions in the multipole expansion of the nuclear density and their Fourier transforms. We have also reduced the DF model integrals to the sum of the single dimensional integrals using the obtained relations for the radius dependent functions in the multipole expansion and their Fourier transforms.

Fold catastrophe model of strike-slip fault earthquake

Using a differential form of the potential energy function and taking the effect of work applied by external force in far field into account, the mechanism of strike-slip fault earthquake is analyzed. The research indicates that each characteristic displayed with a fold catastrophe model in the catastrophe theory corresPonds to a specific primary characteristic of the strike-slip fault earthquake. The fold catastrophe can describe the positions of starting and end points of a fault failure and the distance of fault dislocation. These include the description of stability of the surrounding rock-fault system before and after the earthquake. Two different illustrations about elastic energy releasing amount of the surrounding rock with the fault failure are shown with the primary characteristics mutually demonstrated. The intensity of strike-slip fault earthquake is related to the surrounding rock press and the stiffness ratio of surrounding rock and fault. The larger the surrounding rock press, the smaller the stiffness ratio. The larger the included angle between the tangential stress axis and the causative fault surface, the stronger the earthquake.

Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies

The hindrance in heavy-ion fusion reactions a deep sub-barrier energies is investigated using the double folding model with a hybrid method between the frozen and adiabatic density approximations.In this method,the density distributions of the projectile and the target depend closely on the distance between them.As the distance decreased,the half-density radii of the colliding nucle gradually increased to the half-density radius of the compound nucleus.The total potential based on this non-frozen approximation generates a slightly shallower pocket and becomes more attractive inside the pocket compared to that obtained from the frozen approximation.A damping factor was used to simulate the decline of the coupled channel effects owing to the density rearrangement of the two colliding nuclei.The calculated fusion cross-sections and astrophysical S factors at the deep sub-barrier energies are both in good agreement with the experimental data for the medium-heavyNi+Ni and medium-lightMg+Si mass systems.In addition,it was concluded that the apparent maximum of the S factors most likely appears in fusion systems with strong coupling effects.

MECHANISM AND CATASTROPHE THEORY ANALYSIS OF CIRCULAR TUNNEL ROCKBURST

Mechanism of circular tunnel rockburst is that, when the carrying capacity of the centralized zone of plastic deformation in limiting state reduces, the comparatively intact part in rock mass unloads by way of elasticity; rockburst occurs immediately when the elastic energy released by the comparatively intact part exceeds the energy dissipated by plastic deformation. The equivalent strain was taken as a state variable to establish a catastrophe model of tunnel rockburst, and the computation expression of the earthquake energy released by tunnel rockburst was given. The analysis shows that, the conditions of rockburst occurrence are relative to rock＇s ratio of elastic modulus to descendent modulus and crack growth degree of rocks; to rock mass with specific rockburst tendency, there exists a corresponding critical depth of softened zone, and rockburst occurs when the depth of softened zone reaches.

Analysis of main shock of thrust fault earthquake by catastrophe theory

The relationship between work and energy increment of a thrust fault system with quasi-static deformation can be decomposed into two parts： volume strain energy and deviation stress energy. The relationship between work and energy increment of the deviation stress of a simplified thrust fault system is analyzed based on the catastrophe theory. The research indicates that the characteristics displayed by the fold catastrophe model can appropriately describe the condition of earthquake generation, the evolvement process of main shock of thrust fault earthquake, and some important aftershock proper- ties. The bigger the surrounding press of surrounding rock is, the bigger the maximum principal stress is, the smaller the incidences of the potential thrust fault surface are, and the smaller the ratio between the tangential stiffness of surrounding rock and the slope is, which is at the inflexion point on the softened zone of the fault shearing strength curve. Thus, when earthquake occurrs, the larger the elastic energy releasing amount of sur- rounding rock is, the bigger the earthquake magnitude is, the larger the half distance of fault dislocation is, and the larger the displacement amplitude of end face of surrounding rock is. Fracturing and expanding the fault rock body and releasing the volume strain energy of surrounding rock during the earthquake can enhance the foregoing effects to- gether.

Double folding model calculation applied to fusion reactions

The interaction potential between a spherical and a deformed nucleus is calculated within the double-folding model for deformed nuclei. We solve the double folding potential numerically by using the truncated multipole expansion method. The shape, separation and orientation dependence of the interaction potential, fusion cross section and barrier distribution of the system ^16O＋^154Sm are investigated by considering the quadrupole and hexadecapole deformations of ^154Sm. It is shown that the height and the position of the barrier depend strongly on the deformation and the orientation angles of the deformed nucleus. These are quite important quantities for heavy-ion fusion reactions, and hence produce great effects on the fusion cross section and barrier distribution.

Calculation of α decay half-lives for superheavy elements using the double folding model

α decay half-lives of some new synthesized superheavy elements, possibly synthesized superheavy elements and decay products are calculated theoretically within the WKB approximation by using microscopic α-nucleus interaction potentials. These nuclear potentials between the α particle and daughter nuclei are obtained by using the double folding integral of the matter density distribution of the α particle and daughter nuclei with a density-dependent effective nucleon-nucleon interaction, in which the zero-range exchange term is supplemented. The calculated α decay half-lives are compared with those of the different models and experimental data. It is shown that the present calculation successfully provides the half-lives of the observed decays for some new superheavy elements and therefore gives reliable predictions for α decay of possibly synthesized superheavy elements in future experiments.

Folding model calculations for ~6He+^(12)C elastic scattering

In the framework of the double folding model, we used the α＋2n and di-triton configurations for the nuclear matter density of the ~6He nucleus to generate the real part of the optical potential for the system ~6He＋^（12）C. As an alternative, we also use the high energy approximation to generate the optical potential for the same system. The derived potentials are employed to analyze the elastic scattering differential cross section at energies of 38.3, 41.6 and 82.3 Me V/u. For the imaginary part of the potential we adopt the squared Woods-Saxon form. The obtained results are compared with the corresponding measured data as well as with available results in the literature. The calculated total reaction cross sections are investigated and compared with the optical limit Glauber model description.

Proton emission from the drip-line nuclei I-Bi using the WKB approximation with relativistic mean-field densities

We study the properties of proton rich nuclei reported as proton emitters in the region from I to Bi with Z =53 to 83 and N = 56 to 102 as a crucial application to the existence of exotic nuclei. The effective relativistic meanfield formalism(E-RMF), with NL3, FSUGarnet, G3 and IOPB-I interactions, is adopted for analysis of the ground state properties of proton emitters. Furthermore, in the E-RMF background, the Wentzel-Karmers-Brillouin(WKB)barrier penetration method is used for the calculation of proton emission half-lives. It is found that the calculated halflives are in good agreement with the experimental results for all emitters considered in this study.

Analysis of strong refractive effect within 11Li projectile structure

In the context of the double folding optical model,the strong refractive effect for elastic scattering of 11Li+12C and 11Li+28Si systems at incident energies of 29,50,and 60 MeV/n is studied.Real folded potentials are generated based on a variety of nucleon-nucleon interactions with the suggested density distributions for the halo structure of 11Li nuclei.The rearrangement term(RT)of the extended realistic density dependent CDM3Y6 effective interaction is considered.The imaginary potential was taken in the traditional standard Woods-Saxon form.Satisfactory results for the calculated potentials are obtained,with a slight effect of the RT in CDM3Y6 potential.Successful reproduction with a normalization factor close to one for the observed angular distributions of the elastic scattering differential cross section has been achieved using the derived potentials.The obtained reaction cross-section is studied as a guide by extrapolating our calculations and previous results.

Reanalysis of Elastic Scattering of ~6Li + ^(209)Bi Reaction Using a New DensityDistribution of ~6Li Nucleus

In the present paper, the elastic scattering of6 Li + 209 Bi system is reanalyzed by using the double folding model (DFM) at energies near the Coulomb barrier (ELab=29.9 and 32.8 MeV). With this goal, a new density distribution of6 Li nucleus, the no-core full configuration (NCFC) density distribution (DD), is used to obtain the real potentials in DFM calculations. The NCFC DD results are compared with the results of both gaussian shape (GS) DD and an earlier study as well as the experimental data. This comparison provides information about the similarities and differences of the models used in calculations.

Elastic scattering of ~6He from ^(12)C at 38.3 MeV/nucleon

The microscopic optical potential of nucleus-nucleus interaction is presented via a folding method with the isospin dependent complex nucleon-nuclear potential,which is first calculated in the framework of the Dirac-Bruecker-Hartree-Fock approach. The elastic scattering data of ^6He at 229.8 MeV on 12C target are analyzed within the standard optical model. To take account of the breakup effect of 6He in the reaction an enhancing factor 3 on the imaginary potential is introduced. The calculated ^6He＋^12C elastic scattering differential cross section is in good agreement with the experimental data. Comparisons with results in the double-folded model based on the M3Y nucleon-nucleon effective interaction and the few the body Glaubermodel calculations are discussed. Our parameter free model should be of value in the description of nucleusnucleus scattering,especially unstable nucleus-nucleus systems.

Pauli blocking potential applied to heavy-ion fusion reactions

In this study,the Pauli blocking potential between two colliding nuclei in the density overlapping regionis applied to describe the heavy nuclei fusion process.Inspired by the Pauli blocking effect in theα-decay of heavynuclei,the Pauli blocking potential of single nucleon from the surrounding matter is obtained.In fusion reactionswith strong density overlap,the Pauli blocking potential between the projectile and target can be constructed using asingle folding model.By considering this potential,the double folding model with a new parameter set is employedto analyze the fusion processes of 95 systems.A wider Coulomb barrier and shallower potential pocket are formed inthe inner part of the potential between the two colliding nuclei,compared to that calculated using the Akyüz-Win-ther potential.The fusion hindrance phenomena at deep sub-barrier energies are described well for fusion systems^(16)O+^(208)Pb and^(58)Ni+^(58)Ni.