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.     

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.     

Coulomb Potentials between Spherical and Deformed Nuclei

Coulomb potentials for spherical-deformed reaction as well as the conventional formulas. Our results approaches have quite different behaviours in the partners are calculated in terms of the double folding model show that the Coulomb potentials calculated with different internal region of the potential. Because fusion process is sensitive to the barrier height and the internal part of the potential, the fusion excitation function, especially the fusion barrier distribution, should provide a strict test of the interaction potentials. Therefore, we calculate the fusion excitation function and barrier distribution for the ^16O ＋^154Sm system with different versions of the Coulomb potentials, in comparison with the experimental results. It is found that the fusion excitation function and barrier distribution of ^16O＋^154Sm are obviously different for the different versions of the Coulomb potentials. By means of this comparison, we may conclude that the double folding model with the accurate approximate form can provide rather reasonable Coulomb potentials.     

Finding a Probe for Extracting Information on the Momentum Dependent-Interaction in Heavy Ion Collisions

The effect of momentum-dependent interaction on the kinetic energy spectrum of the neutron-proton ratio （ （n/p）gas）b（ Ek ） for 64Zn ＋64Zn is studied. It is found that （ （n/p）gas）b（ Ek ） sensitively depends on the momentumdependent interaction and weakly on the in-medium nucleon-nucleon cross section and symmetry potential. Therefore （ （n/p）gas）b（ Ek ） is a possible probe for extracting information on the momentum-dependent interaction in heavy ion collisions.     

Nuclear Potential and Fusion Cross Sections for Synthesizing Super-Heavy Elements in Di-nuclear Systems

A double foMing method with simplified Skyrme-type nucleon nucleon interaction is used to calculate the nuclear interaction potential between two nuclei. The calculation is performed in tip-to-tip orientation of the two nuclei if they are deformed. Based on this method, the potential energy surfaces~ the fusion probabilities and the evaporation residue cross sections for some cold fusion reactions leading to super-heavy elements within di-nuclear system model are evaluated. It is indicated that after the improvement, the exponential decreasing systematics of the fusion probability with increasing charge number of projectile on the Pb based target become better and the evaporation residue cross sections are in better agreement with the experimental data.     

Relativistic Energy Pb Projectile Fragmentation with Heavy Target Nuclei

We investigate the fragmentation of 158A GeV ^207Tpb projectiles with Bi, Pb, Cu and AI targets using CR-39 nuclear track detectors. The exposures were made at SPS-CERN. After the etching, the detectors were scanned using an optical microscope to collect the data of etched cone diameters and lengths. We measured the partial charge-changing cross sections using the data of etched cone lengths. The predicted cross sections are compared to similar measurements reported in literature and their dependences on projectile and target mass are described.     

INFLUENCE OF SHELL STRUCTURE ON DEEP INELASTIC COLLISIONS

A kinematically complete study of the symmetric systems ¹⁵⁴Sm+¹⁵⁴Sm and ¹⁴⁴Sm+¹⁴⁴Sm has been performed at energies 30% in excess of the interaction barrier. They have been chosen because of their different internal structure: ¹⁴⁴Sm has a closed N=82 neutron shell and hence a spherical ground state confighration; ¹⁵⁴Sm with ten neutrons outside this shell is strongly deformed. Over the whole range of kinetic energy loss the variances of the measured mass distributions were found to be similar in both reactions, whereas the variances of the element distributions are considerably larger at small energy losses in the ¹⁴⁴Sm system. Based on the shell-corrected potential energy surface these observations are attributed to the closed N=82 neutron shell which, for ¹⁴⁴Sm, hinders the neutron exchange and leads to a preferential transfer of protons.     

Entrance channel mass asymmetry dependence of compound nucleus formation

The fusion reactions ⁴⁸Ca + ¹⁵⁴Sm and ¹⁶O + ¹⁸⁶W leading to the same compound nucleus ²⁰²Pb are studied within the framework of an improved isospin dependent quantum molecular dynamics model. The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies, Coulomb barriers and fusion cross sections. The calculated fusion cross sections agree quantitatively with the experimental data. We conclude that the compound nucleus formation is favorable for the system with larger mass asymmetry.     

Shell Correction and Pairing Energies in the Dinuclear System Model

We investigate the dependences of the potential energy surfaces （PES） and the fusion probabilities for some cold fusion reactions leading to super-heavy elements on the nuclear shell effect and pairing energy. It is found that the shell effect plays an important role in the fusion of the super-heavy element while pairing energy＇s contribution is insignificant. The fusion probabilities and evaporation residue cross sections as functions of the Ge-isotope projectile bombarding ^208Pb are also investigated. It is found that evaporation residue cross sections do not always increase with the increasing neutron number of Ge-isotope.     

CHARGE DENSITY DISTRIBUTIONS OF DEFORMED NUCLEI

A simple calculation method for charge for charge density distributions of deformed nuclei by using macroscopic model has been proposed.The calculations of charge density distributions for ¹⁹²Os,¹⁵⁴Gd,¹⁵²Sm,¹⁷⁴Yb, and ^{144,148,150,152}Sm nuclei have been performed.The results show that the calculated charge densities are in good agreement with experiments.Consequently,on the base of experimental data of the transition probabilities for ground state to 2⁺,4⁺,6⁺ rotational states or its electric multipole moments,The charge density distributions of deformed nuclei can be predicted theoretically by this method.     

Fusion-evaporation cross-sections for 48Ca + 154Sm near the Coulomb barrier

Measurements of fusion-evaporation cross-sections for the system ⁴⁸Ca + ¹⁵⁴Sm have been performed in the sub- and near-barrier energy range. Barrier-passing cross-sections have been obtained by adding recently measured capture-fission cross-sections at the same energies, and the barrier distribution for capture has been extracted. The data have been analyzed within a coupled-channel model, and a large subbarrier cross-section enhancement is observed, due to the ground-state prolate deformation of ¹⁵⁴Sm. The ⁴⁸Ca + ¹⁵⁴Sm capture cross-sections are compared to existing data on ¹⁶O + ¹⁸⁶W fusion, leading to the same CN, where a few higher-energy points have also been measured. The evaporation residue cross-sections for the two systems above the barrier indicate that complete fusion is inhibited for ⁴⁸Ca + ¹⁵⁴Sm by 40% in that energy region, with respect to ¹⁶O + ¹⁸⁶W.     

Electrical Characterization of Deep Trap Properties in High-k Thin-Film HfO2 Dielectric

Deep-trap properties of high-dielectric-constant （k） HfO2 thin films are investigated by deep-level transient spectroscopy and capacitance-voltage methods. The hole traps of the HfO2 dielectric deposited on a p-type Si substrate by sputtering are investigated in a metal-oxide-semiconductor structure over a temperature range of 300-500K. The potential depth, cross section and concentration of hole traps are estimated to be about 2.5eV, 1.8 ×10^-16 cm^2 and 1.0 × 10^16 cm^-3, respectively.     

Effects of E2 and El-E2 Interference on Coulomb Dissociation of 19C

We investigate the effects of higher order multipole transitions, in particular electric quadrupole （E2） and El-E2 interference, on the Coulomb dissociation of 19 C within the framework of the first order eikonal approximation. The sensitivity of the total Coulomb breakup cross section and the longitudinal momentum distribution of the core fragment to these effects are checked. The breakup occurs predominately through the dipole transition and the contribution of E2 transition to the total cross section is found to be within the range from 1 to 3% of that of El. It is further observed that the El-E2 interference term contributes nothing to the integrated cross section. On the other hand, the longitudinal momentum distribution is observed to be insensitive to the E2 transition while the El-E2 interference introduces a small asymmetry in its shape.     

The sub-barrier fusion of40Ar with144,148,154Sm

The cross sections for production of evaporation residues (σ _er) and for fusion-fission (σ _ff) have been measured for⁴⁰Ar+^{144, 148, 154}Sm at sub-barrier energies by observation of x-ray emission from radioactive products and by direct,ΔE?E identification of fission fragments, respectively. These isotopes span the transition region from spherical (¹⁴⁴Sm) to strongly deformed (¹⁵⁴Sm) equilibrium shapes. The cross section for fusion,σ _fus=σ _er+σ _ff, is found to vary markedly at low energies with the isotope number and, hence, with the quadrupole collectivity of the target. The thresholds for fusion of¹⁴⁸Sm and¹⁴⁴Sm are, respectively, ～3.5 MeV and ～7 MeV (c.m.) higher than for fusion with¹⁵⁴Sm. These differences and the energy dependence of the fusion cross sections are discussed in terms of the effect of nuclear deformation on heavy-ion fusion. A comparative analysis of results for¹⁶O+Sm and⁴⁰Ar+Sm in terms of static deformation indicates thatσ _fus for the Ar+Sm system at very low energies is enhanced relative to the prediction for a one-dimensional barrier based on a fit toσ _fus for¹⁶O+Sm. This may be an indication that additional degrees of freedom (such as formation of a neck or fragment elongation) may be important for fusion with the larger projectile. At energies above the fusion barrier, values ofσ _fus for^{144, 148}Sm are nearly equal, but are significantly smaller than for¹⁵⁴Sm. This is in contrast to the results of previous experiments with¹⁶O projectiles in whichσ _fus (¹⁶O+¹⁴⁸Sm) andσ _fus (¹⁶O+¹⁵⁴Sm) were nearly equal above the barrier. These differences, observed for^{144, 148}Sm and¹⁵⁴Sm at energies above the barrier may reflect a new mechanism which is not encompassed by a static theory.     

Systematic study of deformation effects on fusion cross-sections using various proximity potentials

The influence of static quadrupole and hexadecapole (positive & negative) deformation of targets are studied using eleven different versions of nuclear potentials. The height and position of the interaction barrier for the reactions induced by spherical projectile (¹⁶O) on the deformed targets such as ¹⁶⁶Er, ¹⁵⁴Sm and ¹⁷⁶Yb have been estimated. It is found that the nucleus-nucleus potential strongly depends on the value of the deformation parameters and orientation of the target. The experimental fusion cross-section of the reactions ¹⁶O + ¹⁷⁶Yb, ¹⁶O +¹⁶⁶Er and ¹⁶O +¹⁵⁴Sm are investigated by applyingWong’s formula using various parameterizations of the proximity potential as well as an assessment of the results of a multi-dimensional barrier penetration model (BPM). The fusion cross-sections by Prox 77, Prox 88, Prox 00, Prox 00DP, Denisov DP, Bass 80, CW 76 and AW 95 potentials are found to be better than the rest in comparison to experimental data.     

Alpha-induced reaction cross-section for Sm,U, Np targets: influence of hexadecapole deformation and deformed surface diffuseness

Alpha-induced reactions on~(154)Sm,~(233,235,236,238)U, and ~(237)Np deformed nuclei are studied theoretically.The effects of hexadecapole deformation, deformed surface diffuseness parameter, and orientation on barrier height and position, fusion cross-section at any angle, and fusion cross-section have been investigated. Both hexadecapole deformation and deformed surface diffuseness can affect barrier characteristics and enhance fusion cross-section. Good agreement between experimental data and theoretical calculations with quadrupole and hexadecapole deformation and deformed surface diffuseness were observed for the ~4He+~(154)Sm,~(235)U,~(237)Np reactions.     

On the Gross Structure of Fusion Cross Section for 16O+12C System

The gross structure appeared in the total fusion cross section for ¹⁶O+¹²C system is studied by using the LCNO theory and the folding model of the paritydependent potential.The experimental data of the fusion cross section,elastic scattering excitation functions and angular distributions for this system are well explained.     

Fragmentation Cross Sections of 12C on Different Targets at Beam Energies from 50 to 100MeV/Nucleon

The fragmentation cross sections of reactions ^12C＋^2H, ^12C, ^14N, ^16O at beam energies from 50 to 100 MeV/nucleon are investigated using the isospin-dependent Boltzmann-Langevin equation model. It is found that fragment species increase approximately with the increasing target mass. The fragment species and some fragments production cross sections in reactions of ^12C＋^12C, ^14N, ^16O show an obvious variation at the beam energies from 50 to 80 MeV/nucleon. However the calculated fragment production cross sections do not change much when the incident energy increases from 80 to 100 MeV/nucleon.