A study on the Fresnel diffraction of 6He by means of different microscopic density distributions

The elastic scattering of the halo nucleus ⁶He from heavy targets such as ¹⁹⁷Au and ²⁰⁸Pb has been investigated in order to explain the Coulomb rainbow peak due to the Fresnel-type diffraction observed in the experimental data. In order to examine the role of nuclear potential to describe ⁶He + ¹⁹⁷Au and ⁶He + ²⁰⁸Pb systems, we have used the no-core shell model, few-body and Gaussian-shaped density distributions at various energies. The microscopic real parts of the complex nuclear potential have been obtained by using the double-folding model for each of the density distribution and the phenomenological imaginary potentials have been taken as the standard Woods-Saxon shape. We have observed that fewbody and Gaussian-shaped density distributions have given standard Fresnel-type diffraction results, a classical scattering pattern with Coulomb rainbow peak whereas the nuclear potential obtained by using the no-core shell-model density distribution has provided the reduction at Fresnel peak and has given more consistent results with the experimental data.     

Heavy-ion potentials for ellipsoidally deformed nuclei and application to the system 238U + 238U

The nuclear potential between deformed nuclei is calculated within the framework of the double-folding model. An analytical expression for the potential is obtained on condition that the two-body interaction is of gaussian type and the nuclear densities have ellipsoidal equidensity surfaces. The computed potential values are used for a least-square fit of the radial potentials in a multipole expansion of the heavy-ion potential. The method is applied for the calculation of the ²³⁸U + ²³⁸U potential.     

Studying the reactions of deuteron interaction with <Superscript>9</Superscript>Be nuclei at low energies

Data on elastic and inelastic scattering, and the reactions of few-nucleon transfers in the interaction between the nuclei of deuteron and ⁹Be at energies of around 10 MeV/nucleon, are analyzed. A theoretical analysis is performed using the double-folding potential model with the wave function of the ground state of the ⁹Be nucleus, constructed in the three-cluster α + α + n-approximation. Calculations of the cross section of elastic scattering for the reaction d + ⁹Be using the calculated folding potential are preformed using the optical model. The resulting optical potential is used to analyze cross sections of transfer reactions and inelastic scattering in the context of the distorted waves method. A comparative analysis of the experimental data and theoretical calculations is performed.     

Microscopic analysis of the energy dependence of the 6He, 6Li + 28Si total reaction cross sections in the energy range E = 5−50 A MeV

The experimental data on the total cross sections of the ^{4, 6}He, ^{6, 7}Li + ²⁸Si reactions at energies E=5−50 A MeV are reported. The data for the ⁶Li, ⁶He + ²⁸Si reactions have been analyzed within the microscopic model of double-folding optical potential, in which the real and imaginary parts are calculated at different densities of the projectile nucleus. The cross sections calculated with the microscopic double-folding Coulomb potential and the standard Coulomb potential for uniform charge distribution are compared with each other. Semimicroscopic potentials providing agreement with experimental data have been constructed on the basis of renormalized microscopic potentials and their derivatives, added to take into account collective effects. Original Russian Text ￠ K.V. Lukyanov, E.V. Zemlyanaya, V.K. Lukyanov, I.N. Kukhtina, Yu.E. Penionzhkevich, Yu.G. Sobolev, 2008, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2008, Vol. 72, No. 3, pp. 382–386.     

奇Z超重核的禁戒α衰变(英文)

采用密度依赖的结团模型研究了奇Z 超重核的禁戒α衰变, 粒子与子核之间的微观核势通过双折叠模型对M3Y 核子-核子相互作用势以及 粒子与子核的密度积分给出。 粒子与子核之间的库仑相互作用也通过 粒子与子核的电荷密度积分给出。计算发现,由于非零角动量带来的禁戒效应和小的α粒子预形成几率,奇Z 超重核的α衰变寿命会明显变长。We investigate the α-transition of odd-Z superheavy nuclei by the density-dependent cluster model (DDCM). The microscopic nuclear potential between the -particle and the daughter nucleus is evaluated numerically from the double-folding model with the standard M3Y nucleon-nucleon interaction. The Coulomb potential is also obtained from the double-folding integral of the proton-proton Coulomb interaction with the charge density distributions of α-particle and daughter nucleus. From our calculations, enhanced stability againstα-decays is found for the odd-Z superheavy nuclei due to the hindrance effect of non-zero angular momentum and the small preformation factor of the -particle.     

重核大集团发射半衰期的计算

重核大集团（¹⁴C-³⁴Si）发射的半衰期在理论上用Wentzel-Kramers-Brillouin近似进行了计算.利用双折叠模型计算大集团和剩余子核间的核相互作用,在折叠积分中选取了密度依赖的、零力程交换项的核子-核子相互作用.计算得到的半衰期和液滴模型结果、系统公式的结果以及实验数据进行了比较,表明目前的计算能够很好地给出重核大集团（¹⁴C-³⁴Si）发射的寿命.这可为重核其他大集团（¹⁵N, ⁴⁶Ar,⁴⁸Ca等）的发射提供可靠的预测. 关键词： 半衰期 双折叠模型 集团发射     

An Approximation for the Density Matrix in Calculations of the Mean-Field Potential of the Interaction of Nuclei

An approximation has been proposed for the nucleus single-particle density matrix in calculating the exchange component of the mean-field potential in the double-folding model. The method is based on the pseudo-oscillator representation of the density matrix and makes it possible to separate single-particle and internucleon variables, which greatly simplifies and accelerates the process of calculating the mean-field potential. Test calculations based on examples of alpha-particle interactions with ¹²C, ¹⁶O, and ⁴⁰Ca nuclei have shown the adequacy of the proposed approximation.     

6Li scattering: A failure of the double-folded potential model

Data for ⁶Li scattering elastically from various nuclei were analyzed using the double-folding model together with a recently introduced “realistic” effective interaction which has reproduced the potentials for heavier ions. However, it is concluded that the potential for ⁶Li is not given by this model which systematically overestimates it by nearly a factor of two.     

Excitation of nuclear collective states by heavy ions within the model of semimicroscopic optical potential

The (semi)microscopic double-folding nucleus-nucleus optical potentials are suggested for consideration of inelastic scattering with excitation of collective nuclear states by using the adiabatic approach and the elastic scattering amplitude in the high-energy approximation. The analytical expression for inelastic scattering amplitude is obtained keeping the first-order terms in the deformation parameter of a potential. Calculations of inelastic cross sections for the ¹⁷O heavy ions scattered on different nuclei at about hundred MeV/nucleon are made, and the acceptable qualitative agreement with the experimental data is obtained without introducing free parameters. The prospect of the method for further applications is discussed. The text was submitted by the authors in English.     

Inelastic scattering of heavy ions at intermediate energies with excitations of nuclear collective states

Excitation of low-lying nuclear collective states upon scattering of heavy ions with energies of several tens of MeV/nucleon has been studied. The interaction potential leading to excitation is chosen in the form of a derivative of the microscopic (or semimicroscopic) nucleus-nucleus double-folding optical potential. Elastic and inelastic scattering cross sections have been calculated within the high-energy approximation; the inelastic scattering amplitude was obtained in the first order in the deformation parameter. The cross sections are compared with the experimental data on scattering of ¹⁷O from a series of nuclei with excitation of the 2⁺ level.     

Hindrance of heavy-ion fusion due to nuclear incompressibility

We propose a new mechanism to explain the unexpected steep falloff of fusion cross sections at energies far below the Coulomb barrier. The saturation properties of nuclear matter are causing a hindrance to large overlap of the reacting nuclei and consequently a sensitive change of the nuclear potential inside the barrier. We report in this Letter a good agreement with the data of coupled-channels calculation for the 64Ni + 64Ni combination using the double-folding potential with Michigan-3-Yukawa-Reid effective N - N forces supplemented with a repulsive core that reproduces the nuclear incompressibility for total overlap.     

Dispersive semimicroscopic analysis of nuclear-nuclear collisions on the basis of a corrected folding-model potential

A procedure for correcting the energy dependence determined for the mean-field component of the optical potential on the basis of the double-folding model with allowance for exchange effects in the approximation of single-nucleon exchange knockout is used to calculate the mean field and to analyze data on elastic scattering within the dispersive semimicroscopic optical-potential model. The results of an analysis of all data (including those that were obtained quite recently) on ¹⁶O + ¹²C and ¹⁶O + ¹⁴C interactions at energies of up to 100 MeV per nucleon are presented. The energy dependence of the resulting potentials agrees well with that which was obtained previously within the phenomenological approach. A systematics of the positions of Airy minima in angular distributions versus the reduced mass in the range from 2 to 8 amu is constructed.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Woods-Saxon-Gaussian potential and alpha-cluster structures of alpha + closed shell nuclei

The Woods-Saxon-Gaussian(WSG) potential is proposed as a new phenomenological potential to systematically describe the level scheme, electromagnetic transitions, and alpha-decay half-lives of the alpha-cluster structures in various alpha + closed shell nuclei. It modifies the original Woods–Saxon(WS) potential with a shifted Gaussian factor centered at the nuclear surface. The free parameters in the WSG potential are determined by reproducing the correct level scheme of ~(212) Po=~(208) Pb+α. It is found that the resulting WSG potential matches the M3 Y double-folding potential at the surface region and makes corrections to the inner part of the cluster-core potential. It was also determined that the WSG potential, with nearly identical parameters to that of ~(212) Po(except for a rescaled radius), could also be used to describe alpha-cluster structures in ~(20) Ne =~(16) O+α and ~(44) Ti =~(40) Ca+α. In all three cases, the calculated values of the level schemes, electromagnetic transitions, and alpha-decay half-lives agree with the experimental data, which indicates that the WSG potential could indeed capture many important features of the alpha-cluster structures in alpha + closed shell nuclei. This study is a useful complement to the existing cluster-core potentials in literature. The Gaussian form factor centered at the nuclear surface might also help to improve our understanding of the alpha-cluster formation, which occurs in the same general region.     

Folding model analysis of 10, 11B, 12C + 27Al, 39K and 40Ca

Elastic scattering angular distributions for ^{10, 11}B + ⁴⁰Ca at E_lab = 46.6 and 51.5 MeV and¹²C+³⁹K at E_lab = 54 and 63 MeV have been measured and compared with Woods-Saxon and double-folding optical models. The oscillatory structure observed previously for ¹²C + ⁴⁰Ca disappears when the projectile is changed to ^10,11B or the target is changed to ³⁹K. The angular distributions are adequately reproduced by a double-folding analysis, which employs the nucleon-nucleon potential of Bertsch et al., with a range of real normalizations N_R = 1.0–1.38. This same range of real normalizations was also able to describe previously measured ^10,11B, ¹²C + ²⁷A1 data. The double-folding analysis of ¹²C + ⁴⁰Ca scattering indicates that this system behaves differently from neighboring systems.     

Allowance for the shell structure of colliding nuclei in the fusion-fission process

The motion of two nuclei toward each other in fusion-fission reactions is considered. The state of the system of interacting nuclei is specified in terms of three collective coordinates (parameters). These are the distance between the centers of mass of the nuclei and the deformation parameter for each of them (the nose-to-nose orientation of the nuclei is assumed). The evolution of collective degrees of freedom of the system is described by Langevin equations. The energies of the Coulomb and nuclear (Gross-Kalinovsky potential) interactions of nuclei are taken into account in the potential energy of the system along with the deformation energy of each nucleus with allowance for shell effects. The motion of nuclei toward each other are calculated for two reaction types: reactions involving nuclei that are deformed (₄₂¹⁰⁰Mo + ₄₂¹⁰⁰Mo → ₈₄²⁰⁰Po) and those that are spherical (₈₂²⁰⁸Pb + ₈¹⁸O → ₉₀²²⁶Th) in the ground state. It is shown that the shell structure of interacting nuclei affects not only the fusion process as a whole (fusionbarrier height and initial-reaction-energy dependence of the probability that the nuclei involved touch each other) but also the processes occurring in each nucleus individually (shape of the nuclei and their excitation energies at the point of touching).     

Folding model analysis of the nucleus–nucleus scattering based on Jacobi coordinates

This paper presents the results of scattering of ¹⁶O+²⁰⁹Bi interaction near the Coulomb barrier. The interaction potential between two nuclei is calculated using the double folding model with the effective nucleon–nucleon (NN) interaction. The calculations of the exchange part of the interaction were assumed to be of finite-range and the density dependence of the NN interaction is accounted for. Also the results are compared with the zero-range approximation. All these calculations are done using the wave functions of the two colliding nuclei in place of their density distributions. The wave functions are obtained by the D-dimensional wave equation using the hyperspherical calculations on the basis of Jacobi coordinates. The numerical results for the interaction potential and the differential scattering are in good agreement with the previous works.