CALCULATION OF MICROSCOPIC OPTICAL POTENTIAL BY USE OF THE GENERALIZED SKYRME FORCES

In this paper the calculation of the microscopic optical potential based on thegeneralized Skyrme forces which describe both the ground and excited state propertiessimultaneously has been carried out for ²⁰⁵Pb ete. The volume integral per nucleon andthe root mean square radii of the real part as well as the imaginary part of the opticalpotential have been obtained. The angular distributions of the elastic scattering andthe total cross sections by use of our computed microscopic optical potential for ^20?Pbhave also been calculated. Compared with the conventional Skyrme forces, the calculat-ed results by the generalized Skyrme forces are evidently improved The presentcalculation is also in a good agreement with experiments for the incident energy lessthan 100 MeV.     

Semi-microscopic optical potential calculation by the nuclear matter approach

In this paper the semi-microscopic nuclear matter approach has been introduced to calculate the microscopic optical potential. The first- and second-order mass operators in asymmetric nuclear matter have been derived with Skyrme effective interactions and the real and imaginary parts of the optical potential for finite nuclei have been obtained by applying a local density approximation. Five Skyrme interactions II–VI have been used and compared with the experimental data to determine how well these Skyrme interaction function for our purposes. Our results obtained in this simple way are to some extent comparable with those obtained with the “nuclear matter” and “nuclear structure” approaches without adjusting the parameters of the Skyrme interactions.     

Nuclear structure calculations using momentum-dependent delta interactions (MDD)

The ground-state properties of a nucleus have been investigated using momentum- and density-dependent δ-interactions. Unlike the Skyrme type of interaction, the two-body interaction used has terms dependent on the fourth power of the relative momenta. The role of these new terms has been investigated by using the density-matrix expansion technique of Negele and Vautherin. The interaction has been used to calculate, amongst other phenomena, the ion-ion interaction potential and the nucleon-nucleus optical potential. The improvements obtained using such an interaction over the Skyrme II type of interactions (which have small odd state components) are discussed in detail. It is shown that the effective mass, $\text{m}{}^1$, is larger in magnitude than obtained by using the Skyrme II type of interaction. It has been suggested that such interactions could be more appropriate than the Skyrme type of interactions in physical situations where large momentum transfers are involved.     

SEMI-MICROSCOPIC OPTICAL POTENTIAL CALCULATION BY THE NUCLEAR MATTER APPROACH——I. SYMMETRIC NUCLEAR MATTER

In this paper semi-microscopic nuclear matter approach is introduced to calculatethe microscopic optical potential. The first and second order mass operator in sym-metric nuclear matter is derived with Skyrme effective interactions and the real andimaginary part of the optical potential for finite nuclei is obtained by applying alocal density approximation. The five kinds of the different parameters of Skyrmeinteractions Ⅱ-Ⅵ are used and compared with the experimental data to study how wellthese Skyrme interactions can work for our purposes. Our results obtained in such asimple way seem to be to some extent comparable with those obtained with "nuclearmatter approach" and "nuclear structure approach" without adjusting the parame-ters of the Skyrme interactions so far.     

A MICROSCOPIC STUDY OF THE LOW-LYING LEVELS OF 18O AND 18F WITH THE SKYRME INTERACTION

The low-lying levels of ¹⁸O and ¹⁸F have been calculated using several Skyrme interactions and the many-body folded diagram theory of Kuo, Lee and Ratcliff. Our results obtained with the Skyrme interactions determined by Vautherin and Brink and by Krewald are not in satisfactory agreement with the experimental spectra.     

MICROSCOPIC OPTICAL POTENTIAL CALCULATIONS OF FINITE NUCLEI WITH EXTENDED SKYRME FORCES

Microscopic optical potential calculations in the Hartree-Fock (HF) approximation with Extended Skyrme forces are investigated. The HF equation is derived from the variation principle and the potential formula of spherical nuclei is obtained by two different ways. Then the calculations for symmetric nuclei ¹⁶O, ⁴⁰Ca and asymmetric nucleus ⁹⁰Zr with eight sets of Skyrme force parameters are presented. Our results show that the potential from and variating tendency with incident energy are reasonable and there apparently appears a "wine-bottle-bottom" shape in the intermediate energy region. Furthermore, our calculations reflect shell effects clearly.     

Comparison between global phenomenological and microscopic optical potentials for proton as projectile below 100 MeV

For 112 target nuclei (52 elements) with proton as projectile, we calculate the reaction cross sections and elastic scattering angular distributions, as well as the X2 values for 16 kinds of proton optical model potentials: two sets of phenomenological global optical potentials and the microscopic optical potentials proposed by Shen et al for 14 sets of Skyrme force parameters: GSI-6, SBJS, SKM, SGI-Ⅱ, SKa-b, SG01-Ⅱ.We find that for obtaining the proton microscopic optical potential based on the nuclear matter approach with Skyrme force, SGI, SKa and SKb are the three sets of optimal Skyrme force parameters.     

Effect of tensor nucleon-nucleon forces on the nucleon-nucleus optical potential

In the approximation of unpolarized nuclear matter, the optical potential for nucleon-nucleus scattering is calculated on the basis of the effective Skyrme interaction with allowance for tensor nucleon-nucleon forces. It is shown that the tensor Skyrme forces make a significant contribution to the imaginary part of the optical potential. The effect of tensor nucleon-nucleon forces on the radial distribution of the imaginary part of the optical potential is investigated by considering the example of elastic neutron scattering by ⁴⁰Ca nuclei at scattering energies of about a few tens of MeV.     

DWIA calculations of proton momentum distributions in 12C and 16O(e,e'p) reactions

The DWIA analysis of the quasi-free (e, e'p) process on ¹²C and ¹⁶O has been performed within the framework of the single-particle shell model. The spherical Hartree-Fock wave functions for the effective Skyrme forces are used in describing the ground-state properties of these nuclei. The competition between the structure effects and the final proton-nucleus interaction in forming the momentum distributions of outgoing protons is studied in a wide range of recoil momenta (up to 3 fm^?1). The distorting optical potential has been calculated on the basis of the Watson multiple scattering theory. The results of the analysis are compared with the new data obtained at Saclay.     

Determining a Skyrme-type effective interaction from realistic two-nucleon interaction

The Variational Monte Carlo (VMC) method is employed to determine characteristics of symmetric and asymmetric nuclearmatter. The realistic Urbana v14 nucleon-nucleon interaction potential of Lagaris and Pandharipande was used in the VMC calculations with addition of a phenomenological density-dependent term to simulate many-body interactions. A new Skyrme parameter set SKaan-U14 is found to consistently reproduce the characteristics of the nuclear matter obtained from VMC calculations. The properties of symmetric and asymmetric nuclear matter are calculated by the new Skyrme parameter set. The results obtained by using the new Skyrme parameter set are compared with results obtained by different Skyrme parameter sets in the literature.     

T-REX

The potential barrier impeding the spontaneous emission of protons in the proton radioactive nuclei is calculated as the sum of nuclear, Coulomb and centrifugal contributions. The nuclear part of the proton-nucleus interaction potential is obtained in the energy density formalism using the Skyrme effective interaction that results into a simple algebraic expression. The half-lives of the proton emitters are calculated for the different Skyrme sets within the improved WKB framework. The results are found to be in reasonable agreement with the earlier results obtained for more complicated calculations involving finite-range interactions.     

Selfconsistent semiclassical calculations using the partial h̵ resummation method

Selfconsistent semiclassical calculations using the partial resummation technique have been performed for a number of spherical nuclei. The results are found in very good agreement with those obtained in the more lengthy selfconsistently Strutinsky averaged Hartree-Fock approach. Our method has also been applied to the determination of liquid drop parameters associated with effective forces of the Skyrme type.     

Comparison between global phenomenological and microscopic optical potentials for proton as projectile below 100 MeV

For 112 target nuclei （52 elements） with proton as projectile, we calculate the reaction cross sections and elastic scattering angular distributions, as well as the X^2 values for 16 kinds of proton optical model potentials： two sets of phenomenological global optical potentials and the microscopic optical potentials proposed by Shen et al for 14 sets of Skyrme force parameters： GSI-6, SBJS, SKM, SGI-Ⅱ, SKa-b, SCOI-Ⅱ. We find that for obtaining the proton microscopic optical potential based on the nuclear matter approach with Skyrme force, SGI, SKa and SKb are the three sets of optimal Skyrme force parameters.     

Energy dependent potential in nuclear collisions

Energy dependence of the real part of the nucleus-nucleus potential is studied using a modified Seyler-Blanchard two-body effective interaction which contains density dependence along with the momentum dependence. The nucleus-nucleus potential is evaluated in the proximity picture of Blocki et al. The calculated energy dependence of the ion-ion potential compares well with the phenomenology. The various sets of the Skyrme force have also been used to study this energy dependence and widely different results are obtained for the different sets. Heavy-ion fusion excitation functions have also been calculated using the energy-dependent potential in the effective mass approximation. It is observed that the high-energy fusion cross sections are significantly suppressed when calculated with the energy-dependent ion-ion interaction. The important deep-inelastic observables are found to be insensitive to the energy dependence of the potential.     

Consistent empirical physical formulas for potential energy curves of 38–66Ti isotopes by using neural networks

Nuclear shape transition has been actively studied in the past decade. In particular, the understanding of this phenomenon from a microscopic point of view is of great importance. Because of this reason, many works have been employed to investigate shape phase transition in nuclei within the relativistic and nonrelativistic mean field models by examining potential energy curves (PECs). In this paper, by using layered feed-forward neural networks (LFNNs), we have constructed consistent empirical physical formulas (EPFs) for the PECs of ^38–66Ti calculated by the Hartree-Fock-Bogoliubov (HFB) method with SLy4 Skyrme forces. It has been seen that the PECs obtained by neural network method are compatible with those of HFB calculations.     

Potential energy surface and formation of superheavy nuclei with the Skyrme energy-density functional

With the Skyrme energy-density functional theory, the nucleus–nucleus potential is calculated and the potential energy surface is obtained with different effective forces for accurately estimating the formation cross sections of superheavy nuclei in massive fusion reactions. The width and height of the potential pocket are influenced by the Skyrme effective forces SkM, SkM^*, SkP, SIII, Ska, and SLy4, which correspond to the different equations of state for the isospin symmetry nuclear matter. It is found that the nucleus–nucleus potential is associated with the collision orientation and Skyrme forces. A more repulsive nuclear potential is pronounced with increasing the incompressible modulus of nuclear matter, which hinders the formation of superheavy nuclei. The available data in the fusion-evaporation reaction of ⁴⁸Ca+²³⁸U are nicely reproduced with the SkM^* parameter by implementing the potential into the dinuclear system model.     

张量力在16O+16O熔合动力学中的效应（英文）

利用时间相关Hartree-Fock 理论和完整Skyrme 有效相互作用研究了16O+16O 碰撞在库仑位垒附近的熔合动力学。数值计算是在没有任何对称性约束的三维笛卡尔基下完成。将时间相关Hartree-Fock 理论和冻结密度近似下的能量密度泛函方法给出的库仑位垒与实验结果进行了比较,发现同位旋标量的张量项能降低自旋饱和体系16O+16O的库仑位垒,而库仑位垒高度随着同位旋矢量的张量项的耦合常数减小而降低。并计算了包含和不包含张量力的16O+16O熔合截面,发现张量力对16O+16O碰撞在库仑位垒附近的熔合动力学影响较小。The fusion dynamics of 16O+16O around Coulomb barrier has been studied in the timedependent Hartree-Fock (TDHF) theory with the full Skyrme effective interaction. The calculations have been carried out in three-dimensional Cartesian basis without any symmetry restrictions. We have included the full tensor force and all the time-odd terms in Skyrme energy density functional (EDF). The Coulomb barrier obtained from the dynamical TDHF calculations and EDF with frozen density approximation has been compared with the available experimental data. The isoscalar tensor terms and the rearrangement of other terms are found to decrease the barrier height in the spin-saturated system 16O+16O, while the energy of Coulomb barrier tends to decrease as the isovector coupling constant decreases. The fusion cross section for 16O+16O collision has been calculated with and without the tensor force. We found that the tensor force has minor effect on the fusion dynamics of 16O+16O at the energies around Coulomb barrier.