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.     

Complex microscopic optical potential between two nuclei based on Dirac-Brueckner theory for nuclear matter

The real and imaginary parts of the optical-model potential between two nuclei are calculated in the energy density formalism. The energy density is derived from the Dirac-Brueckner approach to nuclear matter. In this approach, both free NN scattering and the saturation properties of nuclear matter can be explained starting from a realistic NN interaction. The relativistic features incorporated in the Dirac-Brueckner approach make the real part of the optical potential less attractive than that obtained in a non-relativistic calculation while the imaginary part is enhanced. The comparison of the calculated differential cross section for elastic ¹²C-¹²C scattering with the experimental data suggests that the enhancement of the imaginary part due to the relativistic treatment is favourable while its repulsive contribution to the real part is unfavourable.     

基于壳模型单体密度矩阵的折叠模型质子弹性散射分析

利用折叠模型计算得到折叠势实部并结合Koning和Delaroche光学势的虚部, 计算分析了质子与^30—40S的弹性散射数据. 通过引入Woods-Saxon势下核壳模型单体密度矩阵, 消除了折叠模型计算中常用的定域近似. 分析比较了定域近似对折叠势以及弹性散射截面计算的影响. 计算结果与折叠模型以及JLM模型计算结果进行了比较.     

半微观质子光学势

基于原子核壳模型单体密度矩阵的折叠模型计算光学势的实部,配以唯象光学势虚部,构造半微观光学势.通过拟合质子弹性散射实验数据,得到适用于质量数28~90,能量到200 MeV的半微观质子光学势.该光学势用于质子弹性散射计算分析,在参数大为减少的情况下,计算得到的角分布和分析本领与实验数据的符合程度,总体上好于Koning-Delaroche普适光学势的计算结果.     

Theoretical analysis of <Superscript>6</Superscript>He + <Superscript>12</Superscript>C scattering by means of the model of microscopic optical potential

The ⁶He + ¹²C elastic scattering at E = 3.0, 38.3, and 41.6 MeV/nucleon is analyzed using the microscopic model of optical potential. According to this approach, two or three parameters are fitted that renormalize the depth of real, imaginary, and surface parts of the calculated optical potential. In this case, the ambiguity of the obtained sets of fitting parameters remains, but can be reduced by introducing an additional criterion of selection: the dependence of the volume integrals of the optical potential on the energy. The structure of the obtained optical potential, the role of the nuclear medium, the formation of the imaginary part of the optical potential, and the interconnection between the surface potential and the ⁶He breakup channels are discussed.     

Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions ¹⁶O on nuclei at an energy of E ～ 100 MeV per nucleon.     

Elastic scattering of 11B from 209Bi in the energy range 49.8 ⩽ E ⩽ 84.1 MeV

The elastic scattering of ¹¹B from ²⁰⁹Bi has been measured at laboratory energies of 49.8, 51.3, 52.2, 52.8, 54.3, 55.8, 59.8, 64.8, 69.8, 74.8 and 84.1 MeV. These data have been analyzed using a microscopic optical model and the energy dependence of the real and the imaginary parts of the optical potential at near barrier energies has been determined. The “threshold anomaly” observed in the real part of the potential is found to be consistent with the dispersion relation which connects the real and the imaginary parts of the potential. Inelastic scattering and transfer reactions have also been measured at energies of 51.3, 55.8, 59.8 and 74.8 MeV. DWBA calculations for the 3⁻ state in ²⁰⁹Bi are made. From the measured transfer probabilities, using a semiclassical approach the strength of the form factors have been obtained. The fusion cross sections have been derived at these energies from the corresponding quasi-elastic scattering angular distribution data. The fusion cross sections calculated using the energy dependent barriers extracted from the energy dependent real parts of the potential compare well with, that determined from quasi-elastic scattering data and are also in good agreement with simplified coupled channels calculation for fusion incorporating important inelastic and transfer channels.     

Collision cross-sections for scattering of electrons from NO molecule

Electron-NO scattering is investigated in the energy range 2–1000eV by using a parameter-free spherical complex optical potential (SCOP) approach in the fixed nuclei approximation. The real part of the optical potential consists of three potentials namely, the static, the exchange and the polarization. For the imaginary part of the SCOP, we employ a semi-empirical model absorption potential. The molecular charge density function is calculated from a single-configuration molecular orbital based on Slater type orbitals. The various potential terms are then determined from these charge density functions. Calculations of the elastic (with and without absorption effects), total absorption, momentum transfer and differential cross-sections are obtained and compared with the available theoretical results and experimental measurements.     

Pauli Correlation Effect for the Elastic Scattering of Protons by Different Nuclei at 800 MeV

The angular distributions of the elastic scattering of protons at an energy of 800 MeV by ¹⁶O and ²⁰Ne nuclei are described in terms of the optical model scattering theory. Single folding model is applied to calculate the optical potential taking the effective nucleon-nucleon interaction to be in two forms. One form includes the zero-range pseudo-potential term and the other includes a two-body Pauli correlation function. Analytical expressions for the real part of the optical potential are obtained for both forms. The imaginary part of the optical potential is taken to be of the Woods-Saxon's shape. It is found that introducing the Pauli correlation function improves the agreement with the experimental data for the elastic scattering differential cross-sections of protons with the target nuclei ¹⁶O and ²⁰Ne.     

The Optical Model Analysis of the Elastic Scattering of Alpha Particles Using a Surface Absorption Potential

The optical model analysis has been applied to the elastic scattering of α-particles on silver at energics of 18.7, 22 and 24.7 Mev. Using a volume absorption potential for the real part and a surface absorption potential for the imaginary part, the several sets of parameters giving satisfactory fits to the experimental data are obtained. The effect of varying these optical model parameters on the differential cross section is discussed.     

Calculations of 8He + p elastic scattering cross sections using the microscopic optical potential

The optical potential of ⁸He+p scattering is calculated using the folding model for its real part and the high-energy approximation for the imaginary part. On this basis, the experimental differential elastic scattering cross sections are analyzed at energies below 100 MeV/nucleon. Conclusions are drawn on the applicability of the optical potential model and on the selection of an adequate model of the ⁸He nucleus structure. Original Russian Text ? V.K. Lukyanov, E.V. Zemlyanaya, K.V. Lukyanov, D.N. Kadrev, A.N. Antonov, M.K. Gaidarov, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 6, pp. 887–891.     

Microscopic derivation of a complex heavy ion potential

The energy dependence of a complex heavy ion optical potential is derived in Brueckner Hartree Fock using a local density approximation and a selfconsistent single particle spectrum. The two ions are described by an antisymmetrized cluster model wavefunction. Both real and imaginary part are found to increase with energy. Results are given for the elastic scattering of ⁴⁰Ca+¹⁶O.     

Calculation of the imaginary part of the nucleon-nucleus optical-model potential

The imaginary part of the optical-model potential for the scattering of nucleons by nuclei is studied in the frame of the shell-model approach to nuclear reactions. Special attention is paid to the one-hole target nuclei. The imaginary part of the optical-model potential in the second order in the nucleon-nucleus interaction is divided into two parts. The first corresponds to the average resonant scattering. The second corresponds to the inelastic scattering leading to the non-collective states of the target nuclei. A local potential equivalent to the non-local theoretical one is constructed in order to facilitate comparison with experiment. Numerical calculations concern the scattering of 14.5 MeV protons by ³⁹K. It is found that the imaginary part depends upon the angular momentum and that its radial variation is governed by strong shell effects. The predicted absorption is approximately 60% of the experimental one. The average resonant scattering contributes to the imaginary part of the optical-model potential as much as the inelastic non-collective excitations of the target.     

Improved non-empirical absorption potential for electron scattering at intermediate and high energies: 30–10000 eV

The non-empirical model proposed by Staszewka et al. in 1983 for the imaginary part of the electron scattering optical potential is revised, improving the treatment used for the e⁻ −e⁻ dispersion. New cross-section calculations employing the revised potential are in agreement with available experimental data for elastic and inelastic processes.     

Elastic scattering of protons and neutrons on 40Ca by the density-dependent Hartree-Fock field

We use the self-consistent density-dependent Hartree-Fock field as the real part of the optical model potential. Introducing a phenomenological imaginary potential, we describe elastic scattering of protons and neutrons on ⁴⁰Ca at several incident energies. Results show that the density-dependent Hartree-Fock field, including the rearrangement potential, well reproduces differential cross sections and polarizations simultaneously. This calculation explicitly shows a unified way to understand the ground-state properties and the scattering problem. Detailed study is given the properties of the non-local Hartree-Fock field, via the WKB equivalent local potential.     

The 12C+24Mg elastic scattering: An example of anomalous transparency at coulomb barrier energies

Fifteen complete angular distributions of the elastic scattering of ¹²C+²⁴Mg were measured at energies around the Coulomb barrier (E_cm = 10.67–16 MeV). The angular distributions are strongly oscillating and could be well described by an optical potential family, whose real part was determined without continuous ambiguity. The imaginary part of this optical potential is very shallow. At four energies the inelastic scattering angular distributions leading to the 2⁺ state of the ²⁴Mg were also measured and analysed with coupled-channels calculations. The volume integrals of the optical potentials used in the coupled-channels calculations present the threshold anomaly in their energy dependence, with a clear Q-value dependence.