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.     

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.     

动量空间中能质子-12C弹性散射截面和自旋量的研究

在KMT理论框架下，应用微观的动量空间一级光学势，包括了库仑修正，自旋关联，NN振幅反对称，离壳效应，核子反冲和结合能转换，Lorentz不变的角变换.在整个中能区域系统地计算了质子-¹²C弹性散射微分截面和自旋观测量，并与实验数据及Glauber理论框架下或已有的其他理论计算结果做了比较，其结果显示，在200—1000MeV，该理论与实验结论符合程度较好.     

Microscopic <Emphasis Type="Italic">K</Emphasis><Superscript>+</Superscript>-nucleus optical potential and calculations of differential elastic-scattering cross sections and total reaction cross sections

The differential elastic-scattering cross sections and the total reaction cross sections for the interaction of K ⁺ mesons with ¹²C and ⁴⁰Ca nuclei at beam momenta of 0.635, 0.715, and 0.8 GeV/c are calculated. The microscopic optical potential derived in the high-energy approximation is used in these calculations. It is determined by the amplitude for kaon-nucleon scattering and the density distribution of pointlike nucleons of the target nucleus. In the high-energy approximation, the Klein-Gordon-Fock equation reduces to the form of the Schrödinger equation. It is shown that small distinctions between the reduction methods do not lead to significant changes in differential elastic-scattering cross sections, but the effects of relativization as such are quite large. Good agreement with experimental data on elastic K ⁺ A scattering is attained. The total reaction cross sections can be described upon adding, to the volume potential, a term that takes the form of its derivative and which has a maximum at the periphery, its contribution being fitted to experimental data.     

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.     

6Li(e,e′α) and (e,e′d) reactions

The correlation cross sections for the quasifree scattering in the ⁶Li(e,e′α) and (e,e′d) reactions are calculated in the microscopic model. The internal momentum distributions of clustering particles play an important role for explaining experimental data.     

Analysis of (6Li,d) and (d, 6Li) reactions in the nickel and tin regions

The (⁶Li, d) and (d, ⁶Li) L = 0 transitions in the mass regions $\text{A ? 60}\text{and}\text{A ? 116}$ are analyzed utilizing microscopic form factors. The cross sections follow the pattern given by the two-proton and two-neutron transfer cross sections.     

Positron scattering from alkaline-earth elements

The total (elastic + inelastic) cross sections fore ⁺ impact on alkaline-earth elements from Be to Ra are calculated by employing a complex spherical optical potential. This potential has static, polarization and absorption components. The positron energy range is from a few eV to several thousand eV. We have compared our elastic cross sections for Mg and Ca with the other available results and the agreement is good for energies above 100eV. We have also compared our absorption cross sections withe ⁻ ionization cross sections at high energies where our absorption cross sections are in good accord. We have made Bethe plots fore ⁺ scattering on these elements.     

Microscopic multichannel investigation of the <Superscript>6</Superscript>Li + <Emphasis Type="Italic">n</Emphasis> seven-nucleon nuclear system at low energies

The ⁶Li + n seven-nucleon nuclear system is studied at low energies within a microscopic approach based on the multichannel algebraic version of the resonating group model. The partial and total cross sections for the ⁶Li(n, t)⁴He reaction are calculated. The contributions of the various partial cross sections to the energy dependence of the total cross section are considered. The results of the calculations are found to be in a good agreement with experimental data.     

Microscopic analysis of the elastic scattering of 11Li neutron-rich nuclei on protons

Amicroscopic optical potential is used to calculate cross sections for elastic ¹¹Li +p scattering at the energies of 62, 68.4, and 75 MeV per nucleon, and the results are compared with available experimental data. The potential used does not involve free parameters, but the depths of its real and imaginary parts are renormalized. The known trend in the energy dependence of the volume integrals of the optical potential is taken into account in analyzing experimental data. The role of spin-orbit interaction is studied, and the total reaction cross sections that are proposed to be measured in future experiments are calculated.     

Comparative study of the selectivity displayed by (6Li,d) and (16O, 12C) reactions

Four-particle-transfer processes induced by the (⁶Li, d) and (¹⁶O, ¹²C) reactions to strongly excited 0⁺ states are compared. Although the selectivity displayed by these reactions is similar, the corresponding relative cross sections are rather different. These results emerge naturally from a simple microscopic model.     

The photoproton decay of 27Al

Photoproton spectra from ²⁷Al were measured from 14.8 to 27.6 MeV excitation energy in 400 keV steps. From these, high resolution photoproton cross sections to low-lying states of the residual ²⁶Mg nucleus were deduced. The large integrated cross sections to these states justify the interpretation of the de-excitation γ-ray measurements which consistently indicate strong population of low-lying residual states following photodisintegration. Further, the results are discussed with reference to the particle-hole model. By examination of the microscopic configurations of the possible GDR states an explanation is proposed for the differences in the cross sections to various residual states. Finally, the results are compared with spectroscopic factors determined from pickup reactions on ²⁷Al.     

Microscopic spin-orbit potentials for polarized 3He elastic scattering

The M3Y double folding model is used to calculate real central and spin-orbit potentials for ³He elastic scattering. These potentials are used to fit cross sections and analysing powers at 33 MeV for targets ranging from ¹⁶O to ⁵⁸Ni. The real central potential needs a normalization factor of about 0.85, but no change in the strength of the spin-orbit potential is necessary. Comparison is made with phenomenological and other microscopic studies of ³He elastic scattering.     

Microscopic approach to the nucleon-nucleon effective interaction and nucleon-nucleon scattering in symmetric and isospin-asymmetric nuclear matter

After reviewing our microscopic approach to nuclear and neutron-rich matter, we focus on how nucleon-nucleon scattering is impacted by the presence of a dense hadronic medium, with special emphasis on the case where neutron and proton densities are different. We discuss in detail medium and isospin asymmetry effects on the total elastic cross section and the mean free path of a neutron or a proton in isospin-asymmetric nuclear matter. We point out that in-medium cross sections play an important role in heavy-ion simulations aimed at extracting constraints on the symmetry potential. We argue that medium and isospin dependence of microscopic cross sections are the result of a complex balance among various effects, and cannot be simulated with a simple phenomenological model.     

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.     

Microscopic potentials for polarized triton elastic scattering

The double folding model is used to calculate real central and spin-orbit potentials for triton elastic scattering. These potentials are used to fit cross sections and analysing powers at 17 MeV for targets ranging from ²⁶Mg to ²⁰⁸Pb. For most targets the data are described as well as with phenomenological potentials. The real central potential can be used without any substantial renormalisation, but the spin-orbit potential needs to be increased in strength by a factor between 2 and 6. Comparisons are made with phenomenological studies of triton and ³He elastic scattering and with similar microscopic studies of ³He scattering.     

On the role of indirect processes in the inelastic excitation of low lying 0+ states

Using simple microscopic form factors, we have studied the indirect excitation of low lying 0⁺ states by inelastic scattering through the lowest 2⁺ states in the case of α scattering from ²⁴Mg and ²⁸Si and ³He scattering from ⁴⁶Ti. Scaling amplitudes according to the inelastic scattering and B(E2) data we found that only for α scattering from ²⁴Mg was the indirect excitation small. For the other cases studied, our estimate yields indirect cross sections which were significant in comparison with the data, although this has been well described by the direct one-step process alone. The shape of the indirect cross section may be either strongly oscillatory or flat, depending on the radius of the real optical potential.     

Departures from the Hauser-Feshbach theory due to the level-level correlations in deformed nuclei

A microscopic dynamical model is used for the inelastic scattering of nucleons by deformed nuclei and the fluctuation cross sections are calculated. The case of weak absorption in all channels is considered so that the number of statistical assumptions is minimized. The results are compared with the Hauser-Feshbach expressions as regards the magnitude and structure. The partial width amplitudes calculated from the model are correlated, the simplest type of level-level correlations being due to the similar-channels effect (SCE). When the correlations are due to SCE alone, the following two results are obtained, (i) The fluctuation cross sections are increased over the Hauser-Feshbach estimates, for Γ ? D and Γ ? D, by a factor κ if the entrance and exit channels are similar. The numerical value of κ is found to be 3 for a special case and in the general case it is conjectured to lie between the limits 1 and 3, (ii) The fluctuation cross sections σ_cc′^f1 and σ^f1_cc″ exhibit correlated fluctuations if the exit channels c′ and c″ are similar. The fluctuation cross sections in the cases “SCE+direct channel-channel coupling” and “SCE+intermediate structure” are also investigated. In all cases studied direct reaction cross sections do not vanish and the channelwise factorization assumption of the Hauser-Feshbach theory fails.     

Virtual coupling potential for elastic scattering of Be on proton and carbon targets

The ^10,11Be(p, p) and (¹²C, ¹²C) reactions were analyzed to determine the influence of the weak binding energies of exotic nuclei on their interaction potential. The elastic cross sections were measured at GANIL in inverse kinematics using radioactive ^10,11Be beams produced at energies of 39.1A   and 38.4A MeV$38.4A\text{ MeV}$. The elastic proton scattering data were analyzed within the framework of the microscopic Jeukenne–Lejeune–Mahaux (JLM) nucleon–nucleus potential. The angular distributions are found to be best reproduced by reducing the real part of the microscopic optical potential, as a consequence of the coupling to the continuum. These effects modify deeply the elastic potential. Including the Virtual Coupling Potential (VCP), we show the ability of the general optical potentials to reproduce the data for scattering of unstable nuclei, using realistic densities. Finally, the concepts needed to develop a more general and microscopic approach of the VCP are discussed.