Analysis of <Superscript>8</Superscript>B Proton Halo Nucleus Scattered from <Superscript>12</Superscript>C and <Superscript>58</Superscript>Ni at Different Energies

Angular distributions in the elastic scattering of ⁸B from ¹²C and ⁵⁸Ni targets at different energies have been analyzed in the framework of the double-folding (DF) optical model. The real central part of the nuclear optical potential is obtained by folding the M3Y effective interaction with the cluster density distribution of the ⁸B nucleus. The experimental angular distributions have been successfully reproduced. This confirms the validity of the cluster structure of the ⁸B nucleus.     

Analysis of <Superscript>4</Superscript>He+<Superscript>40</Superscript>Ca and <Superscript>4</Superscript>He+<Superscript>44</Superscript>Ti scattering using different optical model potentials

Elastic scattering of ⁴He+⁴⁰Ca and ⁴He+⁴⁴Ti reactions at backward angles has been analyzed using two differentmodels, microscopic and semimicroscopic folding potentials. The derived real potentials supplemented with phenomenological Woods–Saxon imaginary potentials, provide good agreement with the experimental data at energy E_c.m. = 21.8 MeV without need to renormalize the potentials. Coupledchannels calculations are used to extract the inelastic scattering cross section to the low-lying state 2+ (1.083 MeV) of ⁴⁴Ti. The deformation length is obtained and compared with the electromagnetic measurement values as well as those obtained from previous studies.     

The volume contribution of the ion-ion optical potential from realistic complex nucleon-nucleon interaction

The real and imaginary parts of the optical model potential for several pairs of magic nuclei have been calculated by a double folding procedure. The complex effective interaction is calculated from the Reid soft core potential by solving the Bethe-Goldstone equation in two colliding nuclear matters. The calculated potentials were approximated with a Woods-Saxon shape. We studied the dependence of the parameters of these Woods-Saxon forms on the masses of the interacting nuclei.     

Nucleon--nucleon interactions in the double folding model for fusion reactions

Nucleus--nucleus potentials are determined in the framework of double folding model for M3Y--Reid and M3Y--Paris effective nucleon--nucleon (NN) interactions. Both zero-range and finite-range exchange parts of NN interactions are considered in the folding procedure. In this paper the spherical projectile--spherical target system ¹⁶O+²⁰⁸Pb is selected for calculating the barrier energies, fusion cross sections and barrier distributions with the density-independent and density-dependent NN interactions on the basis of M3Y--Reid and M3Y--Paris NN interactions. The barrier energies become lower for Paris NN interactions in comparison with Reid NN interactions, and also for finite-range exchange part in comparison with zero-range exchange part. The density-dependent NN interactions give similar fusion cross sections and barrier distributions, and the density-independent NN interaction causes the barrier distribution moving to a higher position. However, the density-independent Reid NN interaction with zero-range exchange part gives the lowest fusion cross sections. We find that the calculated fusion cross sections and the barrier distributions are in agreement with the experimental data after renormalization of the nuclear potential due to coupled-channel effect.     

Examination of the <Superscript>16</Superscript>O + <Superscript>28</Superscript>Si system with microscopic and phenomenological potentials

The ¹⁶O + ²⁸Si reaction has been widely studied both experimentally and theoretically and has been claimed to show indications of chaotic scattering. In order to examine this claim and to address whether reaction models such as the optical one could explain the experimental data, we have analyzed the ¹⁶O + ²⁸Si system within the framework of the optical model for ten energies from 29.0 to 45.0 MeV, by using microscopic folded potentials, which are based on M3Y nucleon-nucleon, alpha-alpha effective interactions and a phenomenological shallow potential. All potentials describe the individual angular distributions very well at forward angles. However, they fail to describe the individual angular distributions over the whole angular range up to 180°. Nevertheless, we have been able to explain the experimental data by modifying the surface region of the microscopic real potentials by adding two surface potentials. With these correction potentials, we have obtained very good agreement for the individual angular distributions over the whole angular range for the given energies as well as for the experimental data near the Coulomb barrier. The failure of these optical potentials in explaining the scattering observables of this reaction without corrections puts a question mark on the model and supports the idea of a chaotic behavior. The text was submitted by the authors in English.     

Single Folding Optical Potential for Elastic Scattering of Protons from <Superscript>14</Superscript>N and <Superscript>16</Superscript>O in a Wide Range of Energies

Available experimental data for protons elastically scattered from ¹⁴N and ¹⁶O target nuclei are reanalyzed within the framework of single folding optical potential (SFOP) model. In this model, the real part of the potential is derived on the basis of single folding potential. The renormalization factor N _r is extracted for the two aforementioned nuclear systems. Theoretical calculations fairly reproduce the experimental data in the whole angular range. Energy dependence of real and imaginary volume integrals as well as reaction cross sections are discussed.     

Systematic analysis of 17,19F and 16,17O elastic scattering on 208Pb just below the coulomb barrier

The ¹⁷F, ¹⁷O + ²⁰⁸Pb elastic scattering at 90.4 and 78 MeV (just below coulomb barrier), respectively, are analyzed within the framework of the double folding approach. The folded potentials are constructed by folding the density independent M3Y effective nucleon-nucleon interaction over the nucleon density distribution of ¹⁷F and its mirror ¹⁷O nuclei. Gaussian oscillator (GO) density distribution is considered to represent the (core¹⁶O+nucleon) structure for ¹⁷F and ¹⁷O. The knock-on exchange potentials are introduced to construct the real semi-microscopic potentials. The imaginary potentials are supplemented to derive potentials in two forms: either phenomenological Woods-Saxon (WS) or the same form as real folded potentials and different strengths. Moreover, the analysis of ¹⁹F, ¹⁶O + ²⁰⁸Pb elastic scattering at 91, 78 MeV energies, in that order, is applied in comparison to the ¹⁷F, ¹⁷O + ²⁰⁸Pb systems in an endeavor to investigate the behavior and properties of ¹⁷F and ¹⁷O projectiles.     

Microscopic study on proton elastic scattering of light exotic nuclei at energies below than 100 MeV/nucleon

The proton elastic scattering data on some light exotic nuclei, namely, ^{6, 8}He, ^{9, 11}Li, and ^{10, 11, 12}Be, at energies below than 100MeV/nucleon are analyzed using the single folding optical model. The real, imaginary, and spin-orbit parts of the optical potential (OP) are constructed only from the folded potentials and their derivatives using M3Y effective nucleon-nucleon interaction. These OP parts, their renormalization factors and their volume integrals are studied. The surface and spin-orbit potentials are important to fit the experimental data. Three model densities for halo nuclei are used and the sensitivity of the cross-sections to these densities is tested. The imaginary OP within high-energy approximation is used and compared with the single folding OP. This OP with few and limited fitting parameters, which have systematic behavior with incident energy, successfully describes the proton elastic scattering data with exotic nuclei.     

Theory study of shapes in <Superscript>187,189</Superscript>Tl nuclei

The nuclear shapes of ^187,189Tl were investigated theoretically in this work. The total routhian surface (TRS) calculations were performed for N=106 and 108 isotopes of thallium (Z=81). The single-particle energies were obtained from the deformed Woods-Saxon potential, with the Lipkin-Nogami (LN) treatment of pairing. It is found that the collective oblate rotation coexists with the high-K prolate rotation. Superdeformed prolate rotation is included in this calculation. Supported by the National Natural Science Foundation of China (Grant Nos. 10575036 and 10675046) and the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y605476 and Y604027)     

Dynamic polarization potentials for <Superscript>6</Superscript>He + <Superscript>209</Superscript>Bi and <Superscript>11</Superscript>Li + <Superscript>208</Superscript>Pb systems at near-barrier energies

The Coulomb dipole induced dynamic polarization potentials for ⁶He + ²⁰⁹Bi and ¹¹Li + ²⁰⁸Pb systems within the framework of Feshbach’s formalism with a motive to ascertain the presence or absence of threshold anomaly have been studied. As a result of this study, the threshold anomaly has been found to be present for both systems. It has also been found that at deep sub-barrier energies the imaginary part either starts increasing or at least remains unchanged which indicates the presence of the breakup threshold anomaly. In addition, the Coulomb breakup transmission factors for both systems have been found to have maximum value below and near-barrier energies, but at very high energies due to closure of the breakup channel the breakup transmission coefficients quickly becomes zero.     

An Investigation of 4He+12C and 4He+16O Reactions Using the Cluster Model

The α -target semimicroscopic single folding potentials have been derived by folding a composite (repulsive and attractive) effective α-α interaction with the α -cluster distribution density in the target nuclei. The obtained potentials are considered as the real part of the nuclear optical model potentials, while the imaginary parts are phenomenologicaly expressed using the Woods-Saxon form. Nine sets of measured experimental data of the ⁴He+¹²C and ⁴He+¹⁶O elastic rainbow scattering over the energy range 80-240 MeV are analyzed using the obtained potentials. The data are successfully reproduced using the extracted potentials. The resulted reaction cross sections are also investigated and compared with the available corresponding data.     

Folding model analysis of triton and 3He elastic scattering

A double folding model using the M3Y interaction has been successfully applied to a wide range of triton and ³He data. A projectile energy and mass dependence in the exchange potential proportional to E/A_p is shown to be adequate between 11 and 27 MeV/nucleon. Normalization factors for triton and ³He real potentials of ～ 0.6 and ～ 0.8, respectively, are in accordance with those of other light projectiles subject to break-up.     

Microscopic interpretation of the (<Emphasis Type="Italic">t</Emphasis>, <Superscript>3</Superscript>He) reaction at 130 MeV on <Superscript>90</Superscript>Zr and isovector monopole strength

The 130-MeV primary tritium beam of the AGOR facility with an intensity of up to 10⁸ pps and the Big Bite Spectrometer experimental setup have been used to study the (t, ³He) reaction between 0° and 5° lab angles on ¹²C and ⁹⁰Zr targets. The standard ray-tracing procedure has allowed us to obtain excitation-energy spectra up to 30 MeV in six angular bins for each residual nucleus, with an average energy resolution of 350 keV. We have used the DWBA reaction mechanism model to reproduce those spectra and their angular distributions. In this approximation, the form factor was treated as a folding of an effective projectile-nucleon interaction with a transition density. The effective projectile-nucleon interaction has been adjusted to reproduce the 0° cross section of the 1⁺ ground state of ¹²B populated in the ¹²C(t, ³He) reaction. We have employed RPA wave functions of excited states to construct the form factors. This DWBA+RPA analysis is used to compare calculated and experimental cross sections directly and to discuss the giant resonance excitations in the ⁹⁰Y nucleus. In this talk, we give some details on this analysis. We show that there are important contributions of L = 2 transitions in the observed cross sections for the 1⁺ final states that explain the previous difficulties in clearly identifying the monopole strength distributions. We then have a better indication of where the L = 0 part is located with this reaction and its microscopic analysis. The text was submitted by the author in English.     

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.     

Influence of the transfer reactions on p + <Superscript>6</Superscript>He elastic scattering

We have studied an effect of neutron and triton transfer reactions on the p +^6He elasticscatteringat25 MeVbymeansofcoupled - reaction - channelcalculations.Itisfoundthatwhenthetransferreactionsareexplicitlyincludedinthecalculationstheimaginarypartoftheinput$p + $⁶He optical model potential has to be reduced by 52 percent while its real part enhanced by 15 percent in order to fit the elastic-scattering data. The effect of transfer channels on the real part of this potential is somewhat weaker than that of ⁶He breakup reported previously. However, for the imaginary part, the effect of transfer channels is dominant. It is concluded that while the breakup contribution to proton elastic scattering mainly affects the real part of the bare potential, the contribution of transfer channels affects mainly its imaginary part.     

Microscopic description of the real alpha-nucleus potenial at large distances

The real part of the alpha-nucleus potential is calculated by double folding shell-model matter distributions of the projectile and target nuclei with effective nucleon-nucleon potentials obtained either phenomenologically, or microscopically from the Reid soft-core potential. Comparisons are made with experimental alpha-scattering data at incident energies near the Coulomb barrier, where effects due to the imaginary potential at large distances are negligibly small. The range of the effective nuclon-nucleon force at intermediate distances and the effective nucleon-alpha interaction are investigated.