Folding Model Analysis Research Articles

Cluster folding model analysis of the 7Be+28Si elastic scattering in the near-barrier

In the framework of the optical model, the elastic scattering of the radioactive projectile 7Be on the 28Si target at four energies near the Coulomb barrier has been analyzed. The cluster folding model is used to determine the real part of the nuclear optical potential. For comparison, two microscopic optical potentials have been generated using the DDM3Y effective NN interaction based upon two different forms for 7Be density distribution. All the obtained real potentials, in conjunction with phenomenological Woods-Saxon imaginary parts, have successfully reproduced the elastic scattering angular distributions over the measured angular range. The energy dependence of the real and imaginary strengths that are produced by the best-fit of the experimental data was examined. Neither the usual threshold anomaly nor the breakup threshold anomaly can be observed at the considered energy range. The obtained cross sections have been reduced and compared with earlier theoretical and experimental data of 7Li on the same target near the Coulomb barrier.

Optical and Double Folding Model Analysis of 28Si(α,α)28Si Elastic Scattering from 12.7 to 240 MeV

Optical and Double Folding Model Analysis of 28Si(α,α)28Si Elastic Scattering from 12.7 to 240 MeV

Folding model analysis of 28Si elastic scattering using different density distributions

The elastic scattering cross-sections of [Formula: see text]Si projectile by [Formula: see text]Al, [Formula: see text]Si, [Formula: see text]Ni, [Formula: see text]Ni and [Formula: see text]Pb targets are analyzed using the double folding model based on the effective M3Y interaction which is known as the most popular density independent form. In the calculations of the double folding model, 16 different density distributions of [Formula: see text]Si nucleus are examined. A very good agreement between experimental data and theoretical results is obtained, and also the literature results support our results. In addition, dependence on incident energy, target atomic number and target mass number of the imaginary potential depth is studied, and new and global equations are proposed.

The cluster folding model analysis for the elastic scattering of 6Li and 6He on 12C

To investigate the refractive effect in the scattering of loosely bound and exotic nuclei, the double-folding-cluster potential has been adopted in the optical model analyses of the elastic scattering of 6Li + 12C and 6He + 12C. The experimental angular distributions are reproduced very well over a wide energy range. For 6Li + 12C, the energy dependence of the optical potential agrees well with the dispersion relation. For the elastic scattering of 6He + 12C at intermediate energies, the refractive effect is predicted by the present calculation, accompanied by the abnormally weak absorption.

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.

Folding Model Analysis of Elastic Scattering of 11B from Light, Medium, and Heavy Nuclei

The elastic scattering angular distributions of 11B projectile on light, medium, and heavy target nuclei including 7Li, 9Be, 12C, 16O, 24,25,26Mg, 27Al, 28Si, 40Ca, 58Ni, 59Co, 60Ni, 197Au, 208Pb, and 209Bi have been analyzed at various incident energies. The theoretical results have been obtained by using two different nuclear potentials within the framework of the optical model (OM). Firstly, the double folding potential for real part and the Wood—Saxon (WS) potential for imaginary part have been applied. Secondly, the calculations with double folding potential for both real and imaginary part have been performed and compared with the experimental data. It has been seen that the results are in very good agreement with the experimental data. Also, the volume integrals and cross-sections for each reaction have been obtained. Finally, a new and simple formula for the imaginary potential depth has been derived to clarify the nuclear interactions of 11B nucleus at low energy reactions.

Optical and Double Folding Model Analysis for Alpha Particles Elastically Scattered from 9Be and 11B Nuclei at Different Energies

Optical and Double Folding Model Analysis for Alpha Particles Elastically Scattered from 9Be and 11B Nuclei at Different Energies

Folding model analysis of the 6He elastic scattering using No-core Shell model: Indication of the breakup threshold anomaly

Abstract We present a detailed analysis of the 6 He elastic scattering on different target nuclei over a wide energy range within the framework of the double folding model using a phenomenological imaginary potential. We show the microscopic real potential generated by No-core Shell model density distributions provides good agreement in explaining the elastic scattering angular distributions. In this study we also present a new formulation depending on the incident energy and atomic charge of the target nucleus for the phenomenological imaginary potential and investigate the threshold anomaly in halo nuclei by analyzing the 6 He + 208 Pb system.

Double folding model analysis of elastic scattering of halo nucleus 11Be from 64Zn

Calculations of elastic scattering cross-sections for 9,10,11Be + 64Zn at near-Coulomb barrier energy have been performed using a potential obtained from the double folding model and are compared with the experiment. In the framework of the double folding model, the nuclear matter densities of 9,10,11Be projectiles and a 64Zn target are folded with the complex energy-dependent effective M3Y interaction. The angular distributions of the differential cross-section for 9,10Be scattering from 64Zn at E c.m≈ 24.5 MeV agree remarkably well with the data, while in case of 11Be, calculations show a Coulomb–nuclear interference peak which is not observed in the data.

Folding Model Study of the Elastic Alpha-alpha Scattering at Low Energies

The folding model analysis of the elastic \(\alpha + \alpha\) scattering at the incident energies below the reaction threshold of 34.7 MeV (in the lab system) has been done using the well-tested density dependent versions of the M3Y interaction and realistic choices for the \(^4\)He density. Because the absorption is negligible at the energies below the reaction threshold, we were able to probe the \(\alpha + \alpha\) optical potential at low energies quite unambiguously and found that the α + α overlap density used to construct the density dependence of the M3Y interaction is strongly distorted by the Pauli blocking. This result gives possible explanation of a long-standing inconsistency of the double-folding model in its study of the elastic \(\alpha + \alpha\) and \(\alpha\)-nucleus scattering at low energies using the same realistic density dependent M3Y interaction.

Folding model study of the charge-exchange scattering to the isobaric analog state and implication for the nuclear symmetry energy

The Fermi transition (\Delta L=\Delta S=0 and \Delta T=1) between the nuclear isobaric analog states (IAS), induced by the charge-exchange (p,n) or (3He,t) reaction, can be considered as "elastic" scattering of proton or 3He by the isovector term of the optical potential (OP) that flips the projectile isospin. The accurately measured (p,n) or (3He,t) scattering cross-section to the IAS can be used, therefore, to probe the isospin dependence of the proton or 3He optical potential. Within the folding model, the isovector part of the OP is determined exclusively by the neutron-proton difference in the nuclear densities and the isospin dependence of the effective nucleon-nucleon (NN) interaction. Because the isovector coupling explicitly links the isovector part of the proton or 3He optical potential to the cross section of the charge-exchange (p,n) or (3He,t) scattering to the IAS, the isospin dependence of the effective (in-medium) NN interaction can be well tested in the folding model analysis of these charge-exchange reactions. On the other hand, the same isospin- and density dependent NN interaction can also be used in a Hartree-Fock calculation of asymmetric nuclear matter, to estimate the nuclear matter energy and its asymmetry part (the nuclear symmetry energy). As a result, the fine-tuning of the isospin dependence of the effective NN interaction against the measured (p,n) or (3He,t) cross sections should allow us to make some realistic prediction of the nuclear symmetry energy and its density dependence.

Folding model analysis of pion elastic and inelastic scattering from 6Li and 12C

π±-Nucleus scattering cross sections are calculated applying the Watanabe superposition model with a phenomenological Woods-Saxon potential. The phenomenological potential parameters are searched for π± scattering from 6Li and 12C to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at pion kinetic energies from 50 to 672 MeV. The optical potentials of 6Li and 12C are calculated in terms of the alpha particle and deuteron optical potentials. Inelastic scattering has been analyzed using the distorted waves from elastic-scattering data. The values of deformation lengths thus obtained compare very well with the ones reported earlier.

Folding model analysis of the elastic and inelastic scattering of K+ from 12C

Folding model analysis of the elastic and inelastic scattering of K+ from 12C

Folding Model Analysis of Pion Elastic and Inelastic Scattering from6Li and12C

Folding Model Analysis of Pion Elastic and Inelastic Scattering from⁶Li and₁₂C

Hindrance of the excitation of the Hoyle state and the ghost of the [formula omitted] state in 12C

While the Hoyle state (the isoscalar 02+ excitation at 7.65 MeV in 12C) has been observed in almost all the electron and α inelastic scattering experiments, the second 2+ excited state of 12C at Ex≈10 MeV, believed to be an excitation of the Hoyle state, has not been clearly observed in these measurements excepting the high-precision (α,α′)C12 experiments at Eα=240 and 386 MeV. Given the (spin and isospin zero) α-particle as a good probe for the nuclear isoscalar excitations, it remains a puzzle why the peak of the 22+ state could not be clearly identified in the measured (α,α′)C12 spectra. To investigate this effect, we have performed a microscopic folding model analysis of the α+C12 scattering data at 240 and 386 MeV in both the Distorted Wave Born Approximation (DWBA) and coupled-channel (CC) formalism, using the nuclear transition densities given by the antisymmetrized molecular dynamics (AMD) approach and a complex CDM3Y6 density dependent interaction. Although AMD predicts a very weak transition strength for the direct (01+→22+) excitation, our detailed analysis has shown evidence that a weak ghost of the 22+ state could be identified in the 240 MeV (α,α′)C12 data for the 03+ state at 10.3 MeV, when the CC effects by the indirect excitation of the 22+ state are taken into account. Based on the same AMD structure input and preliminary (α,α′)C12 data at 386 MeV, we have estimated relative contributions from the 22+ and 03+ states to the excitation of 12C at Ex≈10 MeV as well as possible contamination by 31− state.

Elasticα+Ne20scattering in theα+O16model ofNe20

A folding potential for the elastic $\ensuremath{\alpha}+^{20}\mathrm{Ne}$ scattering is constructed based on the $\ensuremath{\alpha}+^{16}\mathrm{O}$ structure model of the $^{20}\mathrm{Ne}$ nucleus. The elastic scattering angular distributions of the $\ensuremath{\alpha}+^{20}\mathrm{Ne}$ system at incident energies ${E}_{\ensuremath{\alpha}}=31.1$, 54.1, and 104.0 MeV have been calculated by using the folding potential. The experimental angular distributions and the anomalous large angle scattering (ALAS) features can be satisfactorily described. The anomaly of the $\ensuremath{\alpha}+^{20}\mathrm{Ne}$ system is clearly reconfirmed in the present folding model analysis and should be further systematically investigated.

G-Matrix Approach to Hyperon-Nucleus Systems

The properties of the new YN · YY interaction model ESC08 are studied on the basis of the G-matrix theory. G-matrix calculations in nuclear matter are performed in the cases of ΛN -, ΣN -, ΞN -a ndΛΛ -starting channels. In the ΛN case, the spin-spin and spinorbit terms are shown to be of reasonable strengths. The folding-model analyses are done extensively for observed spectra of Λ hypernuclei. The experimental energy spectra are nicely reproduced. The shell-model analyses for typical Λ hypernuclei are performed with the Gmatrix interactions. In the ΣN case, the repulsive values of UΣ are obtained owing to the effect of the quark Pauli-forbidden states which are taken into account phenomenologically in ESC08. In the ΞN case, the moderately attractive values of UΞ are obtained mainly due to the strongly attractive contributions in 3 S1 T =1 ΞN -ΛΣ -ΣΣ coupled states, which leads to extensive existence of Ξ hypernuclei. In the ΛΛ case, the BΛΛ values derived from ESC08 are found to be consistent with the experimental values.

Folding Model Analysis to Calculate Differential Cross Sections for the (16O, 12C) System

Folding Model Analysis to Calculate Differential Cross Sections for the (16O, 12C) System

Neutron transition strengths of21+states in the neutron-rich oxygen isotopes determined from inelastic proton scattering

A coupled-channel analysis of the $^{18,20,22}\mathrm{O}(p,{p}^{'})$ data has been performed to determine the neutron transition strengths of the ${2}_{1}^{+}$ states in oxygen targets, using the microscopic optical potential and inelastic form factor calculated in the folding model. A complex density- and isospin-dependent version of the CDM3Y6 interaction was constructed, based on the Brueckner-Hartree-Fock calculation of nuclear matter, for the folding model input. Given an accurate isovector density dependence of the CDM3Y6 interaction, the isoscalar (${\ensuremath{\delta}}_{0}$) and isovector (${\ensuremath{\delta}}_{1}$) deformation lengths of the ${2}_{1}^{+}$ states in $^{18,20,22}\mathrm{O}$ have been extracted from the folding model analysis of the $(p,{p}^{'})$ data. A specific $N$ dependence of ${\ensuremath{\delta}}_{0}$ and ${\ensuremath{\delta}}_{1}$ has been established which can be linked to the neutron shell closure occurring at $N$ approaching 16. The strongest isovector deformation was found for the ${2}_{1}^{+}$ state in $^{20}\mathrm{O}$, with ${\ensuremath{\delta}}_{1}$ about 2.5 times larger than ${\ensuremath{\delta}}_{0}$, which indicates a strong core polarization by the valence neutrons in $^{20}\mathrm{O}$. The ratios of the neutron/proton transition matrix elements (${M}_{n}/{M}_{p}$) determined for the ${2}_{1}^{+}$ states in $^{18,20}\mathrm{O}$ have been compared with those deduced from the mirror symmetry, using the measured $B(E2)$ values of the ${2}_{1}^{+}$ states in the proton-rich $^{18}\mathrm{Ne}$ and $^{20}\mathrm{Mg}$ nuclei, to discuss the isospin impurity in the ${2}_{1}^{+}$ excitation of the $A=18$, $T=1$ and $A=20$, $T=2$ isobars.

Giant resonances inSn116from 240 MeVLi6scattering

Giant resonances in {sup 116}Sn were measured by inelastic scattering of {sup 6}Li ions at E{sub {sup 6}Li}=240 MeV over the angle range 0 deg. - 6 deg. Isoscalar E0-E3 strength distributions were obtained with a double folding model analysis. A total of 106{sub -11}{sup +27}% of the E0 EWSR was found in the excitation energy range from 8 MeV to 30 MeV with a centroid (m{sub 1}/m{sub 0}) energy 15.39{sub -0.20}{sup +0.35} MeV in agreement with results obtained with {alpha} inelastic scattering.