Imaginary Part Of Optical Potential Research Articles

Determination of Differential Cross-Section of (n+89Y) Elastic and Inelastic Scattering using Eikonal Approximation

Neutron differential-elastic and inelastic scattering cross-sections of Yttrium-89 isotope were calculated at energies 8,10,12,14, and 17 MeV, at angles distributed between 20o and 180o in the center of mass frame. The obtained results data were interpreted using a spherical optical potential model and Eikonal approximation, to examine the effect of the first-order Eikonal correction on the effective potential. The real and imaginary parts of optical potential were calculated. It was found that the nominal imaginary potential increase monotonically while the effective imaginary one has a pronounced minimum around r = 6fm and then increases. The analysis of the relative energy of the projectile and reaction product was taken into account. The main results were compared with available experimental data at EXFOR.

Elastic scattering analysis of isobar nuclei A = 6 projectiles on 12C using different models of optical potential

In this research, we have extracted a new systematic global description for the fifteen data sets of the 6Li+12C elastic scattering angular distribution in the energy range of 5.8–600 MeV, and for the seven data sets of the 6He+12C elastic scattering in the energy range of 5.9–493.8 MeV using the simple optical model OM potential with fixed radii parameters. We have reanalyzed the two nuclear systems using a microscopic method within the framework of the double folding São Paulo potential (SPP) and the double folding cluster model (renormalized DFC1 and non-renormalized DFC2), prompted by the cluster structure of both (6He and 6Li) nuclei. We have adding the dynamic polarization potential (DPP) to DFC2, for well reproducing the experimental data, because the elastic scattering of weakly bound nuclei (6He and 6Li) is strongly affected by the coupling to other reaction channels, such as break-up. We have studied the effect of hallo properties of 6He by comparing the reflexion coefficients derivatives and the reduced cross sections (according to different prescriptions) of the two projectiles. The energy dependence for the reaction cross sections σR, real and imaginary volume integrals of the considered reactions and comparing it to the previously reported ones have been investigated. The dispersion relation between real and imaginary parts of optical potential has been investigated for both studied systems.

Analysis of scattering and breakup reactions of 12,14Be within the microscopic model of optical potential

Analysis of the differential cross sections of scattering of neutron-rich nuclei 12,14Be on 12C at 56 MeV/nucleon and on protons at energy near 700 MeV/nucleon is carried out within the microscopic model of optical potential (OP). The real part of the 12,14Be+12C OP is calculated by using the double-folding procedure accounting for the anti-symmetrization effects, while the imaginary part of OP is obtained in the framework of the high-energy approximation (HEA). As to the 12,14Be+p scattering at relativistic energies, calculations of the both real and imaginary OPs were made within the HEA approach. In this framework, the only free parameters of OP are the depths of its real and imaginary parts obtained by fittingto experimental data. The role of the 12,14Be density models is considered when reproducing the experimental data. A contribution of the inelastic channels with excitations of 2+ and 3− states in 12C when calculating the quasielastic cross sections is analysed. Also, the 14Be cluster model, in which this nucleus consists of a 2n-halo and the 12Be core, is applied to calculate the cross sections of diffraction breakup and stripping reactions in the 14Be+12C collisions at the energy of 56 MeV/nucleon. A good agreement of the theoretical results with the available experimental data of both scattering and breakup processes is obtained.

Energy Dependence and Surface Contribution of the Nucleon-Nucleus Optical Potential

The M3Y folding optical potential (OP) is used to analyze $^{9}$Be (p,p) $^{9}$Be elastic scattering at energies from few to 1000 MeV/nucleon. The M3Y folding-model is used for the real part whereas the volume and surface imaginary parts of OP are taken within the high-energy approximation model that based on the Glauber theory. In addition, the Brieva–Rook approximation is used for the spin-orbit OP. The angular distributions for elastic-scattering cross sections and analyzing powers, reaction, and total cross sections, are calculated using the optical model analysis with the partial-wave expansion method. The results show that these experimental data are reproduced well at a wide range of energy. In addition, clear and interesting energy dependencies are found for the different parts of the OP. A new behavior of the surface imaginary is found at scattering at high energies where the results show that the surface contribution to the imaginary part is very important at high energies as well as at low energies. The volume integrals show systematic energy dependencies. A new energy dependence formula is assumed for M3Y-Paris NN interaction to avoid the negative values of the OP at high energies.

Calculation of total reaction cross sections of 6He, 8,9Li on nuclei within the microscopic optical potential model

Experimental data on total reaction cross sections of exotic nuclei 6He, 8,9Li interaction with the 181Ta, 59Co, 28Si and 9Be targets in a wide energy range are analyzed in the framework of a hybrid model of microscopic optical potential (OP). The real part of OP is obtained on the basis of the double folding model, while the imaginary part of OP is calculated within the high energy approximation. This theoretical approach demonstrates the fairly well agreement with experimental data at the wide energy regions.

Elastic scattering and breakup reactions with light proton- and neutron-rich exotic nuclei

A microscopic analysis of the optical potentials (OPs) and cross sections of elastic scattering of 8B on 12C, 58Ni, and 208Pb targets at energies 20 < E < 170 MeV and 12,14Be on 12C at 56 MeV/nucleon is carried out. The real part of the OP is calculated by a folding procedure and the imaginary part is obtained on the base of the high-energy approximation (HEA). The density distributions of 8B evaluated within the variational Monte Carlo (VMC) model and the three-cluster model (3CM) are used to construct the potentials. The 14Be densities obtained in the framework of the the generator coordinate method (GCM) are used to calculate the optical potentials, while for the same purpose both the VMC model and GCM densities of 12Be are used. In the hybrid model developed and explored in our previous works, the only free parameters are the depths of the real and imaginary parts of OP obtained by fitting the experimental data. The use of HEA to estimate the imaginary OP at energies just above the Coulomb barrier is discussed. In addition, cluster model, in which 8B consists of a p-halo and the 7Be core, is applied to calculate the breakup cross sections of 8B nucleus on 9Be, 12C, and 197Au targets, as well as momentum distributions of 7Be fragments. A good agreement of the theoretical results with the available experimental data is obtained. It is concluded that the reaction studies performed in this work may provide supplemental information on the internal spatial structure of the proton- and neutron-halo nuclei.

Study of11Li and10,11Be nuclei through elastic scattering and breakup reactions

The hybrid model of the microscopic optical potential (OP) is applied to calculate the 11 Li+p , 10,11 Be+p , and 10,11 Be+12 C elastic scattering cross sections at energies E Li+p elastic scattering, the microscopic large-scale shell model (LSSM) density of 11 Li is used, while the density distributions of 10,11 Be nuclei obtained within the quantum Monte Carlo (QMC) model and the generator coordinate method (GCM) are utilized to calculate the microscopic OPs and cross sections of elastic scattering of these nuclei on protons and 12 C. The depths of the real and imaginary parts of OP are fitted to the elastic scattering data, being simultaneously adjusted to reproduce the true energy dependence of the corresponding volume integrals. Also, the cluster models, in which 11 Li consists of 2n -halo and the 9 Li core having its own LSSM form of density and 11 Be consists of a n -halo and the 10 Be core, are adopted. Within the latter, we give predictions for the longitudinal momentum distributions of 9 Li fragments produced in the breakup of 11 Li at 62 MeV/nucleon on a proton target. It is shown that our results for the diffraction and stripping reaction cross sections in 11 Be scattering on 9 Be, 93 Nb, 181 Ta, and 238 U targets at 63 MeV/nucleon are in a good agreement with the available experimental data.

Using the microscopic optical potential model to analyze 10,11Be elastic scattering on protons and nuclei

The density distributions of 10,11Be nuclei obtained via the generator coordinate method (GCM) and quantum Monte Carlo (QMC) model are used to calculate the microscopic optical potentials (OP) and elastic scattering cross sections of these nuclei on protons and the 12C nucleus. The real part of the OP is obtained by means of folding while the imaginary part is estimated within a high-energy approximation. The depths of the real and imaginary parts of OP are varied by fitting these calculations to experimental data on cross sections. The known energy dependence of the respective volume integrals of potentials is used to resolve ambiguities in magnitudes of these depths. These OPs can be applied to the further calculations of the cross sections of different reactions in which they take part.

Modelling Effects of Halo Breakup on Fusion

Theories of breakup and fusion of two-body projectiles are examined, to see how complete and incomplete fusion may be predicted separately. A proposal is made for an 'optical decoherence model' which uses semigroup evolution equations to describe the decoherence effects of the imaginary parts of optical potentials without also losing flux.

Elastic scattering threshold anomaly and near-barrier heavy-ion fusion

From an analysis of heavy-ion elastic scattering and fusion data available for three systems, Udagawa et al. presented evidence that the ``threshold barrier'' (T) determined from fusion is approximately equal to the ``threshold energy'' (${\mathit{E}}_{\mathit{a}}$) extracted from the imaginary part of optical potential for elastic scattering in the vicinity of the Coulomb barrier. We have extended this investigation to include seven more systems for which the relevant data are available. Furthermore, from a comparison of sets of \ensuremath{\Delta}V, the polarization potential (deduced from elastic scattering), and B-T, the barrier difference (deduced from fusion) values, it is suggested that the two quantities are correlated.

Real and imaginary parts of the microscopic optical potential between nuclei in the sudden and adiabatic approximation and its application to medium energy 12C- 12C scattering

Real and imaginary parts of the optical potential between two nuclei have been calculated from the realistic two-nucleon interaction of Reid using the approach of Faessler and collaborators but with the following modifications: (a) A surface curvature term proportional to the square of the gradient of the density has been added to the energy density functional and the parameters are determined so as to reproduce the binding energies and rms radii of nuclei considered and (b) in addition to the sudden approximation, an adiabatic situation is also considered. Whereas, in the sudden approximation the density of the composite system is obtained by adding the densities of the two colliding nuclei, in the adiabatic approximation, the maximum density in the composite system is limited to the saturation value while conserving the nucleon number. Although the real part of the potential is in the center quite different in these two approximations, the cross sections are not. The real and imaginary parts of the optical potential are calculated for the nuclear pairs 12C+ 12C, 16O+ 16O, 40Ca+ 40Ca and 208Pb+ 208Pb for relative momenta per nucleon k r = 0 and 1 fm −1. Elastic, inelastic and reaction cross sections are calculated for 12C+ 12C scattering at E lab = 300, 360 and 1016 MeV using the calculated potential and coupling the elastic channel to the 2 + at 4.44 MeV and 3 − at 9.64 MeV, and compared with the experimental data. The agreement with the data at 1016 MeV is satisfactory and the theory can also reproduce the general trend of the angular distributions at 300 and 360 MeV but the calculated values at larger angles overestimate the data. The energy dependence and the magnitude of the observed reaction cross section are well reproduced by the theory.

Volume integrals of real and imaginary parts of optical potentials for light projectiles

Abstract From a systematic analysis of the real and the imaginary parts of the light projectile (Ap = 1-6) phenomeno-logical optical potentizls, global formulee which describe successfully the volume integrals in terms of the projectile energy, the target and the projectile mass numbers have been found.

Proximity limit of the imaginary part of the heavy ion optical potential due to nucleon transfer

In an earlier work it was assumed that the imaginary part of the optical potential due to nucleon transfer could be described by a proximity-type formula. Here we derive such a formula starting from the transfer probabilities between specific quantum states and assuming leptodermous nuclei.

Surface and volume contributions to real and imaginary parts of the heavy-ion optical potential

Starting from the Feshbach expression for the optical potential, explicit formulae for the real and the imaginary parts of the optical potential between two heavy ions (HI's) are obtained. They are each composed of a volume and a surface term. The contributions to the volume term are calculated in two nuclear Fermi liquids which flow through each other starting from the realistic Reid soft core nucleon-nucleon (NN) interaction. Since the Fermi surface is formed by two spheres one obtains a complex Brueckner reaction matrix which is approximated by a complex, effective local interaction. It is used in a fully antisymmetrized double folding procedure to obtain the volume terms of the optical potential between the two HI's. The surface contributions are directly calculated in the collision of the two finite HI's. The collective surface vibrations (3 − octupole state and 2 +, 4 + ( T = 0) giant resonances for the 16O− 16O collision) are included as intermediate states. This yields especially an imaginary contribution at the surface which reduces the transparency found with the volume terms alone. The method is applied to 16O− 16O scattering at 83 and 332 MeV laboratory energy. The local approximations to the real and imaginary parts obtained in this way agree well with phenomenological fits. The surface terms improve the agreement of the differential cross section at 80 MeV where experimental data are available.

Effects of imaginary potentials on the vector analyzing power in elastic scattering of polarized deuterons

In elastic scattering from nuclei, the vector analyzing powers of polarized deuterons are found to be strongly affected by the imaginary parts of optical potentials. A definite relationship is postulated between the analyzing power and the imaginary potential depth. The relationship shows that the shell-closure effect of the analyzing power observed for Se isotope targets is the reflection of the isotope dependence of the imaginary potential. Coupled-channel calculations show that some low-lying levels of the target nuclei are responsible for the isotope dependence. By the use of the relationship, deuteron scattering from medium-weight nuclei at incident energies of about 15 MeV are reanalyzed to give a systematic variation with target mass number for the potential parameters, which is emphasized by a nearly constant volume integral of the real potential per pair of interacting nucleons.

Semiphenomenological Model Approach to Continuous Spectrum States. I

AbstractThe Semiphenomenological Model of the Nucleus (SPM) is applied to describing the mechanisms of the inelastic and elastic scattering of nucleons by nuclei. Perturbation theory for the SPM “residual” interaction (including the first and second order) is used as calculational method. Cross sections, angular distributions, widths of resonant states and the imaginary part of optical potential are considered in a unified manner (one‐step and two‐step transitions being taken into account). Numerical estimates are given for the target nucleus 41Ca, quasiparticle states being taken as intermediate ones.

The effect of shell closure on the angular distribution of elastically scattered particles

In elastic scattering from nuclei, the vector analyzing powers of polarized deuterons are found to be strongly affected by the imaginary parts of optical potentials. A definite relationship is postulated between the analyzing power and the imaginary potential depth. The relationship shows that the shell-closure effect of the analyzing power observed for Se isotope targets is the reflection of the isotope dependence of the imaginary potential. Coupled-channel calculations show that some low-lying levels of the target nuclei are responsible for the isotope dependence. By the use of the relationship, deuteron scattering from medium-weight nuclei at incident energies of about 15 MeV are reanalyzed to give a systematic variation with target mass number for the potential parameters, which is emphasized by a nearly constant volume integral of the real potential per pair of interacting nucleons.

Distribution of the imaginary part of the optical potential

The radical dependence of the imaginary part of the nuclear optical potential is calculated by the semi-classical independent particle model with a diffuse nuclear boundary. Our method is completely the same as the one proposed by Harada and Oda, whose results are extended for various energies in this work. It is found that the strong absorption at the nuclear surface is less important for intermediate incident energies.