Semiclassical treatment of heavy ion elastic scattering

A generalized semiclassical treatment for the elastic scattering of heavy ions is developed in the presence of a complex optical potential. The scattering phase shift and its derivatives with respect to the impact parameter are calculated after extending the JWKBL approximation. The results are compared with experimental data for the elastic scattering of¹⁶O from medium and heavy target nuclei and relation between the present treatment and that of the optical model and Regge pole analysis is established     

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.     

Description of proton-calcium scattering using the α-particle model

The theoretical proton-⁴⁰Ca optical potential is constructed based on theα-particle model of the nucleus. With this potential, the differential cross section, analysing power and the spin rotation function for 200 MeV proton-⁴⁰Ca elastic scattering are calculated. The results are in good agreement with the experimental data.     

Studying the reactions of deuteron interaction with <Superscript>9</Superscript>Be nuclei at low energies

Data on elastic and inelastic scattering, and the reactions of few-nucleon transfers in the interaction between the nuclei of deuteron and ⁹Be at energies of around 10 MeV/nucleon, are analyzed. A theoretical analysis is performed using the double-folding potential model with the wave function of the ground state of the ⁹Be nucleus, constructed in the three-cluster α + α + n-approximation. Calculations of the cross section of elastic scattering for the reaction d + ⁹Be using the calculated folding potential are preformed using the optical model. The resulting optical potential is used to analyze cross sections of transfer reactions and inelastic scattering in the context of the distorted waves method. A comparative analysis of the experimental data and theoretical calculations is performed.     

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.     

Optical potential analysis of proton elastic scattering from <Superscript>12</Superscript>C based on the <Emphasis Type="Italic">α</Emphasis>-particle model

Based on an α-particle model of ¹²C, an optical potential for intermediate-energy proton- ¹²C scattering is presented in the framework of the KMT theory. The parameterized proton- ⁴He amplitude, the required basic input for constructing the optical potential, is obtained by fitting the proton- ⁴He scattering data. The differential cross-sections and analyzing powers of the proton- ¹²C elastic scattering at incident energies ranging from 0.2 to 1.0GeV have been calculated by using the obtained optical potential. The main features of the measured angular distributions of the cross-section and the analyzing power can be satisfactorily described. The proton- ¹²C total cross-sections have also been calculated, and the results are in good agreement with the experimental data at energies below 0.6GeV but underestimate the data about 6% at higher energies.     

Phenomenological optical model for p-4He elastic scattering

The results of a Dirac equation optical model analysis of p-⁴He elastic scattering data are reported. The optical potential obtained at 1029 MeV reproduces the systematics of p-⁴He data over the energy range from 560 to 1730 MeV.     

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 e∓ by Na atoms

ABSTRACT

The differential, integrated elastic, momentum transfer, viscosity and total cross-sections along with Sherman function for the elastic scattering of electrons and positrons by sodium atoms have been calculated within the framework of complex projectile–atom optical potential model at the impact energies 0.1 ≤ E_i ≤ 10⁴ eV for both the projectiles. The relativistic Dirac partial wave techniques, with accurate analytical charge densities, are used to obtain the scattering amplitudes. The present results produce satisfactory agreement with the experimental measurements and other theoretical calculations available in the literature.     

Effective nucleon-nucleon forces and interaction of light exotic nuclei with stable nuclei at low energies

The effect of the density dependence of effective nucleon-nucleon forces on the folded potential of the interactions of the light exotic nuclei ⁶He, ¹¹Li, ¹¹Be, and ⁸B with the stable nucleus ¹²C is studied, and the corresponding experimental data on the total reaction cross sections and on elastic scattering are analyzed. A semimicroscopic double-folding model featuring various density-dependent forces based on the M3Y interaction is used together with the nucleon densities as calculated within the density-functional method by using a unified set of parameters for all the above nuclei. It is shown that the angular distributions recently measured for elastic ⁶He scattering on ¹²C at an energy of 41.6 MeV per projectile nucleon and for elastic ¹¹Be scattering on ¹²C at an energy of 49.3 MeV per projectile nucleon can be described satisfactorily if the real part of the optical folded potential is supplemented with a surface term mimicking the contribution of the dynamical polarization potential.     

Elastic and inelastic scattering of protons from Li between 25 and 45 MeV

The elastic and inelastic scattering of protons from ⁶Li has been studied at incident energies of 25.9, 29.9, 35.0, 40.1 and 45.4 MeV. The 2.18 MeV (3⁺, T = 0) first excited state of ⁶Li was found to be strongly excited, but the 3.56 MeV (0⁺, T = 1) second excited state was quite weakly excited. Angular distributions for excitation of the 2.18 MeV level were measured at all five energies, while angular distributions for excitation of the 3.56 MeV level were extracted only at 25.9 and 45.4 MeV. To test the applicability of the optical model for the scattering of protons from such a light nucleus the elastic scattering angular distributions have been analyzed using the eleven-parameter search code SEEK. Available polarization angular distributions were included in the analysis. Reasonable fits to the data have been obtained with an average geometry potential. Theoretical estimates of the real part of the optical potential and the inelastic scattering differential cross sections have been made using the microscopic model for proton-nucleus scattering. Both phenomenological and realistic forces have been considered and the necessary nuclear transition densities have been extracted from experimental elastic and inelastic electron scattering data. An estimate of a possible spin-spin term in the optical potential has also been made.     

Elastic scattering of 33 MeV tritons and isospin dependence of mass-3 optical potential

Differential cross section data are presented for the elastic scattering of 33 MeV tritons from a range of nuclei from ¹²C to ²³²Th. These data have been analysed using a phenomenological optical model. Parameters are presented for three families of the real potential. A comparison of the triton optical model potential with those from a re-analysis of ³He scattering from fp shell nuclei has allowed the isospin dependence of the optical model potential for mass-3 projectiles to be obtained in this mass region.     

Elastic and the 2+ inelastic scattering of high energy protons on12C and the alpha-particle model

The alpha-particle model has been applied to calculate the elastic and the 2⁺ inelastic angular distribution of 1 GeV protons on¹²C within the framework of Glauber multiple scattering theory. The results are compared with the recent experimental data and with some previous calculations. The model gives a fairly good account of the inelastic data and its predictions for the elastic scattering are essentially the same as those of the shell model.     

Elastic and inelastic scattering of identical heavy ions

The elastic and inelastic scattering of ¹²C, ¹²C, ²⁴Mg, ²⁴Mg, ²⁸Si, ²⁸Si was studied at bombarding energies E_c.m. = 5–18.8, 20–33, 29–36 MeV, respectively. The experimental arrangement includes two position sensitive detectors covering the angular ranges from O₁₂₄ = 20°–70°. The results are compared to calculations within the framework of the diffraction and optical model. A phase shift analysis is performed for the elastic scattering data of the ¹²C+¹²C system. It is shown that a shallow nuclei potential in needed to reproduce the ²⁸Si+²⁸Si results and that the ¹²C, ¹²C scattering shows evidence of resonance formation in the elastic channel.     

Global optical model potentials for symmetrical lithium systems: 6Li+6Li, 7Li+7Li at Elab = 5–40 MeV

Angular distributions of ⁶Li+⁶Li elastic scattering were measured for E_lab = 5–40 MeV. An optical model analysis of these data together with older data of ⁷Li+⁷Li elastic scattering taken at E_lab = 8–17 MeV was performed with the aim to search for a “global” OM potential which describes elastic scattering in both LiLi systems in a broad energy range. Both surface and volume absorbing potentials can be found which fulfill this requirement if a linear energy dependence is assumed of the depths of the real as well as the imaginary potential. These depths, if fitted to individual angular distributions, are found to vary in a correlated manner with the beam energy. This is taken as indication of strong coupling between elastic, inelastic, and reaction channels. This is corroborated by the existence of resonances in reaction channels at these energies where the potential depths are most pronouncedly changing.     

Microscopic interpretation of 7Li+24Mg inelastic scattering at 34 MeV

Theoretical differential cross sections for ⁷Li+²⁴Mg inelastic scattering have been calculated in the DWA using a double folding model. The projectile and target transition densities are matched to electron scattering data and the nucleon-nucleon interaction is chosen to reproduce the real part of the optical potential at the distance $\text{D}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ where there is 50 % transmission in the elastic channel. There are no free parameters in the calculations. The agreement between the theoretical results and the available experimental data is good which serves to establish a consistency between elastic and inelastic scattering. The cross section for a mutual transition which leaves both the projectile and target in their first excited states is found to come mainly from relative L_r = 4 transfer. It is speculated that a quadrupole term in the optical potential might make important contributions at backward angles in the elastic cross section.     

Applicability of ~9Be global optical potential to description of ~(8,10,11)B elastic scattering

We achieved a set of 9Be global phenomenological optical model potentials by fitting a large experimental dataset of the elastic scattering observable for target mass numbers from 24 to 209.The obtained 9Be global optical model potential was applied to predict elastic-scattering angular distributions and total reaction cross-sections of 8,10,11B projectiles.The predictions are made by performing a detailed analysis comparing with the available experimental data.Furthermore,these elastic scattering observables are also predicted for some lighter targets outside of the given mass number range,and reasonable results are obtained.Possible physical explanations for the observed differences are also discussed.     

Exact finite-range DWBA description of the60Ni(160,12C)64Zn reaction at 60 MeV incident energy

Cross section angular distributions of⁶⁰Ni(¹⁶O,¹²C)⁶⁴Zn reactions leading to three strongly excited states at 60 MeV incident energy and the¹⁶O+⁶⁰Ni and¹²C+⁶⁴Zn elastic scattering at 60 MeV respectively 45 MeV and 54 MeV have been measured using aQ3D magnetic spectrograph. EFR-DWBA calculations assuming the transfer of anα-cluster in its 0s ground state are able to describe the general features of the strongly oscillating experimental angular distributions using a surface transparent optical model potential. The optical model parameters used in the DWBA calculations are obtained from fits of the elastic scattering data of incident and exit channels. The importance of “correct” optical model parameters in the exit channels for relative spectroscopic factors will be discussed and the extracted relative spectroscopic factors will be compared to previous (⁶Li,d) results.     

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.