An optical model analysis of neutron scattering

Neutron elastic scattering data in the range A > 16, 7 < E < 30 MeV are analyzed using a standard local optical model potential. The obtained parameters are compared with similar optical model parameters derived from proton elastic scattering. Empirical values for the Coulomb correction term, isospin dependence and energy dependence are obtained. The results are compared with theoretical calculations.     

A study of the odd isotopes of copper using the 58, 60, 62, 64Ni(τ, d) 59, 61, 63, 65Cu and 48Ca(τ, d)49Sc reactions

Experimental measurements are reported for the ^{58, 60, 62, 64}Ni(τ, d) ^{59, 61, 63, 65}Cu and ⁴⁸Ca(τ, d)⁴⁹Sc reactions and for the elastic scattering of ³He particles from ^{58, 60, 62, 64}Ni and ⁴⁸Ca targets at an incident energy of 18 MeV. The (τ, d) angular distributions cover the angular range from approximately θ_c.m. = 5° to 90° and the elastic scattering angular distributions range from θ_c.m. = 12° to 172°. In the (τ, d) reactions several weakly excited states, not previously seen in stripping reactions, have been identified and assignments of the transferred angular momentum made. The ⁴⁸Ca(τ, d)⁴⁹Sc reaction data are used in conjunction with the theoretical sum rules of MacFarlane and French to determine the normalization factors to be used with DWBA calculations for different sets of optical potentials. These normalization factors are used to extract spectroscopic strengths and centroid energies from the Ni(τ, d)Cu data which are compared with published model calculations for the odd copper isotopes. It is concluded that these calculations invariably fail to give a consistent picture of the odd copper isotopes mainly due to the use of centroid energies as variable parameters in the model calculations.     

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.     

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.     

Interference of isovector and isoscalar giant quadrupole resonances in Y and Pb

We present the calculations of the fore-aft asymmetry of γ-rays in fast nucleon capture reactions ⁸⁹Y(n, γ)⁹⁰Y, ²⁰⁸Pb(n, γ)²⁰⁹Pb and ²⁰⁸Pb(p, γ)²⁰⁹Bi which are based on a consistent version of the direct-semi-direct (DSD) capture model. The results are in good agreement with observed differential cross sections.     

Elastic and inelastic scattering of 11.8 MEV polarized deuterons from 34S

The elastic and inelastic scattering of 11.8 MeV vector polarized deuterons from ³⁴S has been studied. Angular distributions of the cross section σ(θ) and vector analyzing power iT₁₁(θ) have been measured for the ground state and the first three excited states in ³⁴S. Optical model parameters were first obtained by fitting the elastic deuteron scattering data alone. DWBA calculations with a collective model form factor were performed for the inelastic scattering to the excited states. Coupled-channels calculations were also done both for the one-phonon and the two-phonon excited states. The optical model parameters were suitably modified to obtain simultaneous fit to elastic and inelastic data when channel coupling was introduced. The values of the vibrational parameter β₂ for one- and two-phonon states are discussed and compared with those obtained from γ-decay width studies.     

Generalized fresnel model for very heavy ion scattering: (II). Relation to the optical model

The generalized Fresnel model presented in part I as a simplified method for analyzing angular distributions of very heavy ion scattering is used here with an alternative parameterization of the partial-wave S-matrix. Its form is suggested by analytic expressions for the reflection function and nuclear phase shifts derived by Kauffmann from conventional optical potentials. This enables us to formulate explicitly the relationships between the l-space and r-space properties of the elastic heavy ion interaction, in particular the continuous ambiguities and other features found empirically from optical model calculations.     

The OptModel high-precision optical-model program code

The OptModel high-precision optical-model program code aimed at solving a wide set of problems related to the elastic scattering and n, p, d, t, ^3,4,6He, ⁶Li nuclear reactions on spherical nuclei (or ones close to spherical) is described. A phenomenological optical potential in the Woods–Saxon form is used in this code. The main features of the program are described. The technique for solving a Schrödinger radial equation in the interior region is given in detail. The results from tests and research calculations are described. The results from executing a simultaneous analysis of a great deal of experimental data on elastic scattering at different energies to obtain the energy dependence of optical potential parameters are also presented.     

Heavy-ion fusion cross sections

The absolute cross sections for heavy-ion induced reactions in the rare earth region are studied systematically as functions of projectile energy, charge and mass. Targets and projec-tiles are chosen so that the same final states are fed in erbium, holmium and dysprosium nueleides with mass numbers A = 159–162. As the low lying states in these final nucleides are well known, the cross sections for the various reaction channels can be determined from singles γ-ray spectra. By summing these cross sections, the heavy-ion fusion cross sections are determined, and compared to theoretical calculations based on the Bass model as well as to total reaction cross sections deduced from optical model fits to elastic scattering data.     

Deuteron elastic scattering and (d,p) reactions on 208Pb at Ed = 22 MeV and j-dependence of T20 in (d,p) reaction

An experimental study of deuteron elastic scattering and (d,p) reactions at E_d = 22 MeV was made for ²⁰⁸Pb target. A new j-dependence of T₂₀ for (d,p) reaction at backward angles was observed. A “model independent” optical potential method was applied to analyze deuteron elastic scattering in the 10–22 MeV energy range. A continuum discretized coupled channels (CDCC) analysis was performed for deuteron elastic scattering at 22 MeV and the deuteron breakup effect was elucidated. DWBA and CDCC (d,p) analyses were made for (d,p) reactions.     

Elastic scattering of6Li on12C at 20 MeV

The elastic scattering of lithium nuclei from carbon was measured atE _lab=20 MeV. The obtained angular distribution was fitted by an optical model calculation. Parameter sets and the corresponding transmission coefficients are given.     

Energy dependence of the elastic scattering 40Ca(3He, 3He) in the energy range 10.0 to 18.0 MeV

Differential cross sections for the elastic scattering of 18, 16, 14, 12 and 10 MeV ³He particles by ⁴⁰Ca were measured and analyzed in terms of the optical model with volume imaginary and real spin-orbit potentials. Angular distributions have been measured in 5° steps between 25° and 175°. Four sets of optical model parameters were established and in two of these, sets A and B, systematic variations with energy of the real, volume imaginary and spin-orbit potentials were obtained. The geometrical parameters were not varied as a function of energy. The effect of the matching radius R_M on the optical model calculations, was investigated. It was found that the matching radius should be calculated using the geometrical parameters of the potential that yields the largest value for R_M according to the receipe R_M = R + 7a where R is the nuclear radius and a is the diffuseness.     

What kind of optical model potentials should be used for deuteron stripping reactions?

This paper presents the results of a study that compares CTOM, a microscopic optical model potential(OMP), which is an optical model co-created by the China Nuclear Data Center & Tuebingen University, to CH89, which is a typical phenomenological OMP.The respective OMPs were tested by applying them to the modelling of nucleon elastic scattering and(d,p) transfer reactions involving14C,36S, and58Ni targets at both low and relatively high energies. The results demonstrated that although both potentials successfully accounted for the angular distributions of both the elastic scattering and transfer cross sections, the absolute values of the transfer cross sections calculated using CTOM were approximately 25% larger than those calculated using CH89. This increased transfer cross sections allowed CTOM to produce single particle strength reduction factors for the three reactions that were consistent with those extracted from(e,e′p) reactions as well as with more recent(p,2p) and(p,pn) reactions. Notch tests suggested that nucleon elastic scattering and transfer reactions are sensitive to different regions of the OMP;accordingly,phenomenological OMPs, which are constrained only by elastic scattering cross sections, may not be sufficient for nucleon transfer reactions. Therefore, we suggest that microscopic OMPs, which reflect more theoretical considerations, should be preferred over phenomenological ones in calculations of direct nuclear reactions.     

Observation of the nuclear rainbow scattering for12C+12C atE Lab =300 MeV

The elastic and inelastic scattering of¹²C on¹²C has been measured in the angular range between 2.8° and 70.4° in the c.m. system atE _Lab =300 MeV. Optical model calculations have been performed with Woods-Saxon and folded potentials, the ground state and the first 2⁺-state were coupled in the calculations. The large cross sections of the elastic scattering at large angles is related to the nuclear rainbow scattering, which is centered at about 56°. This requires a potential depth of 100 MeV at a distance of 3 fm, the fit to the data is sensitive down to this region. The calculations with the folded potential show a better agreement with the data than those with the Woods-Saxon shape. The total reaction cross section of 1,420 mb, obtained from the optical model analysis, corresponds to the geometrical value; no transparency is observed.     

Microscopic approach to calculating cross sections and optical potentials for nucleus-nucleus interaction at intermediate energies

Nucleus-nucleus scattering is considered in the high-energy approximation and on the basis of Glauber-Sitenko microscopic theory in the optical limit. Analytic expressions for eikonal phase shifts are given for the case of Fermi-type realistic potentials and nuclear-density distributions. The effect of taking into account the distortions of the trajectories of the nuclei involved and the nuclear-density dependence of nucleon-nucleon forces on the total reactions cross sections is illustrated. The sensitivity of the reaction cross sections to the choice of model for the ⁶He projectile nucleus, which involves a neutron halo, is explored. Semimicroscopic optical potentials are introduced in order to describe differential cross sections for elastic scattering. The results of the present calculations are compared with available experimental data.