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.     

Energy dependence of the optical model parameters for 3He ions scattered from 40Ca and 58Ni

The differential cross sections for the elastic scattering of ³He ions on targets of ⁴⁰Ca and ⁵⁸Ni have been measured at incident energies of 27.7, 51.4, 73.2 and 83.5 MeV. The results of optical model analyses showed that only one unique potential (J_R ≈ 330 MeV · fm³) with a surface absorptive term can provide acceptable fits to the large angle elastic scattering cross sections at 83.5 MeV. The particular geometrical set found at 83.5 MeV could not, however, give an adequate fit to the data with energy less than 40 MeV. Subsequent analyses indicated that a break in the energy dependence of the real potential is observed for the low energy data. Explicit energy dependent terms were obtained by fitting all the data simultaneously. These phenomenological potentials were also compared with the folded nucleon-nucleus potential. The influence of the α-particle channels on the elastic scattering of ³He ions at 83.5 MeV was also examined.     

Elastic 3He scattering from even Ar isotopes and backward-angle anomalies in the systematics of elastic 3He scattering

Angular distributions have been measured for ³He elastic scattering from ^{36, 38, 40}Ar at 26.5 MeV and from ³⁶Ar and ⁴⁰Ca at energies between 24.5 and 28 MeV. This scattering clearly shows features of “anomalous” backward-angle scattering, which is discussed in the systematics of ³He scattering from heavier target nuclei. The data for “anomalous” scattering can be described by optical potentials which show features significantly different from those of “normal” scattering. These features are smaller radius parameters for the real optical potential and a strongly reduced volume integral for the imaginary potential.     

Optical model analysis of p+6He scattering over a wide range of energy

Optical-model analysis of proton elastic scattering from ⁶He has been carried out for eight sets of elastic scattering data at energies, 24.5, 25.0, 36.2, 38.3, 40.9, 41.6, 71.0 and 82.3 MeV/n respectively. The vector analyzing power and differential cross section for the elastic scattering of ⁶He nucleus from polarized protons at 71 MeV have been analyzed in the framework of the optical model potentials. The data are, first, analyzed in term of phenomenological potentials using the Woods-Saxon form for the real and imaginary parts supplemented by a spin-orbit potential of Thomas form. The analysis has been also performed using microscopic complex potentials.     

Elastic scattering of 11B from 209Bi in the energy range 49.8 ⩽ E ⩽ 84.1 MeV

The elastic scattering of ¹¹B from ²⁰⁹Bi has been measured at laboratory energies of 49.8, 51.3, 52.2, 52.8, 54.3, 55.8, 59.8, 64.8, 69.8, 74.8 and 84.1 MeV. These data have been analyzed using a microscopic optical model and the energy dependence of the real and the imaginary parts of the optical potential at near barrier energies has been determined. The “threshold anomaly” observed in the real part of the potential is found to be consistent with the dispersion relation which connects the real and the imaginary parts of the potential. Inelastic scattering and transfer reactions have also been measured at energies of 51.3, 55.8, 59.8 and 74.8 MeV. DWBA calculations for the 3⁻ state in ²⁰⁹Bi are made. From the measured transfer probabilities, using a semiclassical approach the strength of the form factors have been obtained. The fusion cross sections have been derived at these energies from the corresponding quasi-elastic scattering angular distribution data. The fusion cross sections calculated using the energy dependent barriers extracted from the energy dependent real parts of the potential compare well with, that determined from quasi-elastic scattering data and are also in good agreement with simplified coupled channels calculation for fusion incorporating important inelastic and transfer channels.     

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.     

The elastic and inelastic scattering of 33 MeV polarized 3He from oxygen and iron isotopes

Angular distributions of differential cross sections and analysing powers have been measured for elastic and inelastic scattering of polarized 33 MeV ³He from ¹⁷O, ¹⁸O, ⁵⁴Fe and ⁵⁶Fe targets. The elastic data have been analysed to deduce the optical model parameters. The inelastic scattering together with the elastic scattering have been interpreted in terms of a macroscopic model within a coupled-channels framework. From this analysis the deformation parameters, β, were deduced.     

Neutron elastic scattering from 116,118,120,122,124Sn

Accurate measurements of neutron differential elastic cross sections have been obtained from even isotopes of Sn. Data are presented for the elastic scattering of 11 MeV neutrons from ^{116, 118, 120, 122, 124}Sn, the elastic scattering for 24 MeV neutrons from ^{116, 118, 124}Sn and the neutron total cross section from ^{118, 120, 122, 124}Sn in the energy ranges 5.0–10.6 MeV and 20.0–26.0 MeV. The elastic scattering data are analyzed in terms of an empirical optical-model potential. The obtained optical-potential parameters are analyzed in terms of energy and isospin dependence and compared with those obtained from proton elastic scattering on even Sn isotopes.     

Deuteron stripping to the single particle states of 17O

Angular distributions for deuteron-¹⁶O elastic scattering and the ¹⁶O(d, p)¹⁷O reaction leading to levels with E_x = 0.0, 0.87, and 5.08 MeV have been measured at energies of 25.4, 36.0 and 63.2 MeV. The elastic deuteron data have been fit with a standard spin one optical model potential to obtain parameters for use in a DWBA analysis of the (d, p) data. The potential found in the search is shown to be consistent with other data taken in the range from 25 to 82 MeV. In addition to this deuteron optical potential, an adiabatic deuteron potential, which includes the effects of deuteron breakup, was used in the DWBA analysis. The neutron form factor was selected independent of the width of any state. The mean square radius, a single particle property, is used to find the well parameters and it determines the width of the single particle state. The spectroscopic factors obtained for the ground and first excited states are between 0.8 and 1.0 and are consistent with a large single particle parentage for these states and lower energy data. The width extracted from the DWBA analysis of the 5.08 MeV unbound state was 20% less than that obtained from elastic neutron scattering to the same state, possibly pointing up some difficulties with DWBA procedures commonly used. The adiabatic deuteron potential yields spectroscopic factors that are energy independent to 20% and gives satisfactory calculated angular distribution shapes for angles less than 40°. The conventional deuteron potential gives less satisfactory calculated shapes with the consequent introduction of some ambiguity in the derived spectroscopic factors.     

The elastic scattering of 33 MeV He particles from Ni,Cu and Zn

Differential cross sections have been measured for the elastic scattering of 33 MeV ³He particles from targets of ^58,60,62,64Ni,^63,65Cu and ^64,66,68Zn over the angular range 5° to 175°. The data have been analysed with the optical model, with particular emphasis on the investigation of the ambiguities in the real potential, the form of the imaginary potential and the use of a spin-orbit term.     

Global optical model potential describing 12C-nucleus elastic scattering

We construct a new global optical model potential to describe the elastic scattering of ¹²C. The experimental data of elastic-scattering angular distributions and total reaction cross sections for targets from ²⁴Mg to ²⁰⁹Bi are considered below 200 MeV within the framework of the optical model. The results calculated using the derived global optical potential are then compared with the existing experimental data. The reliability of the global optical potential is further tested by predicting the elastic scattering data out of the mass and energy ranges, within which the global potential parameters are determined, and reasonable results are also obtained.     

3He-scattering from the stable even Sm-isotopes atE τ=40.9 MeV

Differential cross sections of the scattering of³He-particles were measured from^{144, 148, 150, 152, 154}Sm nuclei atE _τ=40.9 MeV. The elastic scattering data were analysed with the simple optical model. The ambiguities of the real central potential and some trends depending on the target mass in the optical potential parameters are discussed.     

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.     

Optical-model analysis of Li elastic scattering

The elastic scattering cross sections of 28 MeV ⁶Li ions from the nuclei ¹¹B, ¹²C and ¹³C were analyzed using the optical model. The analysis has been extended to other ⁶Li elastic scattering data on ¹⁶O (29.8 MeV) and on ¹²C (24.5 and 30.6 MeV) previously measured elsewhere. The fits obtained with the usual six-parameter Woods-Saxon potential are good. Parameter ambiguities were studied and the results of the analysis were compared with the predictions of the folding model.     

Analysis of inelastic scattering of 3He on 13C at 37.9 MeV

The differential cross section of elastic and inelastic scattering of ³He ions on the ¹³C nucleus has been measured at an energy of 37.9 MeV. By fitting the shape of the measured angular distribution of the elastic scattering the parameters of the optical model have been found. These parameters have been used for the DWBA calculations of angular distributions corresponding to excitations of the ¹³C levels 3.09(1/2⁺) MeV, 3.68(3/2^–) MeV, 3.85(5/2⁺) MeV, 7.55(5/2^–) MeV, 8.84(1/2^–) MeV and 11.85(7/2⁺) MeV. Several sets of transition densities calculated with different effective nucleon-nucleon interactions and six different M3Y interactions between a projectile and target nucleon have been tested. Analysis of the inelastic scattering of 135 MeV protons on ¹³C is also presented, which enabled us to obtain additional information about the tested structure models.     

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.     

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.     

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.