Analysis of inelastic scattering of3He on14C at 37.9 MeV

The differential cross sections of elastic and inelastic scattering of³He ions on the¹⁴C nucleus have 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 standard DWBA calculations of angular distributions corresponding to excitations of the¹⁴C levels 6.73(3^?), 7.01(2⁺) and 8.32(2⁺) MeV and for coupled channels calculations of the level 8.32(2⁺) MeV. The vibration parametersβ _L of the¹⁴C nucleus have been deduced.     

Elastic and inelastic scattering of 185 MeV protons from 12C

The polarization of 185 MeV protons in elastic scattering and in the excitation of the 2⁺ state at 4.44 MeV and the 0⁺ state at 7.65 MeV in ¹²C has been measured in the angular region 2°–60°. Optical model calculations are performed for the elastic scattering. Angular distributions for the inelastic scattering from the 2⁺ state at 4.44 MeV and the 3^? state at 9.64 MeV are calculated in the distorted-wave impulse approximation (DWIA) as well as in the distorted-wave Born approximation (DWBA).     

Isobaric analog resonances in the 82se+p system investigated by (p,p'γ) angular correlations and low-lying states in 83Se

Low-lying states in ⁸³Se have been studied through proton-induced isobaric analog resonance (IAR) reactions. Excitation functions for elastic and inelastic proton scattering were measured in the bombarding energy range 4.5– to 7.7 MeV. Angular distributions of proton inelastic scattering cross sections for the reaction ⁸²Se(p, p')⁸²Se(0.655 MeV 2⁺) and angular correlations of the inelastic protons and the associated 2⁺-0⁺ de-excitation γ-rays were measured on observed resonance peaks. In the analysis for the inelastic scattering, direct reaction contributions to the IAR were taken into account. Correlations between the low-lying states in ⁸³Se and the excited 2⁺ core state are discussed.     

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.     

A second-order vibrational model applied to the scattering of electrons and α-particles from 12C

Transition densities for monopole excitations and for virtual excitations are derived in the second-order vibrational model. Form factors for electron scattering calculated in the Born approximation and angular distributions for α-particle scattering, obtained in coupled channel calculations, are compared with experimental results for the elastic scattering and the inelastic scattering from the 2⁺ level at 4.44 MeV, the 0⁺ level at 7.65 MeV and the 3^? level at 9.64 MeV in ¹²C.     

Inelastic scattering of 12C and 13C on 63Cu leading to core-excited states

The inelastic scattering of ¹²C and ¹³C projectiles has been studied on ⁶³Cu at 45 MeV incident energy. The core-excited states (based on 2⁺ in ⁶²Ni) show individual differences in the angular distributions which are due to second-order couplings (transfer and inelastic transitions). However, the sum of the core-excited states yields the same cross section as observed in the inelastic scattering of ¹²C at 48 MeV on ⁶²Ni (2⁺).     

Elastic and inelastic scattering of 178 MeV protons from 58Ni and 60Ni

The elastic and inelastic scattering of 178 MeV protons from ⁵⁸Ni and ⁶⁰Ni has been studied. Angular distributions were measured for the differential cross sections for elastic scattering as well as inelastic scattering from excited states below about 5 MeV, all with natural parity. For the elastic and for the inelastic scattering from the first excited state (2⁺ in both nuclei, the angular distributions for the polarization were also measured. The measurements extend out to c.m. angles of about 60°, corresponding to a momentum transfer of about 600 MeV/c.The elastic and inelastic scattering data were compared to the results of coupled-channel calculations in the vibrational model using a deformed spin-orbit interaction of the full Thomas form. Good agreement was found in general showing that the main features of the experimental results are well described in this model.     

Investigation of α-particle scattering from Mg as a test of hauser-feshbach calculations in the continuum region

The elastic and inelastic scattering of α-partieles by ²⁴Mg is investigated at bombarding energies between 15.4 and 19.1 MeV. Particular attention is given to the analysis of the inelastic scattering to the 3⁺ unnatural-parity state at 5.22 MeV. Both energy-averaged angular distributions and fine-energy-resolution excitation functions are used in the analysis. It is found that the inelastic scattering to the (3⁺, 5.22 MeV) state may be interpreted as pure compound nucleus scattering. This fact is used to investigate whether the incoherent addition of a compound nucleus cross section and a direct cross section, as has been done in recent analyses, is a realistic way to describe energy-averaged scattering data which contain both direct and compound contributions.     

Alpha scattering from nonclosed shell nucleus 12C and alpha-nucleus interaction

In order to understand the α-nucleus interactions for the α+¹²C～α+¹⁶O systems systematically, α scattering from ¹²C is studied in a microscopic coupled-channel model using a folding potential and realistic microscopic wave functions of ¹²C. The experimental angular distributions of elastic and inelastic scattering to the 2⁺(4.43 MeV), 3^? (9.64 MeV), and 0 ₂ ⁺ (7.66 MeV) states in the range of E _α = 41–172.5 MeV are analyzed.     

Study of the diffraction scattering 12C + 12C with the excitation of the 12C exotic state 0 2 + (the Hoyle state)

New results from a series of experiments dedicated to the study of the ¹²C exotic state (the so-called Hoyle state) are presented. In spite of the many investigations that have been carried out, the structure of this state (which lies above the threshold for breaking up into three alpha particles) is still unknown. The different models assume that the nucleus has an abnormally large size in this excited state. However, until recently, methods for measuring the radii of unbound states have not been suggested. The best way to solve this problem seems to be by measuring the angular distributions of elastic and inelastic scattering of ¹²C on different target nuclei, and the determination of the radii is based on the fact that, at small scattering angles, the cross sections for direct reactions at high enough energies behave like Frauenhofer diffraction on a black ball. Accordingly, an experiment was performed aimed at measuring the elastic and inelastic angular distributions of ¹²C with an energy of (121.5 ± 0.5) MeV on a ¹²C target. The elastic scattering was measured in the angular range from 18° to 50° in the c.m. system with uncertainty in the angle of measurement equal to Δθ = ± 0.6°. The inelastic cross section was measured for the ¹²C excited state 2⁺ (4.44 MeV) and 0⁺ (7.65 MeV). Estimates were made for the diffraction radii for the ground and excited states. An increase was observed in the radius of the state at 7.65 MeV compared to those of the ground and first excited states.     

High energy elastic and inelastic p-12C scattering and nuclear deformation

Starting from a microscopic deformed picture of the ¹²C nucleus, and using angular momentum projected wave functions, the elastic and inelastic 1 GeV p-scattering differential cross sections have been analysed within the framework of the Glauber theory. From a comparison of the results obtained in a full Glauber calculation and in the optical limit, it has been shown that the elastic scattering and, to a lesser extent, the transition to the 2⁺(4.44 MeV) level are only weakly affected by the long-range correlations. In contrast the scattering to the 4⁺(14.08 MeV) state includes crucial multi-step contributions which affect the differential cross section both in shape and magnitude. Similarly the corrections to the DWIA are essential for the transition to the 3^?(9.64 MeV) state and a satisfactory explanation of the qualitative differences observed between the 2⁺ and 3^? inelastic cross sections in ¹²C is given. The great sensitivity of the cross sections to the nuclear deformation is shown and a generally good agreement with experiment for both the electron form factors and 1 GeV p cross sections has been obtained for the ground-state intraband transitions using a single oblate intrinsic state. The importance of a correct treatment of the rotational motion through the angular momentum projection is underlined and the use of the adiabatic approxmation is critically examined.     

Phenomenological local potential analysis of π+ scattering

π⁺-nucleus scattering cross section are calculated by solving a Schrödinger equation reduced from the Klein-Gordon equation. Local potentials are assumed, and phenomenological potential parameters are searched energy dependently for π⁺ scattering from ¹²C, ⁴⁰Ca, and ²⁰⁸Pb to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at 800 MeV/c pion laboratory momentum. The collective model is used to calculate the angular distributions of differential inelastic cross sections for pions leading to the lowest 2⁺ and 3^? states of ¹²C. The deformation parameters and lengths are extracted and compared to the corresponding ones from other works. Local potentials well describe the scattering of pions from nuclei.     

Elastic and inelastic scattering of carbon ions at intermediate energies

Elastic and inelastic scattering have been measured at E_lab = 360 MeV and 1016 MeV for the ¹²C + ¹²C system, as well as elastic scattering for ¹³C + ²⁰⁸Pb at 390 MeV. An optical-model analysis is reported and nuclear surface transparency effects are discussed, together with the energy dependence of the nuclear potential. A DWBA analysis of data on the 2⁺, 4.4 MeV state of ¹²C is reported and trends in the energy dependence of mean-field excitations are deduced.     

Cluster Folding and Coupled-Channels Analysis of 16O + 16O Elastic and Inelastic Scattering

The data of elastic and inelastic ¹⁶O?+?¹⁶O scattering to the lowest 0⁺, 2⁺, and 3^? excitation channels of ¹⁶O in the energy range of 250–1,120 MeV is reanalyzed using the derived double folding cluster (DFC1) potential in the framework of the coupled-channels (CC) mechanism. The potential provides a very good agreement with the experimental data for the elastic and inelastic scattering angular distribution. Furthermore, the deduced deformation length and quadrupole and octupole deformation parameter are quite consistent with the corresponding electromagnetic measurements.     

Tensor polarization of 12C(2+), 24Mg(2+), and 28Si(2+) oriented nuclei

Measured and calculated angular dependences of components of the polarization tensor of a ¹²C nucleus in the 2⁺ state at 4.44 MeV formed in various reactions involving light particles, as well as ²⁴Mg(2⁺, 1.369 MeV) and ²⁸Si(2⁺, 1.78 MeV) nuclei formed in inelastic alpha-particle scattering, are presented. The experimental tensor polarization in question was reconstructed on the basis of the densitymatrix spin-tensors found previously for these nuclei. The parameters of the quadrupole and hexadecapole orientation of the nuclei under study were obtained. The experimental polarization features were compared with the results of calculations based on the coupled-channel method. Special features of the behavior of tensor polarizations in various reactions were discussed. The similarity of the experimental angular dependences of the components of tensor polarizations in inelastic deuteron and ³He scattering on ¹²C nuclei, as well as in inelastic alpha-particle scattering on ²⁴Mg and ²⁸Si nuclei, was demonstrated.     

Electron scattering and α-cluster description of 12C and 20Ne

The elastic and inelastic electron scattering form factors in the ground-state band of ¹²C and ²⁰Ne have been calculated using the Brink α-cluster model projected wave functions. From a systematic comparison with experiment it is concluded that usual central forces like the Brink-Boeker B1 force give an unrealistically large clustering while that obtained using density dependent interactions like the Skyrme S1 force is too low. For intermediate values of the clustering it is possible in ¹²C to reproduce simultaneously the elastic as well as the inelastic form factors to the 2₁⁺(4.44 MeV), 3₁^?(9.64 MeV) and 4₁⁺(14.08 MeV) states for not too large transfers. Noticeable discrepancies between calculated and experimental 2₁⁺ and 3₁^? inelastic form factors at transfers higher than 1.5 fm^?1 reveal inherent weaknesses of the α-cluster wave functions which are not corrected after inclusion of the θ-vibrations.     

Scattering and reactions of 14C + 14C and 14C + 14C

We have studied elastic scattering, inelastic scattering and several transfer channels of the systems ¹⁴C + ¹⁴C and ¹⁴C + ¹²C over a wide range of energies up to E_c.m. = 35 eMeV and 32 MeV, respectively. The reaction channels were identified by means of kinematic coincidences between solid-state detectors, γγ coincidences were measured to determine cross sections for mutual inelastic scattering of ¹⁴C + ¹⁴C.Pronounced regular gross structures, similar to those found for ¹⁶O + ¹⁶O, are observed in the elastic excitation function of ¹⁴C + ¹⁴C at θ_c.m. = 90°, The angular distributions measured at the energies of the maxima and an optical-model analysis suggest that one or a few surface partial waves dominate the scattering behaviour. Correlated structure of narrower width is found in the inelastic channels and, to a lesser degree, in the transfer channels which appear with rather small cross sections.In ¹⁴C + ¹²C elastic scattering the gross structures are strongly fragmented, in contrast to ¹⁴C + ¹⁴C but similar to ¹²C + ¹²C. While the ¹²C(2⁺) excitation is very weak, the observed strengths of the ¹⁴C(3^?) excitation and of neutron transfer point to a substantial role of these channels as coupling partners to the elastic configuration and to their influence on the elastic scattering behaviour. A correlated intermediate structure is observed near 23.5 MeV, where a dominance of l = 18 is suggested by the elastic scattering angular distribution. This unexpectedly high l-value exceeds l_graz at this energy by at least two units of ?.     

The He scattering and reactions on C and cluster states of C

The ⁶He+¹²C elastic and inelastic scattering and the ⁶He+¹²C→α+¹⁴C reaction have been measured using a 18.0 MeV ⁶He beam. Experimental results for the elastic scattering are in fair agreement with optical model predictions, using the potentials found in the analysis of ⁶Li scattering on ¹²C at similar energies. In triple coincidences, the ⁶He+¹²C→¹⁰Be+2α reactions were clearly seen, with the ¹⁰Be nucleus left in ground and several excited states. The dominant mechanism of this reaction is sequential decay through cluster states of ¹⁴C.     

π+ and π− scattering from 12C at 150 MeV

High-resolution elastic and inelastic data were obtained for π⁺ and π^? scattering ¹²C. Spectra were taken with the SIN pion spectrometer at 148 MeV over a wide angular range.