Large-angle 6Li + 28Si elastic and inelastic scattering at 27 and 34 MeV

Elastic and inelastic scattering data extending to θ_c.m ≈ 175° are reported for ⁶Li + ²⁸Si at 27 and 34 MeV. Optical model analyses of the elastic data were made using a variety of real potential forms. The large-angle data cannot be fitted with a Woods-Saxon real potential, but are well described by Woods-Saxon squared, double-folded or Fourier-Bessel potentials. The real potential is the same at both energies, but the imaginary potential is weaker at 27 MeV. The inelastic data were analyzed using the DWBA and coupled channels techniques with folded real form factors and deformed Woods-Saxon imaginary potentials, with the deformations taken from electron scattering. The 2⁺ state was fitted well at both energies with the DWBA, while the prediction decreased too rapidly at large angles for the 4⁺ state. The large-angle 4⁺ data were better described when two-step excitations were included in the coupled-channels calculations. The forward-angle 2⁺ data are sensitive to the interference between Coulomb and nuclear scattering and show that the nuclear and Coulomb deformation parameters β₂ are equal for this transition.     

Folding model analysis of pion elastic and inelastic scattering from 6Li and 12C

π ^±-Nucleus scattering cross sections are calculated applying the Watanabe superposition model with a phenomenological Woods-Saxon potential. The phenomenological potential parameters are searched for π ^± scattering from ⁶Li and ¹²C to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at pion kinetic energies from 50 to 672 MeV. The optical potentials of ⁶Li and ¹²C are calculated in terms of the alpha particle and deuteron optical potentials. Inelastic scattering has been analyzed using the distorted waves from elastic-scattering data. The values of deformation lengths thus obtained compare very well with the ones reported earlier.     

Refractive scattering and the nuclear rainbow in the interaction of12, 13C with12C at 20MeV/N

The elastic and inelastic scattering and the neutron transfer have been measured for the systems¹²C +¹²C and¹³C +¹²C at 20MeV/N up to θ_cm= 60° with theQ3D -spectrometer. The angular distributions of the elastic scattering show an enhanced cross section at angles larger than 40°. It can be identified as refractive scattering with the clear signature of a nuclear rainbow.L-cut-off calculations show that these contributions come fromL-values which are significantly lower than the grazingL-value. The deflection function has a broad minimum in thisL-range which is typical for rainbow scattering. TheS-matrix is decomposed by a phenomenological parametrization into a refractive and a diffractive part. The interference of these amplitudes plays an important role in the rainbow enhancement. The spatial localization of the refractive scattering is deduced from the turning points of the corresponding trajectories; a localization between 2.5 fm and 4 fm is found. Semi-classical calculations with complex trajectories in the single-turning-point approximation show good agreement with the quantummechanical calculations. Refractive contributions are not observed in the inelastic scattering. This can be explained by reducing the strength of the conventional collective form factor in the internal region. In contrast to this the enhancement at large angles is seen in the one-neutron transfer channels where the refractive scattering is dominant. This is the first observation of such contributions to heavy-ion transfer reactions.     

Sub-coulomb energy 12C + 10, 11B and 14N + 10B fusion cross sections

Total fusion cross sections have been measured for the following reactions and energy intervals: ¹²C + ¹⁰B, E_c.m. = 2.10–5.38 MeV; ¹²C + ¹¹B, E_c.m. = 2.10–5.99 MeV; ¹⁴N + ¹⁰B, E_c.m. = 2.64–5.97 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by two large NaI detectors. No resonance structure was observed in the three reactions. The elastic scattering excitation function was also measured at θ_c.m. = 90.4° for ¹²C + ¹⁰B over the energy range E_c.m. = 3.18–6.82 MeV. Optical model potentials were found which could consistently describe both the fusion and elastic scattering data.     

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.     

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 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).     

Elastic scattering of positive pions from 12C at 29 MeV

The elastic scattering cross section of positive pions at 29 MeV scattered from ¹²C has been measured at scattering angles between 15° and 150°. The cross section drops to a sharp minimum at about 40° and then rises to about 4 mb/sr at back angles.     

Comparison of the noncoplanar 6Li(p,pd)4He reactions at 120 and 200 MeV

The ⁶Li(p, pd)⁴He reaction was studied at 200.2 MeV, at the quasi-free angle pair (θ_p, θ_d) = (54°, ?48.9°), for noncoplanarity angles φ from 0° to 28°. ⁶Li αd spectroscopic factors of 0.84 and 0.76 are deduced from our coplanar data at this energy and 120 MeV, respectively, for ground-state 2S Woods-Saxon wave functions. A recent microscopic three-body calculation predicts spectroscopic factors from 0.70 to 0.75; using the ground-state wave functions from this study, we deduce a factor of 0.76 from the 200 MeV data. DWIA calculations fit the measured integrated cross sections versus φ for spectator momenta P_α ? 100 MeV/c at both bombarding energies, but underpredict them for larger P_α. Momentum form factors were better reproduced with 1S αd cluster wave functions for a soft-core bound-state potential than with the 2S Woods-Saxon wave functions, but the former wave functions generate unphysically large (～1.25) spectroscopic factors.     

Elastic scattering of 3He nuclei on 13C nuclei at 50 and 60 MeV and V-W ambiguity in choosing optical potentials

At energies of 50 and 60 MeV, the elastic scattering of ³He nuclei on ¹³C nuclei is investigated at laboratory angles in the range 10°–170°. The measured differential cross sections are analyzed on the basis of the optical model of the nucleus by using Woods-Saxon potentials, including both volume and surface absorption. The potential parameters are determined by fitting the computed cross sections to experimental data. It is found that, even in the region of sensitivity, the values of the real and imaginary parts of the potentials (V and W, respectively) show considerable scatter, with extreme values differing by a factor greater than two. This scatter is explained by the existence of a V-W ambiguity in choosing optical potentials.     

Elasticp+12C scattering between 0.3 and 2 MeV

Absolute differential cross-sections ofp+¹²C elastic scattering have been measured atθ _cm=89.1°, 118.7°, 146.9° for bombarding energies between 0.3 and 2.0 MeV. Revised level parameters of the first three excited states in¹³N have been extracted with aR-matrix analysis. It is shown that the influence of the bound ground-state of¹³N has an appreciable effect on low-energy scattering. Recent predictions concerning Mott-Schwinger polarization are also discussed.     

12C + 7Li Reaction measurements and the 12C(7Li,t)16O reaction

A measurement of the residues from the ¹²C + ⁷Li reaction has been obtained for ⁷Li energies from 10 to 38 MeV. From these measurements the fusion cross sections and critical angular momenta for the ¹²C + ⁷Li system have been deduced. Cross sections for the ⁷Li(¹²C, t)¹⁶O reaction have been obtained for ¹²C energies from 54 to 62 MeV at θ_lab = 2.7°. The critical angular momenta obtained from the fusion cross sections have been used to perform Hauser-Feshbach calculations for the ¹²C(⁷Li, t)¹⁶O reaction. These calculations have been compared to measured angular distributions over a wide energy range. By comparing the fusion cross sections required by the Hauser-Feshbach calculations to fit the ¹²C(⁷Li, t)¹⁶O(8.87 MeV) reaction and the measured residue cross section it is estimated that at least 80 % of the measured residues are fusion products. The calculations also indicate that direct processes dominate the population of many ¹⁶O levels at forward angles and the 10.35 MeV state at backward angles. The necessity for using a critical angular momentum in Hauser-Feshbach calculations is discussed.     

Elastic scattering of polarised deuterons from 16O at 200, 400 and 700 MeV

Angular distributions of cross section, and A_y and A_yy analysing powers were measured for polarised deuteron elastic scattering from ¹⁶O at 200, 400 and 700 MeV. The data at 200 MeV bear evidence of the nuclear rainbow phenomenon while those at 400 and 700 MeV are reminiscent of the proton scattering results at equivalent energies. The data were analysed in terms of the optical model. The real central potential shape changes from an attractive Woods-Saxon form at 200 MeV to a wine-bottle-bottom form with a repulsive interior at 700 MeV. The total reaction cross sections deduced display a clear nuclear transparency effect in the present energy domain in agreement with predictions from the Glauber theory optical limit. Comparison with previous results for ⁴⁰Ca and ⁵⁸Ni targets is made.     

Accurate determination of the 13C-12C+n spectroscopic factor

We have measured ¹²C-¹³C elastic cross sections at 12 MeV between 40°–140° in 1° steps to ±1%. The observed oscillatory interference between Coulomb scattering and the neutron transfer process is analyzed using exact finite-range DWBA, and a model-independent value of C² = 2.55±0.10 for the asymptotic normalization of the $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ neutron wave function in ¹³C is obtained. Using radial wave functions determined by elastic electron scattering the spectroscopic factor is found to be S = 0.81±0.04.     

Elastic scattering and fusion cross sections of 13C+13C

The ¹³C+¹³C total fusion cross section has been determined in the range 3.26⩽E_c.m.⩽8.0 MeV using Ge(Li) detector measurements of low-lying transitions in the residual nuclei and a statistical model calculation of excited state populations. The six most abundantly produced residual nuclei have been observed and their yields are given. To constrain the parameters in fusion models for these reactions, we have also taken elastic scattering data at θ_c.m.=60°, 70°, 80°, and 90° for 4.5⩽E_c.m.⩽8.5 MeV, as well as angular distributions at E_c.m.=7.0 and 8.0 MeV. The IWBC model and an optical model with a “shallow” potential have been used for parametrizing the nucleus-nucleus interaction.     

Messung der Neutronenpolarisation bei der Reaktion12C(d,n 0)13N mit Hilfe der Mott-Schwinger-Streuung

The polarization of neutrons produced in the reaction¹²C(d, n ⁰)¹³N was measured. Deuterons from the Karlsruhe isochronous cyclotron were used to induce this reaction at 51,5 MeV laboratory energy. The degree of polarization was determined by using the special features of Mott-Schwinger scattering. With an uranium scatterer analysing efficiencies of up to 0.92 can be obtained at very small angles (0.23°). The analysing efficiency can be calculated if the differential cross section at 0° and the total cross section is known. These quantities were experimentally determined. The differential cross section for 49.4 MeV neutrons, scattered by uranium, was measured between 0.88° and 2.10°. By an extrapolation the value 43.4±2.6 b/sr was found for the nuclear differential cross section at zero degree. A total cross section ofσ _t=4.80±0.22 b was obtained. The neutron polarization was measured at a reaction angle of 24.5° and the result isP=?0.45±0.07. This value is fairly above the semiclassical 1/3 limit and can be only explained, if spin orbit forces are taken into account. For (d, n) reactions this is the first neutron-polarization measurement above an energy of 20 MeV.