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.     

A global optical-model analysis of neutron elastic scattering data

Differential cross sections for neutron elastic scattering in the energy range 7–26 MeV from ⁴⁰Ca, ⁹⁰Zr, ⁹²Mo, ^{116, 124}Sn and ²⁰⁸Pb are analyzed in terms of a global optical-model potential. A smooth variation of the real radius parameters with mass number is investigated. Otherwise, optical-model geometrical parameters are kept fixed at values obtained by averaging individual best fits. The energy and isospin dependences of potential strengths and volume integrals per nucleon are presented.     

Resonant structures in24Mg+28Si elastic and inelastic scattering

The data on the excitation functions of²⁴Mg+²⁸Si elastic and inelastic (2⁺ ?0⁺, 2⁺ ?2⁺, 4⁺ ?0⁺ and 4⁺ ?2⁺) scattering fromE _c.m.=48.97 to 57.21 MeV have been subjected to a statistical analysis consisting of the calculations of deviation function, cross-correlation function, summed excitation function, cross-channel correlation coefficients, coherence widths, and the distribution of cross sections. Based on the outcome of the analysis resonant structures atE _c.m.=49.23, 50.02, 50.51, 52.10, 52.53, 53.27 and 54.14 MeV have been confirmed and three new structures of the same nature have been identified atE _c.m.=51.42, 54.88 and 55.60 MeV.     

Optical-model analysis of the elastic scattering of 100 MeV protons from Mg and Si

Elastic scattering differential cross sections for the interaction of 100 MeV protons with ²⁴Mg and ²⁸Si have been measured using a high-resolution Ge(Li) spectrometer to resolve the inelastic scattering contribution to the elastic peak. The results have been analysed using the conventional optical model, and the experimental differential cross sections and total reaction cross section are excellently reproduced. The results agree with previous analyses of the elastic scattering of 100 MeV protons on 1p shell nuclei in that no set of geometric parameters can provide a quantitative fit to both nuclei. It is observed, however, that the fluctuations of the optical-model parameters for optimum fits are decreased over the fluctuations observed for the 1p shell nuclei. The present results combined with previous optical-model analyses on ²⁴Mg and ²⁸Si at 50 MeV and 40 MeV respectively, are found to be consistent with an energy dependence of dV/dE ≈ −0.3 for the depth of the real central potential in agreement with other, more extensive, investigations of the energy dependence for protons elastically scattered from ¹⁶O and ⁴⁰Ca.     

The (3He,t) reaction on 24Mg and 28Si

The (³He, t) charge exchange reaction on ²⁴Mg and ²⁸Si has been studied at 38.5 MeV. The angular distributions provide a number of new spin assignments in ²⁴Al and ²⁸P. A two-step excitation through intermediate α-particle channels was used to predict the ²⁴Al cross sections. The fits are fair in shape, but about a factor of three too large when a perfect overlap of initial and final shapes is assumed. The data to three 1⁺ states of ²⁸P are compared to the known electromagnetic reduced transition rate B(M1) to the analog states in ²⁸Si.     

The elastic and inelastic scattering of 30.5 MeV protons by24Mg

Measurements of the differential cross sections for the elastic scattering of 30.5 MeV protons by ²⁴Mg and for the inelastic scattering to the 1.37, sum of 4.12 and 4.23, 5.22 and 6.0 MeV states are reported. Optical model fits to the elastic data, a distorted wave calculation for the first excited state, and coupled channel calculations are also presented.     

Elastic scattering of He from Be,B, B,Mg, Mg,Mg and Al

Elastic scattering angular distributions of ³He particles from ⁹Be, ¹⁰B, ¹¹B, ²⁴Mg, ²⁵Mg, ²⁶Mg and ²⁷A1 at E(³He) ≈ 13 to 27 MeV have been measured and some of the representative results are reported. In most cases the angular range of the measured cross sections was from 8° to 150° (lab). The results have been analyzed in terms of a six-parameter optical model and are compared with previous work.     

Elastic scattering of 32S on 24Mg, 27Al and 40Ca and the effect of nuclear forces on the grazing collision

Elastic scattering of ³²S ions on ²⁴Mg, ²⁷Al and ⁴⁰Ca has been measured at energies between 67 MeV and 120 MeV. Angular distributions were analyzed with the optical model with Woods-Saxon potentials. Strong absorption radii are extracted with and without consideration of the nuclear interaction at the surface. The nuclear potential decreases the otherwise anomalously large strong absorption radii which can then be described by a radius parameter of r₀ = 1.41 fm.     

Closed-form quantal description of inelastic heavy ion scattering

The amplitude for inelastic heavy ion scattering, given by the distorted-wave theory for excitation of low-lying collective states, is evaluated in closed form. Use is made of the Austern-Blair relation and of other approximations appropriate for strongly absorptive interaction to express the inelastic partial-wave amplitude entirely in terms of the elastic S-matrix elements in the initial and final channels. The resulting formulae display explicitly the various contributions to the transition amplitude, whose superposition gives rise to the variety of interference patterns observable in the angular distributions and excitation functions of inelastic heavy ion scattering. It is shown that, as for elastic scattering, the dominant mechanism in inelastic heavy ion collisions near and above the Coulomb barrier is diffractive scattering of Fresnel type.     

Inelastic scattering of 185 MeV protons from Mg and Al

A magnetic spectrometer was used for the energy analysis of protons scattered from targets of magnesium (natural isotopic composition) and aluminium. The mean energy of the incident protons in the targets was 185 MeV. A total energy resolution of 350 keV (FWHM) was achieved, which made possible the observation of the excitation of a large number of discrete levels. Energy spectra were measured in the angular region of 4° to 40° (lab system).

The results are presented partly in the form of tables giving measured excitation energies and maximum cross sections for resolved levels and partly in the form of graphs of angular distributions of the differential cross sections.

A qualitative discussion of the results is given in terms of the multipolarities of the transitions involved and comparisons are made with similar results from other experiments in inelastic scattering and in a few cases with theoretical predictions.     

Study of 16O, 20Ne, 22Ne, 28Si and 32S by inelastic scattering of polarized protons

Analyzing powers and cross sections have been measured for elastic and inelastic scattering of 24.5 MeV protons from ²⁰Ne and ²²Ne, and for ¹⁶O, ²⁸Si and ³²S at 30.3 MeV. The experimental results were analyzed in terms of the coupled-channels formalism using the rotational model and (for ³²S and ¹⁶O) the vibrational model. The results for ²⁰Ne, ²²Ne and ²⁸Si show a systematic trend of the hexadecapole deformation. Prolate shapes for ²⁰Ne and ²²Ne and an oblate shape for ²⁸Si are confirmed. The results for ³²S are almost equally well-reproduced by the vibrational or rotational model, and there is a slight preference for the prolate shape for this nucleus. The best fits for the analyzing power for all the nuclei were obtained by using the full Thomas form for the spin-orbit potential     

Elastic and inelastic scattering of 14C from medium heavy nuclei

The elastic and inelastic scattering of ¹⁴C at ⁵¹ MeV from targets of ⁴⁰Ca, ⁵⁶Fe, ⁶⁰Ni, ⁶⁶Zn and ⁸⁸Sr has been measured using a Q3D spectrometer. The ¹⁴C-nucleus potentials have been derived by optical-model analysis of the observed elastic scattering; the inelastic scattering differential cross sections were interpreted in the distorted-wave Born approximation and also in the coupled-channels approach. The analysis yields ¹⁴C-nucleus potentials that closely resemble ^{12, 13}C and ¹⁶O potentials.     

The study of the width for intermediate resonances in the 27Al(d,p)28Al, 27Al(d, α)25Mg, 31P(d,p)32P and 31(d, α)29Si reactions

The protons and α-particles from the reactions ²⁷Al(d, p)²⁸Al(d, α)²⁵Mg, ³¹P(d, p)³²P and ³¹P(d, α)²⁹Si were measured and analyzed with the channel cross correlation function and auto-correlation function to determine the correlating numbers N_d and average width 〈Γ_μ〉. With these values, the theoretical intermediate widths were calculated to be 119 ± 30 keV in the ²⁹Si nucleus and 249 ± 46 keV in the ³³S nucleus, which were in good agreement, within the errors, with the present experimental results of 185 ± 37 keV in ²⁹Si and 204 ± 24 keV in ³³S.     

Study of elastic and inelastic scattering of protons from 74Ge at isobaric analogue resonances

Excitation functions of the elastic and the inelastic proton scattering leading to the ground state and to the 2⁺ (0.596 MeV) state in ⁷⁴Ge were measured at 90°, 125°, 140° and 165° at bombarding energies from 3.34 to 5.4 MeV. Ten isobaric analogue resonances in ⁷⁵As were identified. Five of these resonances decay to the 2⁺ excited state in ⁷⁴Ge. Angular distributions of the inelastically scattered protons were measured at bombarding energies corresponding to these resonances. The partial widths of the isobaric analogue states for decay to the ground state and to the 2⁺ excited state in ⁷⁴Ge were determined as well as the l-values of the captured protons and the spins of the resonances. The Coulomb displacement energy for the pair ⁷⁵As-⁷⁵Ge was found to be 10.01 MeV. A comparison is made with the parent analogue states in ⁷⁵Ge. The results indicate that several levels of ⁷⁵Ge may be described as having a large component of a single particle state coupled to the first 2⁺ excited state in ⁷⁴Ge, and that the 2⁺ state has a configuration with a large 2p-2h component.     

Elastic scattering of polarized deuterons from Al, Si and Ni between 7 and 11 MeV

Polarization parameters have been determined for deuteron elastic scattering from ²⁷Al, Si and ⁶⁰Ni at energies between 7 and 11 MeV and laboratory scattering angles from 30° to 135°. The vector polarization, iT₁₁, and two tensor parameters T₂₀ and T₂₂, were measured by scattering polarized and unpolarized deuterons which were obtained from a tandem accelerator. The largest polarization was |iT₁₁| ≈ 0.3 and |T₂₀| ≈ 0.2 for ²⁷Al at 11 MeV. For ⁶⁰Ni, the observed polarizations were substantially smaller. Angular distributions of the unpolarized cross section were also measured for ²⁷Al and Si. An optical-model analysis of the polarization and cross-section data was performed. The vector polarization was reproduced reasonably well by a vector spin-orbit coupling of similar strength as found for nucleon scattering. A tensor interaction appears to be needed to account for the observed tensor polarizations.     

Proton polarization observables for the elastic and inelastic scattering of 500 MeV protons from Ca and Pb

Measurements for the elastic and inelastic scattering of 500 MeV protons from ⁴⁰Ca and ²⁰⁸Pb at small momentum transfers are reported. The induced proton polarization P and the spin rotation parameter Q were measured for the elastic scattering. The spin rotation parameters D_SS′, D_SL′, D_LL′, d_LS′ and the induced polarization P were measured for transitions to the 3⁻(3.37 MeV) and 5⁻(4.48 MeV) states in ⁴⁰Ca and the 3⁻(2.61 MeV) state in ²⁰⁸Pb. Comparisons of the data with the theoretical calculations were carried out in the framework of nonrelativistic and relativistic approaches. We extracted the spin-up and spin-down channels for the elastic scattering cross sections and found that predictions of the relativistic and nonrelativistic approaches agree well with the spin-up channel data and differ considerably in the spin-down channel.     

Statistical analysis of24Mg+24Mg elastic and inelastic scattering

The data on the excitation functions of²⁴Mg+²⁴Mg elastic and inelastic (²⁴Mg +²⁴Mg^*(2⁺),²⁴Mg^*(2⁺)+²⁴Mg^*(2⁺),²⁴Mg+²⁴Mg^*(4⁺),²⁴Mg^*(4⁺)+²⁴Mg^*(2⁺),²⁴Mg+²⁴Mg^*(6⁺)) scattering fromE _c.m=42 to 56 MeV have been subjected to a statistical analysis consisting of calculations of deviation function, cross-correlation function, cross-channel correlation coefficients, coherence widths, and the distribution of cross sections. On the basis of the analysis resonant structures atE _c.m=45.70, 46.65, 47.35 and 47.75 MeV have been confirmed. Two new resonant structures atE _c.m=44.55 and 50.50 MeV have been identified.     

Optical model analysis of 14 to 40 MeV neutron elastic scattering from 27Al, 28Si and 32S

An optical model analysis of 14 to 40 MeV neutrons elastic scattering from 2s-1d shell nuclei ²⁷Al, ²⁸Si and ³²S is described. A set of spherical optical model parameters is presented for each nucleus. A regional neutron optical model, valid for nuclei near the center of the 2s-1d shell, is proposed. A comparison between neutron and relevant proton data, which entailed the analysis of the latter, confirms earlier determinations of the Coulomb correction term to the real potential and of the strength of the real isospin potential.     

Resonant structures in the excitation functions of elastic and inelastic scattering of 16O on 24Mg

Excitation functions of ²⁴Mg(¹⁶O, ¹⁶O)²⁴Mg were studied between 25 and 64 MeV incident energy. A strongly resonant behaviour was observed for inelastic scattering at backward angles. The data were analysed in terms of coupled channel calculations. While agreement was good at forward angles, at backward angles the calculated cross sections are an order of magnitude too low suggesting that another reaction mechanism or neglected terms in the heavy ion interaction potential are important.