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.     

Polarization in the inelastic scattering of 185 MeV protons

The polarizations produced in the inelastic scattering of 185 MeV protons exciting the lowest octupole states in ¹²C and ²⁰⁸Pb are measured. The data together with earlier similar measurements for ⁴⁰Ca and ⁹⁰Zr are compared with existing theoretical models. The inclusion of a deformed spin-dependent interaction of the full Thomas form in the DWBA amplitude is found to considerably improve the theoretical fits to the data. For ¹²C, however, the DWBA fit is found to be inferior to that obtained using DWIA. The strong absorption model is found to give qualitatively good fits to the data for the heavier nuclei but again fails in the ¹²C case.     

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.     

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.     

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.     

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.     

The elastic and inelastic scattering of intermediate energy protons on deuterium at small momentum transfer

The differential cross sections for the elastic and inelastic scattering of protons on deuterium have been measured for scattering angles less than 14° at 198.5, 297.6 and 456.6 MeV. These quantities were determined relative to dσ / dΩ for pp elastic scattering with a precision of typically 2%. The range of excitation energies for the (p, p') reaction was chosen to emphasize the region near the np threshold dominated by the final-state interaction in the ¹S₀ channel. Particular attention was given to the dependence on excitation energy of the spectra at 198.5 MeV to examine the sensitivity to the ¹S₀ scattering length, a_np In this paper all data are compared with a new, detailed formulation of a simple model of the reaction mechanism based on the impulse approximation. The experimental results differ from the predictions by typically 10% and the differential cross sections exhibit a sensitivity to the intermediate-energy nucleon-nucleon amplitudes. If the impulse approximation is used to estimate a_np from the data at 198.5 MeV a value of − 24.7 ± 0.4 fm is obtained.     

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.     

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.     

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).     

Coupled-channels effects for inelastic scattering of 15 MeV polarized deuterons from Ti and Sm isotopes

Cross sections and analyzing powers have been measured for elastic and inelastic scattering of 15 MeV deuterons from ¹⁴⁸'Sm and ¹⁵²Sm. These data, as well as previous data for the ${}^{\mathrm{48,\; 50}}\text{Ti}\text{(}\text{d}\text{, d'}\text{)}$ reaction have been analyzed in the coupled-channels approximation. Data for ⁴⁸Ti and ¹⁵²Sm are better described by the rotational model than by the vibrational model but the quality of the fits is not sufficiently good to establish ($\text{d}\text{, d'}$) reactions as a sensitive method of discriminating between these two models.     

Large angle cross section and analyzing power for proton-4he elastic scattering between 185 and 500 MeV

The differential cross section for the elastic scattering of protons from ⁴He has been measured for ten proton energies between 185 and 500 MeV in the angular range 144° to 168° in the lab system. The analyzing power has also been measured for seven energies in the same angular range. The differential cross section does not show the marked backward peaking that has been observed at both lower and higher energies. The possible structure in the 180° excitation function suggested for energies around 240 MeV is not observed. The analyzing power is large and negative, and shows strong dependence on both energy and angle.     

Proton-nucleus elastic scattering at 156 MeV

Cross sections for the elastic scattering of 156 MeV protons on eleven targets ranging from ¹²C to ²⁰⁹Bi were measured and an optical model analysis has been performed. The effect of different optical potentials in DWIA inelastic scattering calculations is shown by some examples.     

Spin observables in small-angle elastic → d scattering with an L-type deuteron target at 800 MeV

We have measured spin correlation parameters that describe the elastic scattering of 800 MeV polarized protons from an L-type polarized deuteron target at laboratory angles below 20°. The measured parameters include the correlated analyzing powers A_SL, A_LL and A_NLL and the proton spin-transfer coefficients C_0L,S, C_0L,L, C_SL,N, C_NL,S, C_NL,L and C_LL,N. The results are compared with single-scattering predictions based on different phase-shift solutions for the nucleon-nucleon scattering matrix.     

Elastic and inelastic scattering of 15 MeV polarized deuterons from isotopes of Ca,Cu, Sr,Zr, and Mo

The elastic and inelastic scattering of 15 MeV polarized deuterons from ⁴⁸Ca, ⁶³Cu, ⁸⁸Sr, ⁹⁰Zr, ⁹²Zr, and ⁹²Mo has been investigated. Angular distributions of the cross section and vector analyzing power iT₁₁ have been measured for all these nuclei; the tensor analyzing powers T₂₀ and T₂₂ have been studied for ⁹²Zr. Cross sections and vector analyzing powers are generally well explained by the optical model for elastic scattering and by the DWBA with a macroscopic form factor for the inelastic scattering; this is consistent with previous work. Distributions for ⁴⁸Ca, however, are poorly fitted. Anomalous behavior of the N = 50 nuclei found in the inelastic scattering of polarized protons is not present for deuterons. Tensor analyzing powers are not well explained by standard procedures: use of approximate folding model optical parameters did not improve the fits. The distribution of iT₁₁ for the $\text{1}\text{2}$^? state in ⁶³Cu is significantly different from the distributions for the $\text{5}\text{2}$^? and $\text{7}\text{2}$^? states.     

Elastic and inelastic scattering of 79.5 MeV 11B and 87.5 MeV 10B ions

The elastic scattering of 79.5 MeV ¹¹B ions has been studied for seven targets ranging in mass from ²⁴Mg to ¹⁹⁷Au and of 87.5 MeV ¹⁰B ions for three of these targets (^{24, 25}Mg, ⁶⁰Ni). Angular distributions were measured from ~10° c.m. in steps of 0.5°, to angles beyond 40° c.m. where the elastic cross sections are ? 10^?3 of the Rutherford values (except for ¹⁹⁷Au). Inelastic data for exciting the lowest 2⁺ states of ^24,26Mg and ⁶⁰Ni were also obtained. Important odd-A-even-A differences are observed in the ¹¹B elastic angular distributions for the Mg and Al targets; for ¹⁰B scattering these are obscured by projectile quadrupole moment effects on the elastic scattering. The elastic data were analyzed using the optical model with potentials of both Woods-Saxon and double-folding form. The data for both ¹⁰B and ¹¹B are consistent with the potential obtained in the folding model with the M3Y interaction without renormalization. The inelastic data were analyzed by the distorted-waves method.     

Optical-model analysis of elastic scattering of 53.4 MeV helions from Fe

Elastic helion scattering from ⁵⁶Fe at 53.4 MeV was measured over the angular range 12° to 150°. Using the regular optical model, real-potential ambiguities, the shape of the imaginary term and the need for a spin-orbit term were explored. Coupled-channels (SCA) calculations based on the ground state and principal 2⁺ and 3⁻ states indicate that such coupling effects are not as dominant as the inclusion of a spin-orbit potential in the regular optical model. Previously reported helion scattering from ⁵⁹Co and ⁶⁰Ni at 50.1 MeV has been included in an average parameter analysis to generalise the improvements in the helion optical-model parameterization in this energy region.     

Elastic scattering of 100 MeV protons and systematic optical model analysis

Using a Ge(Li) total energy detector the elastic scattering of 100 MeV protons from ⁵⁸Ni, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb has been measured. Optical model fits with $\text{x}{}^2\text{N}$ of order unity have been made. The parameters of these fits varied systematically with A enabling the isospin dependence of the real part of the potential and its volume integral to be deduced. The limitations of the conventional optical model analysis in the case of ⁵⁸Ni are illustrated and discussed.