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.     

Elastische und inelastische Streuung von 104 MeV Alpha-Teilchen an58,60,62,64Ni

Differential cross sections are measured for the elastic and inelastic scattering of 104 MeV α-particles from^{58, 60, 62, 64}Ni. The experimental results are analyzed in terms of coupled channels on the basis of an anharmonic vibrational model and prove to be quite sensitive to the values of the deformation parameters. For forward angles the 4⁺ angular distributions of^58,60Ni are dominated by aL=4 single excitation mechanism. This is in keeping with theE4-transitions observed in (e, e′) scattering. From the 2 ₁ ⁺ - and 3 ₁ ⁺ -results transition rates are derived which can be compared to results of electromagnetic methods and of inelastic proton scattering studies. The comparison indicates that the transition rates differ and are generally higher for the proton scattering. Especially in the case of the 3^? states of^58,60Ni the differences are obvious. The elastic cross sections are analyzed both on the basis of the usual phenomeno-logical model and in terms of a semimicroscopic folding model resulting in values of rms-radii for the nuclear matter distribution.     

Elastic and inelastic scattering of vector polarized deuterons from even samarium isotopes at 56 MeV

Differential cross sections and vector analyzing powers of deuteron elastic and inelastic scattering have been measured at 56 MeV over the whole range of the even samarium isotopes. Comprehensive analyses were performed with the optical model and the coupled-channels formalism. In the optical model analysis, calculations with a global parameter set could reproduce the experimental data only for the vibrational nuclei. The strong coupling approximation was applied assuming the ^{144, 148, 150}Sm to be harmonic vibrators and the ^152,154Sm symmetric rotators. The 2^λ (λ = 2, 3, 4, 6) pole deformation parameters were deduced from a systematic coupled-channels analysis. The transition strengths were extracted from the deformed optical potentials and compared with the corresponding electromagnetic ones. The transition rates for the rotational nuclei agreed with the electro-magnetic ones, but those for the vibrational nuclei gave the systematically smaller values. The latter fact was attributed to the difference between the proton and neutron transition matrix elements near the neutron-closed-shell nuclei. The ratios of the two matrix elements were obtained.     

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.     

Scattering of <Emphasis Type="Italic">α</Emphasis> particles on <Superscript>11</Superscript>B nuclei at energies 40 and 50 MeV

The differential cross sections for elastic and inelastic scattering of α particles on ¹¹B nuclei at energies of 40 and 50 MeV were measured in the entire angular range. The measured angular distributions were analyzed in terms of the optical model, the distorted-wave Born approximation, and the coupled-channel-method. Optical model potentials and quadrupole (β₂) and hexadecapole (β₄) deformation parameters were found from this analysis. The rise in the cross sections at backward angles was shown to be associated with the transfer mechanism of the heavy ⁷Li cluster.     

Study of nuclear-coulomb interference effects in inelastic deuteron scattering on 238U

The angular distributions of elastically and inelastically scattered deuterons from ²³⁸U at E = 17 MeV are compared to coupled-channel calculations. The cross sections at small scattering angles are strongly influenced by nuclear-Coulomb interference effects and allow a simultaneous extraction of nuclear (optical potential) and charge quadrupole deformation parameters. Two different deformed Coulomb potentials and the parameters of the optical model are discussed.     

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 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.     

Optical model and DWBA analysis of the α-particle scattering for the nuclei26Mg and28,30Si including Hauser-Feshbach contributions

The elastic and inelastic α-scattering cross section has been measured for the nuclei²⁶Mg,^28,30Si at 15 bombarding energies between 15.0 and 16.4 MeV. The energy averaged scattering cross sections can be described by an incoherent sum of contributions from direct and compound reactions. The direct reaction part has been calculated by the optical model or DWBA, the compound reaction part by a simple Hauser-Feshbach formula. From the analyses deformation parameters and spin cut-off parameters are obtained.     

Cross sections and analyzing powers for fast-neutron scattering to the ground and first excited states of 58Ni and 60Ni

Differential cross sections for neutron scattering from ⁵⁸Ni and ⁶⁰Ni to the ground state and first excited state have been measured at 8, 10, 12 and 14 MeV. In addition, analyzing powers were measured for scattering to the same states for ⁵⁸Ni at 10 and 14 MeV, and for ⁶⁰Ni at 10 MeV. The data were analyzed in the framework of a coupled-channel formalism in which the vibrational model was assumed with deformed central and spin-orbit potentials. A spherical-optical-model analysis of the elastic scattering data was also performed following the coupled-channel analysis. Predictions for (p, p) and (p, p') scattering observables have been made and compared with measurements previously published. This approach permits neutron and proton deformation parameters to be deduced similarly from (n, n') and (p, p') scattering measurements for ^58,60Ni. These deformation parameters are compared in the framework of the core-polarization model of Madsen, Brown and Anderson.     

Measurement and folding-potential analysis of the elastic α-scattering on light nuclei

Differential cross sections ofα-elastic scattering have been measured for the target nuclei¹¹B,¹²C,¹³C,¹⁴N,¹⁵N, and¹⁶O atE=48.7 and 54.1 MeV and for the nuclei¹⁷O,¹⁸O, and²⁰Ne atE=54.1 MeV. The experimental results were analysed in terms of the optical model using different complex potentials. Special emphasis is given to the application of the double-folding approach for the real part of the potential. The imaginary part is expressed in terms of Fourier-Bessel functions. Differential cross sections for theα-¹⁶O scattering over a wide energy range and for the elasticα-scattering for nuclei in the mass rangeA=11 up toA=24 atE=54.1 MeV are analysed by this method. A close correlation between the absorptive part of the potential and nuclear deformation is observed.     

Neutron total and scattering cross sections of 6Li in the low-MeV range

Neutron total cross sections of ⁶Li are measured at intervals of ? 10 keV from ≈ 0.1 to 4.8 MeV with precisions of ≈ 1 to 3 %. Differential elastic scattering cross sections are measured at intervals of ? 100 keV from 1.5 to 4.0 MeV at 10 or more scattering angles distributed between ≈ 20 and 160 deg. Differential inelastic scattering cross sections are measured at selected angles in the energy range 3.5 to 4.0 MeV. The experimental results are analyzed in terms of R-matrix theory and the model parameters used to deduce the ${}^6\text{Li(n}\text{,α)}$ cross sections. The implications of the measurements and their interpretation on the level structure of ⁷Li and the reaction mechanisms are discussed.     

Direct neutron scattering from 182W and 184W

Differential elastic and inelastic neutron scattering cross sections for ¹⁸²W and ¹⁸⁴W have been measured at incident energies 4.87 and 6.00 MeV. Cross sections for the first (0⁺, 2⁺, 4⁺, 6⁺), second (0⁺, 2⁺), and some higher excitations are presented. Angular distributions exhibit direct reaction characteristics, suggesting that compound cross sections for these states are small. This is supported by statistical-model calculations. Coupled-channel calculations of cross sections are made using a phenomenological deformed optical potential. Quadrupole and hexadecapole deformations have been searched to optimize fits. The necessity of introducing a β₆ deformation is investigated. Electric multipole transition matrix elements, used in the coupled-channel analysis, are obtained from the rotation-vibration model and the dynamic-deformation theory.     

Analisis of inelastic scattering of π-mesons from nuclei within the microscopic optical potential

Cross sections of inelastic scattering of π-mesons from Si, Ni, and Pb nuclei at energy T _lab = 291 MeV are calculated using the distorted wave approximation. The microscopic direct and transition optical potentials are determined by specifying the pion-nucleon scattering amplitude and the nuclear density distribution, where we use the in-medium πN amplitude parameters obtained earlier by analyzing the elastic scattering data for the same nuclei. The cross sections are calculated on the basis of the relativistic wave equation. The deformation parameters of the nuclei are obtained by comparing inelastic scattering cross sections with the appropriate experimental data.     

Elastic and inelastic scattering of 88 MeV 6Li ions

The elastic scattering of 88 MeV ⁶Li ions has been studied for eleven targets ranging in mass from ²⁴Mg to ²⁰⁸Pb. Angular distributions were measured from about 10° c.m. in steps of 0.5°, mostly out to 60 or 70° c.m. where the elastic cross sections range from 10^?3 to 10^?5 of the Rutherford values. Inelastic data for exciting the lowest 2⁺ states of ^24,26Mg and ⁶⁰Ni were also obtained. The elastic data were analyzed using the optical model, with potentials of both Woods-Saxon and double-folding forms. The analysis confirms that the potentials for ⁶Li obtained from the folding model with the M3Y interaction need renormalizing by about 0.6, in agreement with results obtained at other energies. The inelastic data were compared to distorted-wave calculations. Coupled-channels analyses were also made for ^{24, 26}Mg, ⁶⁰Ni and ⁵⁹Co. Reorientation effects were found to be important to give the correct 2⁺ angular distributions for ^{24, 26}Mg and could also account for the differences between the elastic scattering from the odd-A and adjacent even-A targets.     

Elastic scattering of35Cl from27Al,58, 62Ni,116, 120, 124Sn and141Pr

Elastic scattering angular distributions for³⁵Cl from²⁷Al,^{58, 62}Ni,^{116, 120, 124}Sn and¹⁴¹Pr have been measured at energies between 100 and 170 MeV. Optical model analyses have been performed to determine reaction cross sections, strong absorption radii and grazing angular momenta. The results are compared with the corresponding quantities extracted by means of the Fresnel scattering model. Near the interaction barrier the quarter point method yields reaction cross sections systematically smaller than the optical model results. The interaction radii, however, do not show significant differences or energy dependencies. These radii are compared with trend formulae for interaction radii, and comparisons with fusion radii are made.     

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.     

Scattemng of 14.1 MeV neutrons from 209Bi

Differential cross sections for the elastic and inelastic scattering of 14.1 MeV neutrons from ²⁰⁹Bi have been measured with a time-of-flight system which had an energy resolution of 650 keV. For elastic scattering from ²⁰⁹Bi, an optical-model analysis gave the best-fit potential parameters. The absolute cross sections for excitation of collective (2.66 and 4.36 MeV) states are reproduced by the results of distorted-wave calculations under the assumption of a core (²⁰⁸Pb) excitation model using deformation parameters obtained from (p, p') reactions.