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.     

Elastic and inelastic scattering of 58Ni +90,94Zr

Pure elastic and inelastic scattering cross sections have been measured for the systems ⁵⁸Ni +^90,94Zr at energies near the Coulomb barrier where not only quasi-elastic and fusion but also deep-inelastic process come into play. Coupled channels calculations including both projectile and target inelastic excitations can successfully explain the elastic and inelastic scattering angular distributions with an energy-independent semi-empirical bare potential. The calculation reproduces also the sum of the total quasi-elastic, fusion and deep-inelastic cross sections. Received: 14 September 1998 / Revised version: 21 October 1998     

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 18O by 16O and 18O

Angular distributions have been measured for the elastic and inelastic scattering of ¹⁸O by ¹⁶O and ¹⁸O at laboratory bombarding energies of 42 and 52 MeV. The inelastic scattering data are analyzed in terms of collective excitations using a coupled channel approach. Deformation parameters are obtained for the strongly excited states. The relationship between the strength of inelastic scattering and the amount of structure in the elastic scattering distributions is discussed.     

Elastic and inelastic scattering of 11.8 MEV polarized deuterons from 34S

The elastic and inelastic scattering of 11.8 MeV vector polarized deuterons from ³⁴S has been studied. Angular distributions of the cross section σ(θ) and vector analyzing power iT₁₁(θ) have been measured for the ground state and the first three excited states in ³⁴S. Optical model parameters were first obtained by fitting the elastic deuteron scattering data alone. DWBA calculations with a collective model form factor were performed for the inelastic scattering to the excited states. Coupled-channels calculations were also done both for the one-phonon and the two-phonon excited states. The optical model parameters were suitably modified to obtain simultaneous fit to elastic and inelastic data when channel coupling was introduced. The values of the vibrational parameter β₂ for one- and two-phonon states are discussed and compared with those obtained from γ-decay width studies.     

Elastic and Raman scattering of 8.5–11.4 MeV photons from 159Tb, 165Ho and 237Np

Differential cross sections for elastic and inelastic Raman scattering from the deformed heavy nuclei ¹⁵⁹Tb, ¹⁶⁵Ho and ²³⁷Np were measured at five energies between 8.5 and 11.4 MeV. Angular distributions at four angles between 90° and 140° for both elastic and inelastic scattering at 9.0 and 11.4 MeV were also measured. The monoenergetic photons were obtained from thermal neutron capture in Ni and Cr. All the angular distributions and the elastic and Raman scattering at the higher energies are in good overall agreement with theoretical predictions. The theory is based on a modified simple rotator model of the giant dipole resonance in which the effect of Delbrück scattering was included. A trend of both the elastic and Raman scattering at lower energies to be stronger than expected are suggested by the data. However, the ratio between the Raman and elastic scattering seem to be in good agreement with theory throughout the whole energy range. This shows that there is no need to introduce a direct nonresonant component to the imaginary part of the elastic scattering amplitude to explain the experimental data.     

Analysis of elastic and inelastic α + <Superscript>24</Superscript>Mg scattering within the <Emphasis Type="Italic">S</Emphasis> matrix model involving regge poles

A generalization of the phenomenological S-matrix model taking into account isolated Regge poles is proposed for simultaneously describing refractive effects in the cross sections for the elastic and inelastic scattering of light nuclei. The cross sections for elastic α + ²⁴Mg scattering are analyzed at energies of 50, 54, 65.7, 81, and 119 MeV. The analysis of the cross sections for elastic scattering is supplemented with an analysis of the inelastic scattering of alpha particles that is accompanied by the excitation of the first excited state (2⁺) of ²⁴Mg nuclei. It is shown that the proposed model makes it possible to describe satisfactorily all of the aforementioned cases of elastic and inelastic scattering, correctly reproducing the refraction Airy structures and anomalous large-angle scattering that are observed at large scattering angles.     

Elastic and inelastic scattering of 270 MeV3He particles from58Ni,90Zr,116Sn and208Pb

Differential cross-section angular distributions for the elastic scattering of 270 MeV³He particles from⁵⁸Ni,⁹⁰Zr,¹¹⁶Sn and²⁰⁸Pb have been measured. Optical model analysis of the cross-sections has yielded the optical model parameters for³He particles at 270 MeV. Angular distributions have also been measured for the inelastic excitation of the low-lying levels in the above mentioned nuclei. A collective model analysis using the distorted wave Born approximation (DWBA) of these cross-sections with the distorted waves generated by the optical model parameters determined from the elastic scattering analysis, has yielded the reduced transition probability (B(EL)) values consistent with those reported in the literature.     

Elastic and inelastic scattering of nucleons from 16O

Measurements of differential elastic and inelastic cross sections for neutron scattering from ¹⁶O at incident energies 18 to 26 MeV are presented. In addition to cross sections for neutron scattering differential cross sections for proton scattering up to 66 MeV are described in terms of phenomenological optical model potentials. At 24.5 MeV incident energy inelastic scattering up to 11.5 MeV excitation was measured. The elastic and inelastic compound nucleus contributions were examined. Direct inelastic scattering from the normal parity states was calculated using the DWBA and coupled-channel formalisms. The inelastic scattering cross section from non-normal parity state 2⁻ was calculated using the coupled-channel formalism via multi-step processes. Cross sections due to inelastic scattering from some of the states, which are thought to be members of an excited state rotational band were calculated using both vibrational and rotational approaches and were compared.     

Studying the reactions of deuteron interaction with <Superscript>9</Superscript>Be nuclei at low energies

Data on elastic and inelastic scattering, and the reactions of few-nucleon transfers in the interaction between the nuclei of deuteron and ⁹Be at energies of around 10 MeV/nucleon, are analyzed. A theoretical analysis is performed using the double-folding potential model with the wave function of the ground state of the ⁹Be nucleus, constructed in the three-cluster α + α + n-approximation. Calculations of the cross section of elastic scattering for the reaction d + ⁹Be using the calculated folding potential are preformed using the optical model. The resulting optical potential is used to analyze cross sections of transfer reactions and inelastic scattering in the context of the distorted waves method. A comparative analysis of the experimental data and theoretical calculations is performed.     

Elastic and inelastic scattering of 800-MeV protons on <Superscript>16</Superscript>O and <Superscript>20</Superscript>Ne nuclei

Differential cross sections and polarization observables for the elastic and inelastic scattering of 800-MeV protons on ¹⁶O and ²⁰Ne nuclei are calculated on the basis of the theory of multiple diffractive scattering and the α-cluster model involving dispersion. The single-particle nucleon-density distributions obtained within the α-cluster model involving dispersion are used in the calculations. The differential cross sections and polarization calculated for elastic and inelastic p¹⁶O and p²⁰Ne scattering are compatible with available experimental data. The spin-rotation functions calculated for elastic p¹⁶O and p²⁰Ne scattering within the independent-nucleon model differ qualitatively from their counterparts calculated within the α-cluster model involving dispersion.     

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.     

46.8MeV的p+12C非弹性散射

在Glauber多重散射理论框架下，使用跃迁密度方法和三种N湮没势，计算了46.8MeV的反质子在¹²C上的非弹性散射微分截面. 理论曲线与实验数据符合得较好. 关键词： Glauber理论 反质子 非弹性散射 湮没势 跃迁密度     

R-matrix formalism with physical boundary conditions for heavy-ion scattering and application to 24Mg on 24Mg

An R-matrix formalism for multi-channel scattering problems is developed with special boundary conditions at the matching radius. The boundary conditions in the elastic channels are chosen by means of the phase shifts of the uncoupled problem, while the boundary conditions in the inelastic channels are those of Kapur and Peierls. The method is applied to the elastic scattering and inelastic excitation of ²⁴Mg on ²⁴Mg. The results are compared with coupled channel calculations and experimental data.     

Asymptotic bounds on pion form factor

A technique recently developed for inelastic electron proton scattering is applied for inelastic electron pion scattering. It is found that all the derivatives of off-shell form factor of pion nears=m _π ² and for largeQ ² are bounded from above, provided that the dispersion relation for the form factor requires no more than one subtraction. The elastic pion form factor is bounded by [lnQ ²] ^c /Q ², wherec is any positive constant.     

Multi-step processes in high-energy elastic and inelastic nuclear scattering

Multi-step processes in elastic and inelastic nuclear scattering at intermediate and high energies are investigated using a formulation whereby a finite number of channels are explicitly treated while all the other channels are approximately accounted for through a “second-order potential matrix”. Within the framework of the eikonal approximation the problem reduces to a finite system of first-order coupled integro-differential equations with non-local potentials which depend on the two-body density matrix of the target nucleus. The relationship of the above formulation to the DWIA, the close-coupling method, and the Glauber multiple scattering model is examined. This approach is applied to the elastic and inelastic (2⁺, 4.43 MeV) scattering of 1 GeV nucleons by ¹²C. The corrections to the DWIA are sizeable, and the inelastic scattering appears to be very sensitive to the multi-step contributions and the nuclear structure.     

DWBA approach to inelastic scattering at medium energies

Medium energy proton elastic and inelastic scattering to states of ⁵⁸Ni and ²⁰⁸Pb, and ⁴He elastic and inelastic scattering to states of ⁴⁰Ca, are analyzed using the partial wave approach, by solving the Schrödinger equation with relativistic kinematics and using the distorted wave Born approximation. Our results can be compared with results of several previous analyses of the nucleon inelastic data using the Glauber approximation. Our calculations are absolute, using nuclear collective parameters obtained from a survey of a large number of low-energy analyses of inelastic scattering of electrons, nucleons and nuclei from ⁴⁰Ca, ⁵⁸Ni and ²⁰⁸Pb.     

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.     

Anomaly in α-scattering from 6Li between 35 and 45 MeV

The elastic scattering of α-particles on ⁶Li nuclei has been measured from 20° to 170° (c.m.) and the inelastic scattering to the first excited state of ⁶Li has been measured for forward and backward angles. The elastic scattering angular distributions are calculated (i) in terms of pure potential scattering, (ii) in terms of potential scattering with an l-cut-off on the imaginary part of the potential and (iii) in terms of the coherent addition of the potential scattering amplitude and of the exchange amplitude. The third method gives the best fit to the data. The inelastic angular distributions are compatible with the macroscopic calculations, except in the very backward region where exchange phenomena are also shown to dominate.