Long range absorption and other optical-model effects from strong inelastic coupling

An optical potential component is constructed to represent the effect of a strongly coupled inelastic excitation upon elastic scattering. In the particular case of quadrupole Coulomb excitation a long range imaginary potential component is derived in closed form. The effects of long range absorption upon the elastic scattering are considered in a general way by inserting this potential into a weak absorption model and deriving an elastic scattering cross section in closed form. Below the Coulomb barrier the formula takes a simple form which may be related to the semiclassical theory of Coulomb excitation. The potential component arising from nuclear excitation of an inelastic state may be evaluated numerically on a computer. Two examples computed (50 MeV α-scattering on ¹⁵⁴Sm and 60 MeV ¹⁶O scattering on ⁴⁰Ca) exhibit strong l-dependence in the potential component.     

Coupled channel analysis of asymmetry measurements for low-lying states of Sm and Sm by inelastic proton scattering

Asymmetries and differential cross sections have been measured for elastic and inelastic scattering of 24.5 MeV polarized protons from the spherical nucleus ¹⁴⁸Sm. The comparison with the results of an asymmetry measurement at the same proton energy on the rotational nucleus ¹⁵²Sm shows significant differences for the first 2⁺ states. A coupled-channels analysis for the first 2⁺ and 3⁻ states in ¹⁴⁸Sm and for the 2⁺ and 4⁺ states of the ground-state rotational band in ¹⁵²Sm fits the experimental data very well.     

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.     

3He-scattering from the stable even Sm-isotopes atE τ=40.9 MeV

Differential cross sections of the scattering of³He-particles were measured from^{144, 148, 150, 152, 154}Sm nuclei atE _τ=40.9 MeV. The elastic scattering data were analysed with the simple optical model. The ambiguities of the real central potential and some trends depending on the target mass in the optical potential parameters are discussed.     

Eikonal expansion in electron scattering

We extend a previously developed eikonal expansion method to the case of high-energy electron scattering from dynamic nuclei. Nuclear degrees of freedom can be included either by a DWBA-like expansion or by neglecting the nuclear excitation energies. The latter approach is considered in detail and applied to the elastic and inelastic scattering from deformed nuclei. The impact parameterT-matrix is calculated by diagonalizing the inelastic zeroth-order and first-order eikonal phases in the subspace of the nuclear rotational levels; static eikonal phases are included up to second order. For¹⁵²Sm,¹⁵⁴Sm coupled-channel calculations including three and four rotational states show large multi-step effects for the 0⁺→4⁺ and the 0⁺→6⁺ excitations compared to DWBA results.     

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.     

Nucleon elastic scattering from 40Ca between 11 and 48 MeV

Differential cross sections for the elastic scattering of neutrons from ⁴⁰Ca have been measured in the 19–26 MeV region. The neutron elastic scattering data, previous neutron measurements and additional proton elastic scattering data are analyzed using three different approaches to the optical model potential: Woods-Saxon parameterization, model independent analysis and microscopic calculations. The difference between the phenomenological neutron and proton real potentials is studied in terms of Coulomb effects, nuclear polarization and charge symmetry breaking in the nuclear mean field.     

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.     

Coulomb and nuclear excitation effects on 16O scattering from samarium isotopes

Elastic scattering of ¹⁶O on ^{148, 150, 152}Sm isotopes and inelastic scattering leading to the first 2⁺ state for the three isotopes and the 4⁺ state for ¹⁵²Sm have been measured at several energies in the vicinity of the Coulomb barrier. The whole set of data was reproduced at forward angles with an effective potential taking into account Coulomb excitation and in the full angular range by CCBA calculations including separate nuclear and Coulomb deformations.     

Comparison of the elastic and inelastic scatterings between152Sm+12C and148 Nd+16O

Angular distributions of elastic and inelastic scattering have been measured for¹⁵²Sm+¹²C at 63.2 MeV and¹⁴⁸Nd+¹⁶O at 90.9 MeV. An evident interference pattern in the inelastic scattering has been observed for the first time in a strong Coulomb coupling system.We are indebted to Dr. S. Pieper for supplying the Ptolemy Program. One of us (Chenglie Jiang) would like to acknowledge the Argonne National Laboratory for the opportunity given, to perform theoretical calculations with the code Ptolemy during his visit there. Thanks are also due to Mr. H. Folger (GSI, Germany) for supplying the targets. This work was supported in part by China National Nature Science Fundation.     

Elastic and inelastic scattering of K+ mesons on deformed nuclei

Various aspects of the scattering of medium energy K⁺ mesons on deformed nuclei are investigated in the light of a specific example, viz. the scattering of 800 MeV/c positive kaons on ¹⁵²Sm. The effects of coupled channels are found to be significant despite the fact that the K⁺ meson is a rather weakly interacting hadronic probe. The localization of the reaction mechanism on a deformed target is discussed for both protons and K⁺ mesons to compare the extent of surface and volume probing capability of these two projectiles. The results show the remarkable sensitivity of the elastic and inelastic K⁺ differential cross sections to the differences between the neutron and proton density distributions in deformed nuclei.     

Elastic and inelastic deuteron scattering from 152Sm and 162Dy

Angular distributions are measured for 12 MeV deuterons scattered to the 2⁺ and 4⁺ states in ¹⁵²Sm and ¹⁶²Dy. By including the couplings of the ground state to the low-lying excited states, it is shown that the experimental results can be explained by using optical model parameters form a spherical nucleus. Deformation amplitudes are deduced and compared to those found from inelastic α-particle scattering and from Coulomb excitation.     

Neutron and proton components of nuclear transitions in pion inelastic scattering on 26Mg

The elastic and inelastic scattering of 180 MeV positive and negative pions from ²⁶Mg has been measured. From these data the ratios of neutron and proton nuclear transition matrix elements have been determined for the first and second excited states. These ratios are compared with those obtained from electromagnetic transitions in mirror nuclei and with shell model predictions.     

Neutron total and scattering cross sections of some even Mo isotopes and the optical model

Neutron total cross sections of ⁹²Mo, ⁹⁶Mo, ⁹⁸Mo and ¹⁰⁰Mo were measured at intervals of ? 10 keV from 1.6 to 5.5 MeV with resolutions of ≈ 10 keV. Neutron elastic and inelastic scattering cross sections of these isotopes were measured from 1.8 to 4.0 MeV at intervals of 0.2 MeV. Neutron groups corresponding to the excitation of forty states were identified. The experimental results were examined in the context of optical and statistical nuclear models. It was concluded that the real part of the optical potential includes a term proportional to [(N-Z)/A] and suggested that the imaginary part of the potential was shell dependent with decreasing magnitude as N = 50 is approached. Comparison of measured and calculated inelastic neutron excitation cross sections suggested a number of J^π assignments extending previous knowledge.     

Coulomb-nuclear interference for inelastic deuteron scattering

The interference between Coulomb excitation and nuclear excitation has been observed for ^{54, 56}Fe, ⁶⁰Ni, ¹¹⁴Cd, ¹⁵²Sm, and ¹⁹²Os by measuring excitation functions of elastic and inelastic deuteron scattering at back angles. The interference is strongly constructive, indicating a predominantly imaginary nuclear form factor. DWBA calculations using the collective model, although predicting constructive interference, are unable to predict the magnitude of the observed effect.     

Neutron transition moments and quadrupole T- or F-vector states

A study of low-lying 2⁺ states by proton and deuteron inelastic scattering from ¹⁰⁴Pd, ¹¹⁰Pd, ¹¹²Cd, ¹⁴⁶Nd, ¹⁵⁰Nd and ¹⁵⁰Sm is described. Evidence of neutron components in the excitation of 2⁺ states lying between 2.2 and 3.0 MeV in Pd and Cd isotopes has been obtained. This result is consistent with the predictions of the IBM-2 model for mixed-symmetry states.