Proton inelastic scattering at intermediate energies and Dirac-equation-based optical potentials

The Dirac-equation-based (DEB) optical potential is extended to the study of inelastic excitation of collective states using intermediate-energy protons. Comparison is made with standard calculations using Woods-Saxon potentials. In the energy range 150–800 MeV, the two models give cross sections in close agreement when equal deformation lengths are used. The inelastic polarizations and analyzing powers also agree (to a lesser degree) near or below 200 MeV and at 800 MeV, but show differences at 300 and 500 MeV. We also point out the importance of the deformed spin-orbit terms in inelastic cross section calculations.     

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     

Nuclear-matter distributions of halo nuclei from elastic proton scattering in inverse kinematics

Proton-nucleus elastic scattering at intermediate energies, a well-established method for probing nuclear-matter density distributions of stable nuclei, was applied for the first time to exotic nuclei. This method is demonstrated to be an effective means for obtaining accurate and detailed information on the size and radial shape of halo nuclei. Absolute differential cross-sections for small-angle scattering were measured at energies near 700 MeV/u for the neutron-rich helium isotopes ⁶He and ⁸He, and more recently for the lithium isotopes ⁶Li, ⁸Li, ⁹Li and ¹¹Li, using He and Li beams provided by the fragment separator FRS at GSI Darmstadt. Experiments were performed in inverse kinematics using the hydrogen-filled ionization chamber IKAR which served simultaneously as target and recoil-proton detector. For deducing nuclear-matter distributions, differential cross-sections calculated with the aid of the Glauber multiple-scattering theory, using various parametrizations for the nucleon density distributions as input, were fitted to the experimental cross-sections. The results on nuclear-matter radii and matter distributions are presented, and the significance of the data for a halo structure is discussed. Nuclear-matter distributions obtained for ⁶He and ⁸He conform with the concept that both nuclei compose of α-particle like cores and significant neutron halos. The matter distribution in ¹¹Li exhibits, as expected from previous reaction cross-section studies with nuclear targets, the by far most extended halo component of all nuclei being investigated. In addition the present data allow a quantitative comparison of the structure of the He and Li isobares of either the mass number A = 6 or A = 8. The measured differential cross-sections have also been used for probing density distributions as predicted from various microscopic calculations. A few examples are presented. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: p.egelhof@gsi.de     

Stiffness constant measurement in NiFe alloys by neutron inelastic scattering

Stiffness constant D has been measured in Ni-Fe alloys in a concentration range up to 68% of iron by neutron inelastic scattering, at room temperature and low temperature. Stiffness constant D decreases more strongly in the range of 60–68% iron concentration and a noticeable enhancement of the spin-wave width occurs in that region.     

Theory of resonant inelastic X-ray scattering spectrum for Ni impurities in cuprates

We perform the numerically exact diagonalization calculation for small Cu-O clusters with a Ni impurity site, representing the Ni-substituted cuprate, to examine the single-particle excitation spectra as well as the resonant inelastic X-ray scattering (RIXS) spectra. We clarify relations between low-energy electronic structures near the Ni site and excitations seen in the RIXS spectra.     

Elastic scattering of protons from 9Li in inverse kinematics within diffraction theory

The differential cross section for elastic scattering of protons from the ⁹Li nucleus has been calculated within the framework of the Glauber multiple scattering theory. The calculations were carried out with two versions of cluster wave functions for the nucleus obtained within the α-t-2n and ⁷Li-n-n three-body models with realistic potentials of intercluster interactions. The differential cross section was calculated at E = 700 and 60 MeV/nucleon. A comparison with the experimental data allows the conclusion that the wave function in the ⁷Li-n-n model describes the cross section better than in the α-t-2n model.     

Nuclear inelastic scattering

The development of the new field of nuclear inelastic scattering is reviewed. The experimental technique and the variety of applications are illustrated by recent results obtained at the Nuclear Resonance beamline of the European Synchrotron Radiation Facility. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nuclear inelastic scattering

Nuclear inelastic scattering is a new technique to study lattice dynamics. It gives direct access to the density of phonon states. The instrumentation and data analysis are outlined and illustrated by some distinct examples, such as α-Fe, β-Sn, and FeBO₃. This revised version was published online in July 2006 with corrections to the Cover Date.     

Proton spin conversion of coupled methyl groups in lithium acetate studied by inelastic neutron scattering

The temperature dependence of the tunneling spectrum of methyl groups in lithium acetate dihydrate has been studied in the temperature range between 1.2 and 8.0 K by inelastic neutron scattering. The results unambiguously prove that it is to a first order approximation correct to describe the tunneling motions by a model of coupled CH₃ pairs which are isolated from each other. However, from the fact that the tunneling frequencies shift to higher values with decreasing spin temperature, we conclude that coupling effects are important not only between nearest neighbour CH₃ groups. Quantitatively we can describe the observations by a model of coupled pairs with a fixed value for the interaction potentialW ₃ and a variable single particle potentialV ₃ which depends linearly on the concentration of the spin symmetry species.     

Heavy-ion inelastic scattering

The ²⁴Mg(¹⁶O, ¹⁶O'γ)²⁴Mg(2⁺) reaction has been investigated at 42 MeV incident energy. In-plane (¹⁶O, γ) angular correlations were measured for outgoing ¹⁶O ions between 6° and 40°. The results are compared with DWBA and coupled channels calculations.     

Proton reactions with 17O: (I). Elastic and inelastic scattering reactions

Differential cross sections for the elastic and inelastic scattering of protons by ¹⁷O have been measured at 8.62, 9.45 and 10.5 MeV. Excitation functions at 110° and 140° were measured from 8.5 to 10.5 MeV. The elastic scattering angular distributions were used to find optical model parameters for the scattering. The angular distributions of inelastically scattered protons were analysed using the effective interaction method of Satchler, and also with the microscopic theory of Geramb and Amos.     

Symmetries in inelastic proton-nucleus scattering

Various symmetries of inelastic proton-nucleus scattering within the Glauber model are discussed. They are obtained from symmetries of the corresponding proton-nucleon amplitude. In particular, it is shown that the polarization and analyzing power are in general not equal.     

Spin-dependent effects in inelastic scattering

The differential cross sections for the inelastic scattering of 10 MeV, 19.6 MeV, 30.4 MeV, 40 MeV and 49.35 MeV protons to the 2⁺ state (1.409 MeV) in ⁵⁴Fe and of 19.6 MeV protons to the 2⁺ state (0.846 MeV) in ⁵⁶Fe are analyzed in conjunction with the available data on the asymmetries and spin-flip probability amplitudes. The scattering amplitudes for both one step (valence plus core polarization) and two step (intermediate resonance) processes are evaluated using an antisymmetrized distorted wave approximation. Collective model representations for both the one step (core polarization) and two step (intermediate resonance) processes are used, and included are the effects of deforming the full Thomas spin-orbit potentials. The one step processes are fixed by the analyses of the scattering of 30.4, 40 and 49.35 MeV protons, with the core polarization contributions being constrained by the B(E2) values for the γ-ray deexcitation of the 2⁺ states. The analyses of the 19.6 MeV data demonstrates the need for an extra (two step) contribution to the reaction process and are consistent with the virtual formation of an L = 3 giant resonance. The 10 MeV data most certainly demonstrate compound nucleus effects but could also have some strength due to the virtual formation of an intermediate L = 2 giant resonance. The resonance parameters are consistent with recent information concerning the mass variation of giant resonances.     

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.     

Fluctuations in inelastic proton scattering from58Ni in the energy range 17.1 to 20.6 MeV

Excitation functions of proton elastic and inelastic scattering on⁵⁸Ni have been measured for proton energies in the range 17.1 to 20.6 MeV, at laboratory angles of 90°, 120° and 155°. All show cross section fluctuations. Excitation functions are presented for the elastic and for five inelastic groups in the energy range 18.1 to 18.59 MeV. These were analyzed by the Fourier analysis method, and the average level width found to be about 13 keV. The observation of strong fluctuations in the higher inelastic yields has implications for several microscopic analyses reported in the literature of⁵⁸Ni(p, p′) data obtained at 17.7 MeV incident proton energy.