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.     

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.     

Coulomb-nuclear interference in the scattering of 3He and α-particles by 122,124Te, 124Sn and 114Cd

Angular distributions and excitation functions of the elastic and inelastic scattering of ³He and α-particles by ^122,124Te, ¹²⁴Sn and ¹¹⁴Cd at incident energies around the Coulomb barrier were measured. The experimental results were analyzed in the framework of the optical model and DWBA taking into account the interference between nuclear and Coulomb excitation. Nuclear and charge deformation parameters were deduced.     

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.     

On the interference between Coulomb and nuclear excitation in the inelastic scattering of Li ions

Angular distributions have been measured for inelastic and elastic scattering of ⁶Li ions on ⁵⁸Ni and ¹²⁰Sn. Strong interference between Coulomb and nuclear excitation in inelastic scattering has been observed.     

Scaling laws and higher-order effects in Coulomb excitation of neutron halo nuclei

Essential properties of halo nuclei can be described in terms of a few low-energy constants. For neutron halo nuclei, analytical results can be found for wave functions and electromagnetic transition matrix elements in simple but well-adapted models. These wave functions can be used to study nuclear reactions; an especially simple and instructive example is Coulomb excitation. A systematic expansion in terms of small parameters can be given. We present scaling laws for excitation amplitudes and cross-sections. The results can be used to analyze experiments like ¹¹Be Coulomb excitation. They also serve as benchmark tests for more involved reaction theories.     

Approximate scattering solutions of the dirac equation for electron-nucleus processes in light nuclei

Scattering solutions of the second-order Dirac equation for the case of the Coulomb potential and which are correct to first order in the coupling constantZe ²/hc are investigated and found to describe pure Coulomb scattering equally well as the Sommerfeld-Maue wave functions. Errors introduced by the use of these solutions are studied in a numerical calculation of cross sections for nuclear electric-quadrupole excitation by high-energy electrons. The use of these wave functions is suggested for simplified calculations of lowest-order Coulomb corrections to Born approximation results for various electron-nucleus processes.     

High-energy approach for heavy-ion scattering with excitations of nuclear collective states

A phenomenological optical potential is generalized to include the Coulomb and nuclear interactions caused by the dynamical deformation of its surface. In the high-energy approach, analytical expressions for elastic and inelastic scattering amplitudes are obtained, where all the orders in the deformation parameters are included. The multistep effect of the 2⁺ rotational state excitation on elastic scattering is analyzed. Calculations of inelastic cross sections for the ¹⁷O ions scattered on different nuclei at about tens of MeV/nucleon or higher are compared with experimental data, and the important role of the Coulomb excitation is established. The text was submitted by the authors in English.     

Dipole states in the deuteron,other exotic nuclei,and “Schrödinger’s Cat”

The question whether the “soft giant dipole modes” in halo nuclei are resonances is discussed. It is argued that a resonance picture of these modes can be envisaged with a non Breit-Wigner line shape. The dipole Coulomb breakup of the deuteron is worked out as a specific example of such a picture. The “soft” and “hard” dipole modes of the more complex neutron-rich exotic nuclei are treated from this point of view. An interpretation of the coherent production of these modes in Coulomb excitation as a nuclear instance of Schrödinger cat state is advanced.     

Isomeric Level of the <Superscript>229</Superscript>Th Nucleus and Its Population in the Coulomb Excitation Reaction

Electromagnetical properties of the deformed neutron-odd nucleus of ²²⁹Th are considered on the basis of a unified nuclear model. Particular attention is given to the properties of the low-lying isomeric 3/2⁺ state. The possibility of its population in the Coulomb excitation reaction is studied.     

Role of anharmonicities and nonlinearities in heavy ion collisions A microscopic approach

Using a microscopic approach beyond RPA to treat anharmonicities, we mix two-phonon states among themselves and with one-phonon states. We also introduce nonlinear terms in the external field. These nonlinear terms and the anharmonicities are not taken into account in the “standard” multiphonon picture. Within this framework we calculate Coulomb excitation of ²⁰⁸Pb and ⁴⁰Ca by a ²⁰⁸Pb nucleus at 641 and 1000 MeV/A. We show with different examples the importance of the nonlinearities and anharmonicities for the excitation cross section. We find an increase of 10% for ²⁰⁸Pb and 20% for ⁴⁰Ca of the excitation cross section corresponding to the energy region of the double giant dipole resonance with respect to the “standard” calculation. We also find important effects in the low-energy region. The predicted cross section in the DGDR region is found to be rather close to the experimental observation.     

Quadrupole moments and nucleon excitation strengths in even-A Sm isotopes

We present a coherent coupled-channel analysis of 7 MeV neutron and 16 MeV proton elastic and inelastic scattering from ^{148, 152, 154}Sm. The optical potential and nuclear deformation parameters are determined so as to fit not only these elastic and inelastic scattering data but also the low-energy neutron scattering properties and the total cross sections over a wide energy range. This analysis provides evidence of the same excitation strengths for both projectiles in the case of ^{152, 154}Sm, and of a smaller excitation strength for the proton than for the neutron in case of ¹⁴⁸Sm. Moreover the quadrupole moments of these deformed optical potentials are in good agreement with those extracted from Coulomb excitation measurements and from nuclear matter distribution calculations.     

A multichannel quasi-separable potential approach to nucleon-nucleus scattering

A quasi-separable potential model for two-body multichannel scattering is developed. Spin and Coulomb effects are taken into account. By a suitable choice of the separable nuclear interactions we arrive at simple analytic expressions for the transition amplitudes. Our model is applied to the study of the n-¹²C and p-¹²C scattering processes. Effects arising from the excitation of the target nucleus are well reproduced.     

Structure of excited states in100Mo and102Mo from spectroscopy using18O induced reactions

The lifetimes have been determined for the 2⁺, 0^+～ and 4⁺ states in¹⁰⁰Mo and¹⁰²Mo using the recoil-distance Doppler-shift method. The states have been excited in¹⁰⁰Mo by Coulomb excitation and in¹⁰²Mo by the two-neutron transfer reaction induced by¹⁸O ions on a¹⁰⁰Mo target. The study of the excitation function for the elastic and inelastic scattering on the ground and first excited 2⁺ state in¹⁰⁰Mo at beam energies between 20 and 61 MeV shows that 40 MeV is the highest incident energy for pure Coulomb excitation. Above this energy nuclear absorption sets in and nuclear scattering contributes to the excitation of the 2⁺ state of¹⁰⁰Mo. From the lifetimes of the 2⁺ and 4⁺ states deformation parameters of ¦β¦= 0.21 and ¦β¦=0.31 for¹⁰⁰Mo and¹⁰²Mo respectively were deduced. The 0^+′ levels are not shape isomeric states, as suggested earlier, but they decay by enhancedE2 transitions to the first 2⁺ states. From a comparison with similar states in other transitional nuclei it is suggested that they are band heads forβ vibrational bands.     

The static quadrupole moment of the first excited state of 198Hg

The first direct evidence of oblate nuclear deformation in the even-A mercury isotopes has been obtained by measurement of the static quadrupole moment of the first excited state of ¹⁹⁸Hg using the reorientation effect in Coulomb excitation.     

Effects of neutron skin on the excitation of isovector modes of neutron-rich nuclei

The existence of a neutron skin in neutron-rich nuclei is discussed in connection with the excitation of isovector dipole and quadrupole giant modes via isoscalar nuclear probes. In the case of large neutron excess, important contributions are obtained from the nuclear excitation, which may even become predominant according to proper kinematical conditions. At variance with the usual situation encountered in inelastic processes, constructive interference can be found between nuclear and Coulomb contributions.     

Few-neutron removal from238U at relativistic energies

As part of a comprehensive study of uranium fragmentation at relativistic energies at the GSI projectile fragment separator, FRS, inclusive neutron-removal cross sections have been measured for severalxn channels at projectile energies of 600 and 950A MeV using targets of Al, Cu and Pb. The variation of the experimental cross sections with target nuclear charge is used to disentangle nuclear and electromagnetic contributions. The electromagnetic cross sections agree surprisingly well with a simple harmonic oscillator calculation of giant dipole resonances based on measured photonuclear cross sections and do not require an extra enhancement of the two-phonon giant dipole excitation as concluded from similar measurements with¹⁹⁷Au.     

Pigmy and giant dipole states in stable and unstable oxygen isotopes

We have studied dipole states of oxygen isotopes in large scale shell model calculations. The calculated photoreaction cross sections in ¹⁶O, ¹⁷O and ¹⁸O give reasonable agreement with experimental observations both in the low energy region below ?ω=15 MeV and in the high energy giant resonance region (15 MeV < ?ω ≤ 30 MeV). We found that the transition strength below dipole giant resonance (?ω ≤ 15 MeV) exhausts about 10% of the classical Thomas-Reiche-Kuhn sum rule and more than 40% of the cluster sum rule in heavier oxygen isotopes than ¹⁷O. The predicted Pigmy strengths in ²⁰O and ²²O are also confirmed by recent Coulomb excitation experiment at GSI.     

Enhanced neutron pair transfer and collective excitations in the system 206Pb + 118Sn at barrier energies

At energies below the Coulomb barrier, neutron transfer and Coulomb excitation have been measured in a very heavy asymmetric nuclear system, in ²⁰⁶Pb + ¹¹⁸Sn. These are semi-magic nuclei showing super-fluid properties. Particle-γ coincidence techniques using 5 Euroball Cluster detectors (EB), combined in a set-up with the Heidelberg-Darmstadt NaI Crystal Ball (CB), have been used. Position-sensitive detectors allowed the observation of scattering processes covering angles from 110 up to 150 degrees. The fragments are identified via the known γ-decays of the lowest excited states using the high resolution of EB. Using the unique feature of the set-up with the CB, transfer to well-defined final channels with known quantum numbers is selected using the high-efficiency multiplicity filter of the CB with no second γ-ray, i.e. without feeding. The data are analysed using the semi-classical approach and transfer probabilities are obtained. Coulomb excitation has been analysed using known transition probabilities. The enhancement is deduced for the two-neutron transfer populating the low-lying super-fluid 2⁺ states in ¹²⁰Sn and ¹¹⁶Sn, while the 2n transition remains in the ground state for the ^20NPb nuclei. Large enhancements up to EF ≃ 10³ are observed. This is the first observation of neutron pair transfer enhancement for a heavy nuclear binary system with super-fluid properties with experimentally separated levels. The calculations with microscopic 2-neutron wave functions, with configuration mixing over six shell model configurations and using the coupled reaction channels approach, reproduce well the observed probabilities and the enhancement. Received: 27 August 2002 / Accepted: 9 December 2002 / Published online: 25 March 2003 RID="a" ID="a"e-mail: oertzen@hmi.de Communicated by D. Schwalm