Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions ¹⁶O on nuclei at an energy of E ～ 100 MeV per nucleon.     

Refractive scattering and reactions,comparison of two systems:16O+16O and20Ne+12C

Elastic, inelastic scattering as well as one-neutron transfer channels have been measured over a wide angular range for systems¹⁶O+¹⁶O at the incident energy of 350 MeV and²⁰Ne+¹²C at 390 MeV, respectively, using the Q3D magnetic spectrometer. In both cases differential cross sections have been measured down to about 50 nb/sr (or d/d _R10^–4) at large angles. For the¹⁶O+¹⁶O system refractive contributions are found at the level of these cross sections, whereas in the²⁰Ne+¹²C case a steeper decrease of the differential cross section with the angle is observed and the refractive contribution can not be determined. The elastic scattering data have been analyzed using standard Woods-Saxon potentials and potentials calculated in different versions of the double-folding model. Some properties of these potentials are tested in the calculations for inelastic scattering and one-neutron transfer within the DWBA. With the refractive pattern observed for the¹⁶O+¹⁶O system, the scattering and transfer data are found to be sensitive to the interaction potential at small internuclear distances down to about 2.5 fm.It should be acknowledged that part of the folding analysis reported here was done while one of the authors (D.T.K.) was staying at the Institute for Theoretical Physics, University of Tübingen. We also thank Prof. H. Clement and H. Abele for numerous discussions and contributions and Prof. G.R. Satchler for helpful comments on the use of the DWBA code PTOLEMY.     

Virtual coupling potential for elastic scattering of Be on proton and carbon targets

The ^10,11Be(p, p) and (¹²C, ¹²C) reactions were analyzed to determine the influence of the weak binding energies of exotic nuclei on their interaction potential. The elastic cross sections were measured at GANIL in inverse kinematics using radioactive ^10,11Be beams produced at energies of 39.1A   and 38.4A MeV$38.4A\text{ MeV}$. The elastic proton scattering data were analyzed within the framework of the microscopic Jeukenne–Lejeune–Mahaux (JLM) nucleon–nucleus potential. The angular distributions are found to be best reproduced by reducing the real part of the microscopic optical potential, as a consequence of the coupling to the continuum. These effects modify deeply the elastic potential. Including the Virtual Coupling Potential (VCP), we show the ability of the general optical potentials to reproduce the data for scattering of unstable nuclei, using realistic densities. Finally, the concepts needed to develop a more general and microscopic approach of the VCP are discussed.     

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.     

Unbound excited states in C

The neutron-rich carbon isotopes ^19,17C have been investigated via proton inelastic scattering on a liquid hydrogen target at 70 MeV/nucleon. The invariant mass method in inverse kinematics was employed to reconstruct the energy spectrum, in which fast neutrons and charged fragments were detected in coincidence using a neutron hodoscope and a dipole magnet system. A peak has been observed with an excitation energy of 1.46(10) MeV in ¹⁹C, while three peaks with energies of 2.20(3), 3.05(3), and 6.13(9) MeV have been observed in ¹⁷C. Deduced cross sections are compared with microscopic DWBA calculations based on p-sd   shell model wave functions and modern nucleon–nucleus optical potentials. Jπ$J^{\pi }$ assignments are made for the four observed states as well as the ground states of both nuclei.     

Quasi-Elastic Scattering of 16C from 12C at 47.5 MeV/Nucleon

Differential cross sections for the quasi-elastic scattering of^16 C at 47.5 MeV/nucleon from ^12 C target are measured.Coupled-channels calculations are carried out and the optical potential parameters are obtained by fitting the experimental angular distribution.     

Elastic, inelastic scattering and fusion of the 14N +59Co system at energies close to the coulomb barrier

Elastic and inelastic scattering differential cross sections were measured in the energy range 30 MeV ≤ E _lab ≤ 55 MeV, for the ¹⁴N +⁵⁹Co system. Ambiguities of the optical potential derived from the analysis of the elastic scattering data were removed by performing calculations at the radius of sensitivity and by comparison with the available fusion cross section data. A simultaneous analysis of the three mechanisms was performed by coupled channel calculations, and a unique energy independent nuclear potential was found to be able to fit the data. Discussions and comparisons concerning the optical model, the threshold anomaly, full and approximated coupled channel calculations are presented. Received: 6 February 1997 / Revised version: 1 August 1997     

Absorption and refraction phenomena in proton- and antiproton-nucleus scattering

The experimental data on the 180 MeV proton and 50, 180 MeV antiproton scattering by the nuclei¹²C,⁴⁰Ca and²⁰⁸Pb have been analysed on the basis of the phenomenological diffraction theory. The optical properties of the nuclei with regards to the incident protons and antiprotons are investigated. Various limiting cases of the proton- and antiproton-nucleus scattering are considered. The contribution of the Coulomb and the spin-orbit interactions to the differential cross sections of these processes has been also analysed.The authors are indebted to D.M. Skrypnik for assistance in preparing the English version of this paper.     

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.     

Exploring the <Superscript> 6</Superscript>He continuum sea through proton inelastic collisions

The p-⁶He inelastic scattering at 700 MeV u^-1 is studied using Multiple Scattering expansion of the total Transition amplitude (MST) framework with a pseudo-state representation of ⁶He continuum. We show that the differential cross sections calculated with two different pseudo-state bases are in good agreement.     

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 description of the elastic scattering of 6He from a polarized proton target at 71 MeV/nucleon

The vector analyzing power and differential cross section for the elastic scattering of ⁶He nucleus from polarized protons at 71 MeV/nucleon have been analyzed using the optical model potentials. Different versions of the nuclear potential are constructed using phenomenological potentials and semimicroscopic potentials based upon four different versions of 6He density and three effective nucleon-nucleon interactions. The effects of density dependence and the sensitivity of the cross sections for interactions have been investigated.     

Transfer reactions at high energy and ambiguities in heavy-ion potentials

The smaller impact parameters that contribute to transfer reactions between heavy ions at high energies make them more sensitive to different types of optical potentials than is the case at lower energies. This may allow one to distinguish between potentials that otherwise generate similar elastic scattering cross sections within the limited angular region over which typical elastic data are available. We cite as evidence results for nucleon transfers induced by¹⁸O +²⁸Si at 352 MeV which rule out surface transparent potentials.     

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.     

Nuclear rainbow in the elastic scattering of <Superscript>16</Superscript>O nuclei on carbon isotopes

An investigation of refractive effects in heavy-ion scattering is continued. For the elastic scattering of ¹⁶O nuclei on a ¹³C target at E(¹⁶O) = 132 MeV, the differential cross sections are measured for the first time in addition to previous measurements for targets from the carbon isotopes ¹²C and ¹⁴C. Airy structures that are similar for all isotopes and which have close cross sections are observed and are found to be consistent with the energy systematics of Airy minima that were obtained previously. The volume integrals of the real and imaginary parts of the optical potentials found in the present study are nearly identical for all of the isotopes considered here and are also in good agreement with the systematics obtained previously.     

Measurement and interpretation of heavy ion fusion excitation functions

Fusion excitation functions for ³²S induced reactions on ²⁴Mg, ²⁷Al, ⁴⁰Ca and ⁵⁸Ni are reported at incident ³²S ion energies of 65 to 132.5 MeV. Measurements were made using counter-telescopes with beams from Van de Graaff accelerators. From these data barrier heights and radii for fusion are extracted. These results are interpreted in terms of the nuclear diftuseness, and the nuclear attractive potentials at the fusion radii are deduced. Relative density overlaps at the fusion radius are estimated from electron scattering density distributions. Several parameterizations for the fusion radii and barrier heights are presented. Fusion cross sections are compared with reaction cross sections based on elastic scattering measurements coupled with optical model analysis. It is found that for the systems investigated, 90±10 % of the reaction cross section results in fusion.     

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.     

Ground state reorientation effects in elastic scattering cross sections

Elastic scattering cross sections are shown to be quite sensitive to ground state reorientation amplitudes and cross sections. These effects are dramatically evident when comparing scattering from even-even nuclei with that from high-spin odd-A nuclei, and may affect choices of potentials for odd versus even nuclei. Neutron scattering data from ²³⁵U and ²³⁸U are analyzed via coupled channels methods. The diffraction minima in elastic scattering from ²³⁵U are found to be dominated by reorientation cross sections. The majority of this reorientation is shown to follow from second order virtual nuclear excitations rather than proceeding through amplitudes for direct ground state reorientation.