Neutron scattering from 208Pb

Elastic scattering of 7, 9, 11, 20 and 26 MeV neutrons from ²⁰⁸Pb has been measured with the Ohio University Tandem Van de Graaff accelerator. Standard pulsed beam time-of-flight techniques were employed. Measurements of the incident flux at 0° were used to normalize the differential cross sections. The measured cross sections were corrected for dead time, detector efficiency, flux attenuation, multiple scattering, finite geometry, neutron source anisotropy and compound elastic contribution. Relative uncertainties are estimated to be between 5%–10% and the uncertainty in the normalization is estimated to be less than 5 %. The data were used to obtain neutron optical potential parameters. A comparison with proton optical parameters is presented, and the (p, n) quasi-elastic cross section is calculated and compared with available data. Deformation parameters for the 3^? state (Q = ?2.615 MeV) and 5ā (Q = ?3.198 MeV) in ²⁰⁸Pb were obtained at incident energies of 11 and 26 MeV.     

Elastic and inelastic scattering of 12C ions at intermediate energies

Elastic and inelastic scattering of ¹²C ions on ¹²C and ²⁰⁸Pb targets have been measured at the incident energies per nucleon E / A = 120 MeV/u and E / A = 200 MeV/u. Optical-model analysis is reported and nuclear surface transparency effects are discussed, together with the nuclear potential-energy dependence. The transparency region extends down to a radial internuclear distance of about 3 fm for the ¹²C-¹²C system and 8 fm for the ¹²C-²⁰⁸Pb system. A decrease of the imaginary potential with increasing incident energy is deduced for the two systems. Anomalous collapse of the real potential in the surface region is observed for ¹²C-²⁰⁸Pb system at 200 MeV/u. DWBA analysis of data on the 2⁺, 4.4 MeV state of ¹²C is reported and trends for the energy dependance of mean-field excitations are deduced.     

On the energy dependence of the real central optical potential for proton-nucleus scattering

The energy dependence of the real central optical potential in the energy range 25–1000 MeV has been determined from optical model analyses of p+¹²C, p+¹⁶O, p+²⁷Al, p+⁴⁰Ca and p+²⁰⁸Pb elastic scattering data. The volume integral and the strength can be represented by a relation linear in the incident energy only if a limited energy range is chosen. When the energy range 25–1000 MeV is considered a logarithmic energy dependence gives a better representation of the phenomenological results, especially for the light nuclei.     

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.     

Theoretical Calculations and Analysis of n+208Pb Reaction for Intermediate Energy Neutron

Based on experimental data of total, nonelastic, elastic cross section and elastic scattering angular distributions for n+Pb reactions, a set of neutron optical model potential parameters is obtained in the region of incident neutron energy from 1—300 MeV. The cross sections, angular distributions and energy spectra are calculated and analyzed by optical model, distorted wave Born approximation theory, Hauser-Feshbach theory, exciton model and cascade mechanism inside nuclear. The results indicate that the cross sections can be given for n+ ²⁰⁸Pb reactions which are all in good agreement with experimental data.     

Energy dependence of the optical model parameters for 3He ions scattered from 40Ca and 58Ni

The differential cross sections for the elastic scattering of ³He ions on targets of ⁴⁰Ca and ⁵⁸Ni have been measured at incident energies of 27.7, 51.4, 73.2 and 83.5 MeV. The results of optical model analyses showed that only one unique potential (J_R ≈ 330 MeV · fm³) with a surface absorptive term can provide acceptable fits to the large angle elastic scattering cross sections at 83.5 MeV. The particular geometrical set found at 83.5 MeV could not, however, give an adequate fit to the data with energy less than 40 MeV. Subsequent analyses indicated that a break in the energy dependence of the real potential is observed for the low energy data. Explicit energy dependent terms were obtained by fitting all the data simultaneously. These phenomenological potentials were also compared with the folded nucleon-nucleus potential. The influence of the α-particle channels on the elastic scattering of ³He ions at 83.5 MeV was also examined.     

Time scales for charge equilibration in heavy ion collisions

Charge equilibration was investigated in the reaction²⁰⁸Pb+¹¹⁰Pd at 1,180 and 1,280 MeV incident energy. It is found that the relaxation timeτ′ connected with this degree of freedom shows an increase with increasing bombarding energy. This behaviour can be explained within Langevin's classical theory of Brownian motion.     

6Li elastic scattering ON 12C, 16O, 40Ca, 58Ni, 74Ge, 124Sn, 166Er and 208Pb at E(6Li) = 50.6 MeV

The elastic scattering of ⁶Li ions from a variety of targets, A = 12 to 208, has been measured at a bombarding energy of 50.6 MeV. The angular distributions are characteristic of strongly absorbed particles, such as ³He and heavy ions, and less diffractive than for ⁴He. A simple optical model with Woods-Saxon real and imaginary volume potentials is adequate to fit the data. Spin-orbit effects are not apparent in the data.     

Elastic and inelastic scattering of 120 MeV 18O from 208Pb and the spin alignment of the 2+ state of 18O

The elastic and inelastic scattering of ¹⁸O ions at 120 MeV from a target of ²⁰⁸Pb have been studied. Cross sections for excitation of the 2⁺ state at 1.982 MeV in ¹⁸O and of the 3^? state at 2.61 MeV in ²⁰⁸Pb were measured. In addition, the populations of the m-substates for the ¹⁸O excitation were deduced from the Doppler-broadened line shapes. The data were subjected to a coupled-channels analysis using either Woods-Saxon or folding-model potentials. In addition, the ¹⁸O excitation was found to be described very well by use of a semi-microscopic model. The analyses consistently indicated the presence of a positive static hexadecapole moment of several e · fm⁴ for the 2⁺ state of ¹⁸O. The m-substate population distributions were found to be better fitted if a vector spin-orbit coupling was introduced for the 2⁺ state of ¹⁸O with a sign opposite to that for the nucleon-nucleus case.     

Complex microscopic effective interaction for (p,n) reactions

A simple recipe for generating a complex effective interaction for distorted wave Born approximation calculations from a real, microscopic charge-exchange form factor is investigated. The recipe is tested against angular distribution data for ²⁰⁸Pb(p, n) and ²⁰⁹Bi(p, n) from 25 to 50 MeV incident proton energy. The form factor resulting from the recipe is also compared qualitatively to complex effective coupling potentials, resulting from a charge-independent Lane-model formalism and from coupled-channion-channels calculations for a suggested multistep (p, d)—(d, n) reaction mechanism.     

Der β-Zerfall des208Tl

An iron-free intermediate-imageβ-ray spectrometer was used to investigate theβ-decay of²⁰⁸T1 in coincidence with the 2.615 MeVγ-ray of²⁰⁸Pb. Fourβ-groups were found, three of which were previously known. The fourth group has an endpoint energy of 0.64±0.03 MeV and an intensity of (4.5±1.5)%. It is supposed that this transition is still complex and feeds a group of levels around the known 4.3 MeV level of²⁰⁸Pb. Noβ-ray of maximum energy 1.032 MeV to the 3.961 MeV level could be found.     

Deuteron elastic scattering and (d,p) reactions on 208Pb at Ed = 22 MeV and j-dependence of T20 in (d,p) reaction

An experimental study of deuteron elastic scattering and (d,p) reactions at E_d = 22 MeV was made for ²⁰⁸Pb target. A new j-dependence of T₂₀ for (d,p) reaction at backward angles was observed. A “model independent” optical potential method was applied to analyze deuteron elastic scattering in the 10–22 MeV energy range. A continuum discretized coupled channels (CDCC) analysis was performed for deuteron elastic scattering at 22 MeV and the deuteron breakup effect was elucidated. DWBA and CDCC (d,p) analyses were made for (d,p) reactions.     

Virtual breakup effects in elastic scattering of polarized deuterons

Elastic scattering of polarized deuterons at E_d = 56 MeV is investigated for ¹⁶O, ⁴⁰Ca, ⁵⁸Ni, ¹¹⁸Sn and ²⁰⁸Pb target nuclei by the use of folding interactions. Effects of virtual breakup of the deuteron to S- and D-states in the continuum region are taken into account by the CDCC method and are found to make indispensable contributions to cross sections and analyzing powers, where continuum-continuum couplings are substantial. The contribution of the D-state admixture in the ground state is important for the tensor analyzing powers. The calculated results agree well with experimental data. The invariant-amplitude method and the second-order sum rule study clarify the characteristic feature of the spin dependence of the effective interactions due to the virtual breakup. The near-side/far-side decomposition of scattering amplitudes illuminates the difference of the reaction mechanism between light and heavy target nuclei. The investigation for the ²⁰⁸Pb target at E_d = 21.5 MeV gives important information on the energy dependence of the effective interactions. The use of different parameter sets for the input nucleon-target optical potentials shows that the detailed results depend significantly on the choice of the parameter sets.     

Charge and mass transfer in the reaction136Xe+208Pb at energies close to the coulomb barrier

Mass and charge transfer was investigated for the system¹³⁶Xe+²⁰⁸Pb at 5.9 MeV/nucleon incident energy with aΔE —E-time of flight telescope. The angle and energy integrated cross section for the strongly damped events was found to be 510 mb, very close to the total reaction cross section. The width of the mass distribution as function of the total kinetic energy loss was measured and is compared to the width of the corresponding charge distribution. An upper limit of 1 μb has been found for processes with very large mass transfer.     

Theoretical response to the discovery of deeply bound pionic states in208Pb(d,3He) reactions

Recently, deeply bound pionic states were found experimentally in (d,³He) reactions on²⁰⁸Pb. They found an isolated peak structure in the bound region below the pion production threshold. We study theoretically these excitation functions in (d,³He) reactions on²⁰⁸Pb at T _d =600 MeV. We found very good agreement with the (d,³He) excitation functions and could identify the underlying structures of the pionic states. We study the energy dependence of the (d,³He) reactions and the change of the excitation functions with the incident energy.