The Deep Potential Description of Backward-Angle Anomalous Behavior for a-Type Nucleus Elastic Scatterings

Within the framework of the optical model, the backward-angle anomalous behaviors of the angular distributions for the ¹⁶O+²⁴Mg and the ¹⁶O+²⁸Si elastic scatterings have been well described by using deep optical potentials. The excitation functions of elastic scattering for the ¹⁶O+²⁴Si system at θ _cm = 90° and 180° have also been reproduced well by using the same set of deep potential parameters. The results show that the effect of the deep potential resonance may be responsible for the backward-angle anomalous behavior.     

Pauli exchange effects in the elastic scattering of O + O

The real optical potential for ¹⁶O+¹⁶O system is calculated within a generalized version of the double-folding model with the Pauli knock-on exchange effects between the projectile nucleons and the target nucleons taken into account from first principle. The elastic scattering data at E_lab=350 MeV supplemented by the new measurement at larger angles seem to be the first case in heavy-ion scattering where one can test the reliability of different theoretical heavy-ion optical potentials. Predictions are made for the elastic scattering of ¹⁶O+¹⁶O at laboratory energies of 240–480 MeV to illustrare the energy dependence of the rainbow structure which has been clearly observed in experiment at 350 MeV.     

On the Difference and Similarity Between Elastic Scatterings of Ne + C and O + O1

Based on the LCNO model with double alpha transfer and on the optical model, the experimental excitation functions and the angular distributions of ²⁰Ne + ¹²C and ¹⁶O + ¹⁶O elastic scatterings are respectively reproduced by using approximately equal parameters of optical potentials. The difference and the similarity exhibited in the elastic scattering excitation functions of these two systems are naturally explained.     

Equivalent bare optical potentials in heavy-ion inelastic scattering

The equivalent bare optical potentials have been calculated for the inelastic scattering of ¹⁶O and ¹³C by ⁴⁰Ca at 60 and 68 MeV, respectively. The potentials obtained are quite consistent with those found phenomenologically by coupled-channels calculations. The shape of the bare potential is interpreted by showing the significant contribution of the nuclear—Coulomb cross term.     

Folding Model Analysis of Elastic Scattering of 11B from Light,Medium, and Heavy Nuclei

The elastic scattering angular distributions of ¹¹B projectile on light, medium, and heavy target nuclei including ⁷Li, ⁹Be, ¹²C, ¹⁶O, ^24,25,26Mg, ²⁷Al, ²⁸Si, ⁴⁰Ca, ⁵⁸Ni, ⁵⁹Co, ⁶⁰Ni, ¹⁹⁷Au, ²⁰⁸Pb, and ²⁰⁹Bi have been analyzed at various incident energies. The theoretical results have been obtained by using two different nuclear potentials within the framework of the optical model (OM). Firstly, the double folding potential for real part and the Wood-Saxon (WS) potential for imaginary part have been applied. Secondly, the calculations with double folding potential for both real and imaginary part have been performed and compared with the experimental data. It has been seen that the results are in very good agreement with the experimental data. Also, the volume integrals and cross-sections for each reaction have been obtained. Finally, a new and simple formula for the imaginary potential depth has been derived to clarify the nuclear interactions of ¹¹B nucleus at low energy reactions.     

Intermediate Energy Pion-20Ne Elastic Scattering in the α+16O Model of 20Ne

We present an analysis of π-²⁰Ne elastic scattering at intermediate energy basing on the α+¹⁶O model of the ²⁰Ne nucleus and in the framework of Glauber multiple scattering theory. Satisfactory agreement with the general features of the experimental data of pion elastic scattering on the neighboring 4N-type nuclei is obtained without any free parameters. Compared with the experimental angular distributions of pion elastic scattering on ¹²C, ¹⁶O, ²⁴Mg, and ²⁸Si nuclei, the diffractive patterns and the positions of the dips and peaks in the angular distributions of π-²⁰Ne elastic scattering are reasonably predicted by the calculations.     

Proton–neutron structure of the N=52 nucleus Zr

Following the successful identification of mixed-symmetric one- and two-phonon states in the N=52 nuclei ⁹⁴Mo and ⁹⁶Ru, we have performed a photon scattering experiment on the N=52 isotone ⁹²Zr. Experimental data and shell model calculations show that both, single particle and collective degrees of freedom are present in the low-lying levels of ⁹²Zr. The second excited quadrupole state shows the signatures of the one-phonon mixed-symmetric 2⁺ state, while calculations and data indicate an almost pure neutron configuration for the 2⁺₁ state, in contradiction with the F-spin symmetric limit. Furthermore, two strong dipole excitations, which are candidates for the two-phonon quadrupole–octupole coupled E1 excitation and for the mixed-symmetric 1⁺ two-phonon state, were observed.     

A Study of Intermediate Energy Proton-^16O Elastic Scattering Based on the α-Particle Model

In the framework of KMT multiple scattering theory, an optical potential for the intermediate energy proton-160 elastic scattering is presented based on the α particle model of 160. The differential cross sections, the analyzing powers, and the total cross sections of the intermediate energy proton-160 scattering have been calculated by using the obtained optical potential. The main features of the measured angular distributions of the cross section and the analyzing power can be well described. The calculated total cross sections are in good agreement with the experimental data at energies below 0.7 GeV and underestimate the data about 8% at higher energies.     

Analysis of the scattering of 46 MeV protons from Be and C

An analysis is made of the measurements of the elastic and inelastic scattering of 46 MeV protons by ³Be and ¹²C. The optical and collective models are used. There is considerable ambiguity in the optical parameters, and it was not found possible to obtain good fits to cross sections and polarizations simultaneously. Large quadrupole deformations were found for both ¹²C (β₂ ≈ 0.6) and ⁹Be(β₂ ≈ 1). The inelastic scattering from ¹²C agrees best with deformation of both real and imaginary parts of the optical potential, while ⁹Be shows a preference for real coupling. The 14.1 MeV level in ¹²C is interpreted as the 4⁺ rotational state, while the angular distribution for the 7.6 MeV 0⁺ level is well described by double quadrupole excitation via the lowest 2⁺. Interpretations are suggested for other inelastic transitions, including the excitation of spin and isospin oscillations.     

Polarization of neutrons from the O(d, n)F reaction

The polarizations of neutrons from the ¹⁶O(d, n₀)¹⁷F and ¹⁶O(d, n₁ ¹⁷F reactions have been measured at 30° (lab) in steps of approximately 0.15 MeV from E_d = 3.96 to 5.35 MeV. Polarization angular distributions have been obtained at 3.96 and 5.35 MeV. It is determined that the random phase approximation for the scattering amplitudes is not appropriate for the compound nucleus contributions. The analysis indicates probable interference between the compound nucleus and direct interaction reaction mechanisms.     

Further Analysis of Neutron Double-Differential Cross Section of n ＋ ^16O at 14.1 MeV and 18 MeV

By using a new reaction model for light nuclei, the double-differential cross section of total outgoing neutron with LUNF code for n＋^16O reactions at En=14.1 MeV and 18 MeV have been calculated and analyzed. In this paper the opened reaction channels, which have contribution to emitting the neutrons, are listed in detail. To improve the fitting results the direct inelastic scattering mechanism is involved. The calculating results agree fairly well with the experimental data at E,~ = 14.1 MeV and the deviation from calculated results and experimental data in low energy region at En= 18 MeV has been analyzed. Since the possibility of 5He has been affirmed theoretically [J.S. Zhang, Sci. Chin. G 47 （2004） 137], so 5He emission from n＋ ^16O reaction is taken into account, which plays an important role at the region of the outgoing neutron energy εn〈3 MeV in total outgoing neutron energy-angular spectrum. The calculated results indicate that the pre-equilibrium mechanism dominates the whole reaction processes, and the recoil effect in light nuclear reactions is essentially important.     

Spin alignment in resonant C+O inelastic scattering

The spin alignment of the 3⁻ state (6.13 MeV) of ¹⁶O from inelastic scattering of ¹²C+¹⁶O has been measured in the energy region of known resonances around E_cm=20 MeV. The result, that the population of the m=±3 magnetic substates is enhanced on four resonances at 19.7, 20.5, 22.0 and 22.6 MeV, indicates the dominance of the aligned configuration on these resonances.     

Analysis of N+19F(t+16O) Elastic Scattering with Three-Cluster QRGM and CGCT

The scattering of three-cluster system is studied with the quasi-resonating-group method (QRGM), which is an extended resonating-group method (RGM) by omitting the antisymmetrization of the nucleons in the double-magic cluster with other ones, and CGCT. As an example, the phase shifts and differential cross rrections of N+¹⁹F(t+¹⁶O) elastic scattering are evaluated. In the calculation an imaginary optical potential is introduced to take account of the effect of other reaction channels. The results show that the QRGM is a feaaible approximate method for many-nucleon system such as N+¹⁹F and can be used for other systems containing more nucleons.     

An Investigation of 4He+12C and 4He+16O Reactions Using the Cluster Model

The α -target semimicroscopic single folding potentials have been derived by folding a composite (repulsive and attractive) effective α-α interaction with the α -cluster distribution density in the target nuclei. The obtained potentials are considered as the real part of the nuclear optical model potentials, while the imaginary parts are phenomenologicaly expressed using the Woods-Saxon form. Nine sets of measured experimental data of the ⁴He+¹²C and ⁴He+¹⁶O elastic rainbow scattering over the energy range 80-240 MeV are analyzed using the obtained potentials. The data are successfully reproduced using the extracted potentials. The resulted reaction cross sections are also investigated and compared with the available corresponding data.     

The two-neutron transfer reactions (O, O) with O, C and Mg targets

Excitation functions, angular distributions and differential ranges were measured for the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction at ¹⁸O beam energies of 20–45 MeV. Excitation functions only were measured for the reactions ¹⁴C(¹⁸O, ¹⁹O)¹³C, ¹⁴C(¹⁸O, ¹⁶O)¹⁶C, ¹⁴C(¹⁸O, ²⁰O)¹²C, ¹⁴C(¹⁸O, ¹⁵N)¹⁷N and ¹⁸O(¹⁸O, ¹⁹O)¹⁷O, ¹⁸O(¹⁸O, ¹⁶O)²⁰O, ¹⁸O(¹⁸O, ¹⁵N)²¹F at ¹⁸O beam energies of 13–41 MeV. We have identified these as direct reactions in which a single neutron, a two-neutron cluster, a deuteron and a triton are transferred between projectile and target.

The cross sections for two-neutron transfer reactions were found to be relatively high and those for the ¹⁸O+¹⁸O and the ¹⁴C+¹⁸O reactions were higher than the ones of single-neutron transfers over most of the energy range.

Attempts were made to apply the theory of Buttle and Goldfarb for single-neutron transfer to the case of two-neutron transfer in the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction below the Coulomb barrier. It is shown that for those reactions for which the assumptions, implicit in the model, are valid, good agreement is obtained with experiment. We also tried to apply the diffraction model of Dar and Kozlovsky to the calculation of the angular distribution of these reactions. A good fit to the experimental results could be obtained if quite different sets of parameters were used in the calculations for the two bombarding energies.     

Analysis of Gross Resonant Structures in 12C+12C and 16O+12Ne Systems Using Deep Optical Potentials

Abstract Within the framework of the estended optical model, the gross resonant structures of the fusion escitation functions and the elastic scattering excitation functions for the ¹²C+¹²C and the ¹⁶O+²⁰Ne systems are described well by using deep optical potentials. The origin of the gross resonant structures and the effect of the deep potential and the parity-dependent potential are discussed.     

Effect of the adiabatic process on the absorption in heavy-ion scattering

We have succeeded in obtaining the optical model potential for ¹²C---¹²C scattering at low incident energies (10 MeV E_cm 20 MeV), by applying the adiabatic approximation to the coupled channels equation. As for this potential inelastic channels of single and mutual excitations of ¹²C^*(2⁺, 4.43 MeV) make a contribution to the real part and not to the imaginary part.     

On the elastic and inelastic scattering of O

Elastic and inelastic scattering data on ¹⁷O on ⁴⁰Ca measured at E_1ab=61 MeV are analyzed using collective core contributions plus valence terms which are obtained with the microscopic single-folding model. The role of two-step transfers and reorientation processes is also assessed.