Calculation and analysis of cross-sections for p+~(184)W reactions up to 200 MeV

A set of optimal proton optical potential parameters for p+184W reactions are obtained at incident proton energy up to 250 MeV.Based on these parameters,the reaction cross-sections,elastic scattering angular distributions,energy spectra and double differential cross sections of proton-induced reactions on184W are calculated and analyzed by using theoretical models which integrate the optical model,distorted Born wave approximation theory,intranuclear cascade model,exciton model,Hauser-Feshbach theory and evaporation model.The calculated results are compared with existing experimental data and good agreement is achieved.     

The reactions of 12C with 12C AT 293 MeV

Energy spectra, angular distributions, and elemental yield distributions have been measured for products Z = 1?9 produced in the reactions of ¹²C on ¹²C. A total reaction cross section 1170_?100⁺¹⁷⁰ mb was determined from the measured elemental cross sections and the principle of charge conservation. This total reaction cross section is about 250 mb less than the geometric cross section and agrees with the Glauber-model calculations of DeVries and Peng. The experimental energy spectra, angular distributions, and yield distributions were compared with those from model calculations for the statistical decay of the products of fusion and of incomplete fusion reactions. For both types of calculations, a modified version of the code LILITA was used. By comparing the data to model calculations, an upper limit of 75 mb for the fusion cross section was determined. That limit corresponds to an upper limit of L_crit for fusion of 10? in the sharp-cutoff approximation. The dominant reaction mechanisms appear to be incomplete fusion processes.     

Screening effects on ~(12)C+~(12)C fusion reaction

One of the important reactions for nucleosynthesis in the carbon burning phase in high-mass stars is the ~(12)C+~(12)C fusion reaction. In this study, we investigate the influences of the nuclear potentials and screening effect on astrophysically interesting ~(12)C+~(12)C fusion reaction observables at sub-barrier energies by using the microscopic α-αdouble folding cluster(DFC) potential and the proximity potential. In order to model the screening effects on the experimental data, a more general exponential cosine screened Coulomb(MGECSC) potential including Debye and quantum plasma cases has been considered in the calculations for the ~(12)C+~(12)C fusion reaction. In the calculations of the reaction observables, the semi-classical Wentzel-Kramers-Brillouin(WKB) approach and coupled channel(CC)formalism have been used. Moreover, in order to investigate how the potentials between ~(12)C nuclei produce molecular cluster states of ~(24)Mg, the normalized resonant energy states of ~(24)Mg cluster bands have been calculated for the DFC potential. By analyzing the results produced from the fusion of ~(12)C+~(12)C, it is found that taking into account the screening effects in terms of MGECSC is important for explaining the ~(12)C+~(12)C fusion data, and the microscopic DFC potential is better than the proximity potential in explaining the experimental data, also considering that clustering is dominant for the structure of the ~(24)Mg nucleus.     

Analysis of <Superscript>8</Superscript>B Proton Halo Nucleus Scattered from <Superscript>12</Superscript>C and <Superscript>58</Superscript>Ni at Different Energies

Angular distributions in the elastic scattering of ⁸B from ¹²C and ⁵⁸Ni targets at different energies have been analyzed in the framework of the double-folding (DF) optical model. The real central part of the nuclear optical potential is obtained by folding the M3Y effective interaction with the cluster density distribution of the ⁸B nucleus. The experimental angular distributions have been successfully reproduced. This confirms the validity of the cluster structure of the ⁸B nucleus.     

Study of the diffraction scattering 12C + 12C with the excitation of the 12C exotic state 0 2 + (the Hoyle state)

New results from a series of experiments dedicated to the study of the ¹²C exotic state (the so-called Hoyle state) are presented. In spite of the many investigations that have been carried out, the structure of this state (which lies above the threshold for breaking up into three alpha particles) is still unknown. The different models assume that the nucleus has an abnormally large size in this excited state. However, until recently, methods for measuring the radii of unbound states have not been suggested. The best way to solve this problem seems to be by measuring the angular distributions of elastic and inelastic scattering of ¹²C on different target nuclei, and the determination of the radii is based on the fact that, at small scattering angles, the cross sections for direct reactions at high enough energies behave like Frauenhofer diffraction on a black ball. Accordingly, an experiment was performed aimed at measuring the elastic and inelastic angular distributions of ¹²C with an energy of (121.5 ± 0.5) MeV on a ¹²C target. The elastic scattering was measured in the angular range from 18° to 50° in the c.m. system with uncertainty in the angle of measurement equal to Δθ = ± 0.6°. The inelastic cross section was measured for the ¹²C excited state 2⁺ (4.44 MeV) and 0⁺ (7.65 MeV). Estimates were made for the diffraction radii for the ground and excited states. An increase was observed in the radius of the state at 7.65 MeV compared to those of the ground and first excited states.     

Solution of the reduced occupation-number equation for a fermion system

Using the thin target — thin catchers techniques, masses, mean recoil energies and angular distributions of target residues have been measured for 86 MeV/nucleon¹²C induced reactions. Several different nuclear reaction processes, from peripheral to central collisions have been observed. Experimental results are partly reproduced by intranuclear cascade+evaporation calculations. Up to now, the production of the lightest masses (44<A<71) recoiling with high kinetic energies is not correctly understood by theoretical models. More exclusive experiments are needful to check if the formation of a highly excited quasi-compound nucleus could be a possible explanation of the phenomena.     

Neutron polarizations from the9Be(d,n)10B and11B(d,n)12C reactions

Neutron polarization angular distributions were measured for the⁹Be(d,n)¹⁰B and¹¹B(d,n)¹²C reactions for deuteron energies of 5.47 and 5.34 MeV, respectively. Using neutron time-of-flight techniques, polarizations to eight states in¹⁰B and to six states in¹²C have been measured. Neutron polarization energy excitation functions for both reactions were measured for deuteron energies from 3.0 to 5.5 MeV in 0.25 MeV steps at 30° (lab). Distorted wave method calculations carried out to compare theoretical calculations against experimental results were not in good agreement with the data.     

Folding model analysis of 10, 11B, 12C + 27Al, 39K and 40Ca

Elastic scattering angular distributions for ^{10, 11}B + ⁴⁰Ca at E_lab = 46.6 and 51.5 MeV and¹²C+³⁹K at E_lab = 54 and 63 MeV have been measured and compared with Woods-Saxon and double-folding optical models. The oscillatory structure observed previously for ¹²C + ⁴⁰Ca disappears when the projectile is changed to ^10,11B or the target is changed to ³⁹K. The angular distributions are adequately reproduced by a double-folding analysis, which employs the nucleon-nucleon potential of Bertsch et al., with a range of real normalizations N_R = 1.0–1.38. This same range of real normalizations was also able to describe previously measured ^10,11B, ¹²C + ²⁷A1 data. The double-folding analysis of ¹²C + ⁴⁰Ca scattering indicates that this system behaves differently from neighboring systems.     

Production of α emitters in interactions of 86 MeV/u 12C on targets of mass 166–186

Cross sections, angular distributions, and recoil ranges have been measured for rare earth α emitters produced in the interaction of ¹²C at 1 GeV with medium targets at CERN. The salient features of the experimental data for the production of residues as much as 30 mass units lighter than the target are reasonably well reproduced by a mechanism of intra-nuclear cascade.     

12C + 7Li Reaction measurements and the 12C(7Li,t)16O reaction

A measurement of the residues from the ¹²C + ⁷Li reaction has been obtained for ⁷Li energies from 10 to 38 MeV. From these measurements the fusion cross sections and critical angular momenta for the ¹²C + ⁷Li system have been deduced. Cross sections for the ⁷Li(¹²C, t)¹⁶O reaction have been obtained for ¹²C energies from 54 to 62 MeV at θ_lab = 2.7°. The critical angular momenta obtained from the fusion cross sections have been used to perform Hauser-Feshbach calculations for the ¹²C(⁷Li, t)¹⁶O reaction. These calculations have been compared to measured angular distributions over a wide energy range. By comparing the fusion cross sections required by the Hauser-Feshbach calculations to fit the ¹²C(⁷Li, t)¹⁶O(8.87 MeV) reaction and the measured residue cross section it is estimated that at least 80 % of the measured residues are fusion products. The calculations also indicate that direct processes dominate the population of many ¹⁶O levels at forward angles and the 10.35 MeV state at backward angles. The necessity for using a critical angular momentum in Hauser-Feshbach calculations is discussed.     

Nuclear reactions of medium and heavy target nuclei with high-energy particles IV. Interpretation of mass fragment yields

Target residue mass distributions in 3·65 A GeV¹²C-ion- and 3·65 GeV proton-induced reactions on medium and heavy target nuclei have been interpreted in the theoretical framework of the intranuclear cascade and abrasion-ablation models. While the intranuclear cascade model gives a good approximation to experimental yields of residues produced in both types of interaction, the abrasion-ablation model was found to overestimate mass-yield distributions in the vicinity of the target mass numbers.     

Experimental study of the photoemission of protons off12C using tagged photons in the energy range 200–385 MeV

Data are presented for proton emission off¹²C using tagged photons in the energy range 200–385 MeV. The protons are detected in a magnetic spectrometer. In addition, charged or neutral particles can be measured with a scintillation counter setup. Contributions to the proton energy spectra from primary pion production and quasideuteron reactions are separated using the coincidence data. The total¹²C(γ, p)X cross section is derived as a function of the photon energy. The data are compared to the predictions of an intranuclear cascade calculation. Final state interactions have to be taken into account to describe the data.     

Interfering proton and neutron transfer in the reaction C(N, N)C

Elastic scattering and one-nucleon transfer reactions induced by ¹⁶O have been investigated in the energy region 45–60 MeV on targets of ²⁶Mg, ²⁷Al, ³⁰Si and ⁴⁸Ca. Angular distributions were measured in the angular range 4°–40°. Optical model parameters were derived from the elastic scattering data and the transfer reaction data were analysed using both no-recoil and full-recoil DWBA codes. In the case of proton transfer reactions on ⁴⁸Ca, good agreement was obtained between the data and the DWBA calculations while the data for the lighter targets could not be satisfactorily reproduced. The oscillatory pattern of the angular distributions is discussed in terms of the three-parameter model of Kahana, and it is found that the model qualitatively explains the observed transition from smooth to oscillatory angular distributions.     

Cross sections and dynamical properties of a emitters produced in interactions of 12C at 86 MeV/n on medium and heavy targets

Cross sections, mean recoil ranges and angular distributions of radioactive a emitters produced in ¹²C, induced reactions at 1 GeV on medium and heavy targets are presented. A new on-line electrostatic collection device is used. A wide spectrum of heavy residues corresponding to various mass losses away from the target between D to 60 a.m.u. has been observed. A phenomenological analysis based on the statistical decay of possible precursors gives some information on the properties of the primary interaction. Losses of 10 to 30 nucleons can be partly fitted by the intranuclear cascade model. For greater mass losses, more collective primary interaction is needed. The abrasion-ablation model can produce such residues but in its clean cuts approximation the predicted excitation energy is too low.     

Application of the incoming wave boundary condition to16O+16O and12C+12C elastic scattering

The elastic scattering of¹²C+¹²C and¹⁶O+¹⁶O has been studied in the framework of an incoming wave boundary condition model. Different logarithmic derivatives for the incoming waves have been tested and their effects investigated with the help of Fourier analyses. It is shown that a logarithmic derivative obtained from a JWKB approximation leads to strong absorption of the low partial waves while a logarithmic derivative constant for all partial waves causes reflections. These reflections are necessary to describe the high energy elastic scattering of¹²C+¹²C. The fits thus obtained with shallow real potentials are comparable to those obtained with deep folding potentials. It is shown that not the lowest partial waves, but those within a window just below the grazing angular momentum are most important for the higher energy¹²C+¹²C angular distributions.     

Comparative study for nucleus-nucleus interactions and modified cascade evaporation model at (4.1 – 4.5) AGeV/c

The characteristics of the nucleus-nucleus collisions at high energy for the interactions of ¹H, ⁴He, ¹²C, ¹⁶O, ²²Ne, ²⁸Si and ³²S with emulsion at momentum (4.1 – 4.5) AGeV/c have been investigated. It has been found that the multiplicity distributions of the different emitted particles and their average values can be described by the modified cascade evaporation model. The model reproduces satisfactorily the multiplicity distributions of the shower, grey and black particles and the correlations between their multiplicities. It has been seen that the number of the produced shower particles increases with the increase of the projectile mass number. From the correlation between the average multiplicity of the evaporation particles and the number of the produced particles, it was found that a phase transition in the target system may occur. The calculated pseudo-rapidity distributions of the produced shower particles are typically Gaussian shaped in the mid-rapidity region and agree well with the experimental data. Also, the angular distributions of the grey and black particles have been investigated. The angular distributions of the grey particles show a universal shape independent of the type of projectile. The angular distributions of the black particles are nearly isotropic with a small asymmetry in the forward direction. The modified cascade evaporation model, reproduces the general characteristics of the nucleus-nucleus interactions and gives an explanation for the multiparticle production process.     

Calculation of the wide-angle neutron spectra from the ~9Be(d,xn) reaction in a thick beryllium target

The multi-layer computing model is developed to calculate wide-angle neutron spectra, in the range from0° to 180° with a 5° step, produced by bombarding a thick beryllium target with deuterons. The double-differential cross-sections(DDCSs) for the ~9 Be(d, xn) reaction are calculated using the TALYS-1.8 code. They are in agreement with the experimental data, and are much better than the PHITS-JQMD/GEM results at 15°, 30°, 45° and 60° neutron emission angles for deuteron energy of 10.0 MeV. In the TALYS-1.8 code, neutron contributions from direct reactions(break-up, stripping and knock-out reactions) are controlled by adjustable parameters, which describe the basic characteristics of typical direct reactions and control the relative intensity and the position of the ridgy hillock at the tail of DDCSs. It is found that the typical calculated wide-angle neutron spectra for different neutron emission angles and neutron angular distributions agree quite well with the experimental data for 13.5 MeV deuterons. The multi-layer computing model can reproduce the experimental data reasonably well by optimizing the adjustable parameters in the TALYS-1.8 code. Given the good agreement with the experimental data, the multi-layer computing model could provide better predictions of wide-angle neutron energy spectra, neutron angular distributions and neutron yields for the ~9 Be(d, xn) reaction neutron source.     

Alpha particles from the reaction12C +12C at 28.7 MeV/nucleon

A classical dynamical alpha-cluster model has been developed and applied in order to get inclusive energy spectra of alpha particles produced in the collision of¹²C +¹²C at the beam energy 28.7 MeV/A. Results of the calculations are compared with experimental data. The shapes of the experimental energy spectra and the absolute normalization at forward angles are approximately described without any free parameters. The model makes it possible to distinguish alpha particles originating from the compound system and from direct processes. The spectra at forward angles are dominated by projectile fragmentation processes. The cross section at larger angles is overestimated, which is partially due to emission of particles other than alpha particles in central collisions. The evaporation Hauser-Feshbach model predicts that alpha particles emitted from the compound nucleus constitute less than 26% of all emitted particles.