Energy dependence of heavy ion collisions 4He + 12C and 12C + 12C elastic scattering

We have studied the transparency of heavy ion collisions at high energies by using Glauber's multiple scattering theory. The good agreement between our calculation and the existing data available strongly emphasizes the dominance of the nucleon-nucleon interaction in nucleus-nucleus collisions at high energies.     

Fusion cross sections for 10,11B+12C at sub-Coulomb energies

Total fusion cross sections for the ¹⁰B + ¹²C and ¹¹B + ¹²C reactions have been determined over a 5 MeV (c.m.) energy range extending to ≈ 3 MeV below the Coulomb barrier. Absolute γ-ray yields for specific transitions in the de-excitation of the heavy products following compound nucleus decay were measured using a Ge(Li) detector. Statistical model calculations of the decay modes of the compound nucleus have been used to deduce, from the γ-ray data, cross sections for single proton, neutron and α-particle emission, and to determine total cross sections for compound nucleus formation. No evidence has been found for sub-Coulomb resonances in either reaction. The total reaction cross sections are compared with optical model calculations using different parameter sets and the observed trend in the very low energy cross sections is discussed relative to other reactions in the same mass region.     

Energy dependence of fusion and reaction cross sections in the 9Be + 12C system

Angular distributions of protons, deuterons. tritons and α-particles were measured for the system ⁹Be + ¹²C at lab energies between 12 and 27 MeV. The compound nucleus model with level densities calculated according to the Gilbert-Cameron formula describes satisfactorily the measured proton, deuteron and triton data. In the α-particle spectra contributions from other processes seem to be present. In the analysis the fusion cut-off angular momentum was adjusted at each energy in order to reproduce correctly the proton, deuteron and triton channels. From this analysis the fusion cross section was determined as a function of the energy. The results were compared with fusion and total reaction cross section values calculated from a potential model with the real part of the interaction potential obtained from the double folding procedure of Satchler.     

The 12C + 12C sub-coulomb fusion cross section

The ¹²C + ¹²C fusion cross section has been studied over the energy range 2.46 ≦ E_c.m. ≦ 5.88 MeV. The yields of the γ-rays emitted from the first excited states of ²³Na and ²⁰Ne, following ²⁴Mg compound nucleus decay via proton- and α-emissions, were measured using a Ge(Li) detector. The fusion cross section was obtained by normalizing these yields to previously reported ¹²C(¹²C, p)²³Na and ¹²C(¹²C, α)²⁰Ne cross sections. The data indicate that the cross section below 3.5 MeV is dominated by two or more resonances, and that the average trend in this energy region does not show the absorption-under-the barrier features of the optical model. For astrophysical extrapolations to lower energies, the new results are consistent with the extrapolation proposed by Fowler, Caughlan and Zimmerman.     

Sub-coulomb energy 12C + 10, 11B and 14N + 10B fusion cross sections

Total fusion cross sections have been measured for the following reactions and energy intervals: ¹²C + ¹⁰B, E_c.m. = 2.10–5.38 MeV; ¹²C + ¹¹B, E_c.m. = 2.10–5.99 MeV; ¹⁴N + ¹⁰B, E_c.m. = 2.64–5.97 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by two large NaI detectors. No resonance structure was observed in the three reactions. The elastic scattering excitation function was also measured at θ_c.m. = 90.4° for ¹²C + ¹⁰B over the energy range E_c.m. = 3.18–6.82 MeV. Optical model potentials were found which could consistently describe both the fusion and elastic scattering data.     

Energy integrated photonuclear cross sections

Energy integrated photonuclear cross sections are calculated in the electric dipole approximation for the nuclei ²H, ⁴He, ¹²C, ¹⁶O, ²⁸Si, ³²S and ⁴⁰Ca. The ground-state wave functions are calculated by the Brueckner-Hartree-Fock procedure. The dependence of the cross sections on the different types of realistic nucleon-nucleon potentials is discussed as well as the dependence on the underlying harmonic oscillator states. The enhancement factors κ are also given.     

Elastic scattering and fusion cross sections of 13C+13C

The ¹³C+¹³C total fusion cross section has been determined in the range 3.26⩽E_c.m.⩽8.0 MeV using Ge(Li) detector measurements of low-lying transitions in the residual nuclei and a statistical model calculation of excited state populations. The six most abundantly produced residual nuclei have been observed and their yields are given. To constrain the parameters in fusion models for these reactions, we have also taken elastic scattering data at θ_c.m.=60°, 70°, 80°, and 90° for 4.5⩽E_c.m.⩽8.5 MeV, as well as angular distributions at E_c.m.=7.0 and 8.0 MeV. The IWBC model and an optical model with a “shallow” potential have been used for parametrizing the nucleus-nucleus interaction.     

中速C3+与Ne原子靶相互作用过程中单电子转移绝对截面的测量

实验测量了2.2‰-4.2v0(v0为玻尔速度,v0=2.19×108cm/s)的C3 与Ne原子碰撞过程中单电子转移绝对截面.将实验结果与多体经典轨道蒙特卡罗模拟计算结果进行了比较.用电离能的变化、屏蔽效应、动态关联对实验和理论计算结果间的数值差异做了分析.总体上,实验结果与多体经典轨道蒙特卡罗方法计算结果在趋势上相符很好.此外,还简单分析了多电子原子的转移多电离机制.     

On the energy dependence of inelastic cross sections

The new accurate two-state quantum calculations of the inelastic cross sections in H + Li, Na collisions for energies from the thresholds and till 100 eV or 600 eV are performed, and the results are compared with the Landau-Zener model cross sections in both the diabatic and the adiabatic representations. It is found that the low-energy inelastic cross section is very sensitive to nonadiabatic coupling and, hence, the new NaH coupling is computed. The numerical solutions of the coupled channel equations are checked by independent calculations indicating that the quantum results are accurate. These checks are done by means of the analytic formula for a nonadiabatic transition probability derived within the perturbation approach. Both the Landau-Zener-like and the non-Landau-Zener-like behaviour of the excitation cross sections are found. 34.70.+e Charge transfer     

Velocity dependence of total Penning ionization cross sections

The velocity dependence of the total Penning ionization cross sections,σ(v), is measured in the thermal relative velocity region, using a time of flight method.σ(v) curves are reported for the collision systems He(2¹ S)/Ar, Kr, Xe, N₂, Hg, He(2³ S)/Ar, Kr, Xe, N₂, Hg, Ne(³ P _{2, 0})/Kr, Hg, and Ar(³ P _{2, 0})/Hg. In a qualitative discussion it is shown that all features of the measuredσ(v) curves may be explained within the frame of the theory of Penning ionization, allowing to extract information on the physical quantities governing the process: on the interaction potentialV(R) and on the transition probabilityW(R). A theoretical calculation for the He(2³ S)/Ar system shows good agreement with our experimentalσ(v) curve. On the basis of the present results earlier data onσ(v), and on absolute cross sections and rate constants obtained at certain relative velocity distributions are discussed.     

The energy dependence of nuclear reaction cross sections

The reaction cross section σ_R^pA(E) for proton-nucleus collisions varies with energy as the total cross section σ_t^pN(E) does for proton-nucleon scattering in the energy regime 100 MeV ? E ?400 GeV. We propose several empirical relations, and test them by a χ² analysis of various data. Within the framework of Glauber theory, the parameters in the relations can be linked to the cross section for a single inelastic collision.     

Energy dependence of the x-ray production cross sections of Cu and Ag for 150 to 800 keV proton and He+ bombardment

RelativeK-shell x-ray production cross sections have been measured for thin targets of Cu and Ag for proton and He⁺ impact in the energy range 150 to 800 keV. The experimental values are compared to the nonrelativistic plane wave Born approximation (PWBA), the PWBA with corrections for Coulomb deflection and binding effects (PWBABC), and the binary-encounter approximation (BEA). The PWBABC theory provides the best agreement with relative experimental cross sections. For protons, the agreement is within 2% for values of the scaled energy variableγ=η/(εθ)²>0.011; forψ<0.009, however, the deviation reaches about 10%. For helium a 10% deviation appears atγ～0.007. An explanation for these deviations is given.     

Total reaction and transfer cross sections for 11B + 9Be and 13C + 9Be reactions at low energies

The total reaction cross sections for ¹¹B + ⁹Be and ¹³C + ⁹Be have been measured by the total γ-ray yield method over the energy intervals E_c.m. = 1.4–4.4 MeV and E_c.m. = 2.0–5.2 MeV, respectively. The cross sections for the neutron transfer reactions ¹¹B(⁹Be, ⁸Be)¹²B, leading to the ¹²B 0.953 and 1.674 MeV states, and ¹³C(⁹Be, ⁸Be)¹⁴C, leading to the ¹⁴C 6.094, 6.728 and 6.902 MeV states, have been obtained from the yields of the characteristic γ-rays. The α-transfer reaction ¹¹B(⁹Be, ⁵He)¹⁵N, leading to many unresolved ¹⁵N states, has been observed with large cross section. There is, however, no evidence for the ¹³C(⁹Be, ⁵He)¹⁷O transfer process in the ¹⁷O + nα channels. This different behaviour of the ¹¹B + ⁹Be and ¹³C + ⁹Be systems seems to indicate that the α-transfer reaction at sub-barrier energies is not a direct transfer process, and that it probably occurs via molecular state formation.     

Photonuclear reaction cross sections for 12C, 14N and 16O

The results of an evaluation of the available photonuclear-reaction data for ¹²C, ¹⁴N and ¹⁶O are presented. While some reaction-yield data are given for energies up to 50 MeV, the primary emphasis is on the excitation-energy range extending from the proton separation energies up to 30 MeV. In addition to photodisintegration measurements, cross-section data derived from inverse particle-capture and electrodisintegration experiments are considered. Data are presented in graphical as well as tabular form. Included in the tables are: energy-weighted moments of the cross sections, bremsstrahlung induced reaction-yield data, radioactive-properties of reaction products, and reaction separation energies.     

IWB analysis of scattering and fusion cross sections for the 12C+12C, 13C+16O and 16O+16O reactions for energies near and below the Coulomb barrier

Calculations are presented of the elastic scattering and fusion cross sections for the astrophysically interesting reactions ¹²C+¹²C, ¹²C+¹⁶O and ¹⁶O+¹⁶O. The calculations are performed using the incoming wave boundary condition (IWB) and a real ion-ion interaction potential. The results are compared with the available experimental data for the energy region near and below the Coulomb barrier. With values of two adjustable potential parameters (the radial position of the l = 0 barrier and the diffuseness) determined by fitting elastic scattering data, good agreement is obtained for the average energy dependence of the ¹²C+¹²C and ¹²C+¹⁶O fusion cross sections. In the case of ¹⁶O+¹⁶O, both the calculated absolute magnitude and the energy dependence of the fusion cross section are inconsistent with the data and this discrepancy is discussed.     

Projectile angular-differential cross sections for single electron transfer in fast He~+-He collisions

The four-body Coulomb–Born distorted wave approximation is applied to investigate the integral as well as projectile angular-differential cross sections for single-electron capture in the collision of energetic singly positive charged helium ions with helium atoms in their ground states. The formalism satisfies the correct boundary conditions. The influence of the dynamic electron correlations on the cross sections is studied by considering the inter electronic interactions in the complete perturbation potentials in post form. Also, the sensitivity of the cross sections to the static electronic correlations is studied by using the single-zeta and the highly correlated Byron–Joachain wave functions to describe the initial bound state of the active electrons. The obtained results for the energy range of 40–5000 ke V/amu are reported and compared with other three- and four-body theoretical data and available experimental measurements. The comparison leads us to discuss the validity of the applied approach and survey the interaction effects on the cross sections by recognizing the electron–electron interaction. Particularly, for differential cross sections, the comparison of the present four-body method with the experiment shows that the agreement is not as good as that for its three-body version.