Fusion cross section for 13C + 13C at low energies

The energy dependence of the fusion cross section has been measured over the range E_c.m. = 3.05–6.88 MeV by detecting the γ-rays from residual nuclei in a 4π geometry. Analyzing the 1.37 MeV photopeak, originating from ${}^{24}\text{Mg}\text{1.37}\text{MeV}\text{→}\text{g.s. transition}$, the cross sections for ²⁴Mg+2n channel were also deduced. The measured fusion cross sections have been compared with those for ¹²C + ¹²C and ¹²C + ¹³C systems and found to be significantly different. For ¹³C+¹³C the fusion cross sections agree with the standard optical-model prediction down to the lowest measured energies, while for ¹²C + ¹²C and ¹²C + ¹³C they are, at the lowest energies, too low. It is suggested that the unpaired valence nucleons facilitate fusion at energies well below the Coulomb barrier.     

Fusion cross-section measurements for the 13C+13C reaction

Absolute γ-ray yields from characteristic low-lying levels in nuclei produced in the ¹³C+ ¹³C reaction have been measured from E_c.m. = 4.0 to 15.8 MeV using an intrinsic germanium detector. Statistical-model calculations of the decay modes of the compound nucleus have been used to deduce absolute cross sections for the production of the observed residual nuclei and to determine the fusion cross section. Consistency checks on the adopted procedure lead to an estimated absolute uncertainty of ± 15 % on the deduced cross sections. Over the energy range covered, no striking evidence has been found for either broad single-particle resonances or for narrow non-statistical resonances in the cross sections for individual channels. Comparisons are made with optical-model calculations of the reaction cross section and with different expressions for the fusion cross section.     

Scattering and reactions of 14C + 14C and 14C + 14C

We have studied elastic scattering, inelastic scattering and several transfer channels of the systems ¹⁴C + ¹⁴C and ¹⁴C + ¹²C over a wide range of energies up to E_c.m. = 35 eMeV and 32 MeV, respectively. The reaction channels were identified by means of kinematic coincidences between solid-state detectors, γγ coincidences were measured to determine cross sections for mutual inelastic scattering of ¹⁴C + ¹⁴C.Pronounced regular gross structures, similar to those found for ¹⁶O + ¹⁶O, are observed in the elastic excitation function of ¹⁴C + ¹⁴C at θ_c.m. = 90°, The angular distributions measured at the energies of the maxima and an optical-model analysis suggest that one or a few surface partial waves dominate the scattering behaviour. Correlated structure of narrower width is found in the inelastic channels and, to a lesser degree, in the transfer channels which appear with rather small cross sections.In ¹⁴C + ¹²C elastic scattering the gross structures are strongly fragmented, in contrast to ¹⁴C + ¹⁴C but similar to ¹²C + ¹²C. While the ¹²C(2⁺) excitation is very weak, the observed strengths of the ¹⁴C(3^?) excitation and of neutron transfer point to a substantial role of these channels as coupling partners to the elastic configuration and to their influence on the elastic scattering behaviour. A correlated intermediate structure is observed near 23.5 MeV, where a dominance of l = 18 is suggested by the elastic scattering angular distribution. This unexpectedly high l-value exceeds l_graz at this energy by at least two units of ?.     

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.     

Reaction and fusion cross sections for 32S on 27Al and 48Ti

Elastic scattering and evaporation residues have been measured for the system ³²S + ²⁷Al at E_c.m. = 66.4, 73.2 MeV and ³²S + ⁴⁸Ti at E_c.m. = 96.0 MeV. Reaction cross sections have been obtained by use of the optical theorem and are found to be about 60 % larger than the fusion cross sections.     

On the fusion cross section for 16O + 12C

The total fusion cross section σ_f for ¹⁶O + ¹²c.m. has been measured in 250 keV steps between 17 and 28 MeV c.m. energy via γ-ray techniques. Individual yields for 10 nuclides in the evaporation chain were determined. The oscillations in σ_f, which agree in gross structure but not in detail with previous work, appear to be most closely associated with reactions leading to ²⁰Ne. It is observed that the reaction yield is >80% dominated by nuclides having at least one α particle in the evaporation chain.     

The compound nucleus reaction 12C(11B, 2α) 15N

Energy spectra and differential cross sections of nitrogen products formed in the reaction 28 MeV ¹¹B + ¹²C have been measured using a ΔE?E counter telescope. The energy spectra are smooth and therefore indicate that the nitrogen products were formed by a compound nucleus mechanism, via the formation and decay of the compound nucleus ²³Na. The experimental results are compared with statistical model calculations and good agreement is obtained. This result provides further evidence for the importance of the compound nucleus mechanism in heavy ion reactions with light nuclei and also gives added validity to the statistical model for light compound systems.     

Boron+boron sub-Coulomb energy total reaction cross sections

Total reaction cross sections have been measured for the following reactions and energy intervals: ¹¹B+¹¹B, E_c.m. = 1.56–3.65 MeV; ¹⁰B+¹¹B, E_c.m. = 1.61–3.94 MeV; ¹⁰B+¹⁰B, E_c.m. = 1.84–3.66 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by large NaI detectors. The absolute accuracy of the method is thoroughly discussed and tested via a measurement of the ¹²C+¹²C reaction. For all three boron cases measured neither intermediate nor giant type resonances were observed. The cross sections are well described by optical model calculations based on lowenergy ¹¹B+¹¹B elastic scattering parameter sets.     

Compound transfer and direct transfer reactions induced by 17O on 13C

The elastic scattering, inelastic scattering, single-neutron transfer reactions ¹³C(¹⁷O, ¹⁶O) ¹⁴C, ¹³C(¹⁷O, ¹⁸O)¹²C and ¹³C(¹⁷O, ¹⁸O_{2+, 1.98})¹²C, and seven other exit channels which involve ⁷Li, ⁹Be, ¹¹B and ¹⁵N have been measured for the system ¹⁷O+¹³C at 12.9 and 14 MeV c.m. It is shown that all reactions mentioned above have significant contributions from compound nuclear decay, following fusion of projectile and target.     

12C1 and 8Be production in 12C + 208Pb collisions

The mechanisms involved in the production of fast α-particles in ¹²C-induced reactions have been studied for the ¹²C + ²⁰⁸Pb system at the bombarding energies of E_12c = 132, 187 and 230 MeV. Absolute cross sections for the reactions ²⁰⁸Pb(¹²C. ¹²C¹→α + ⁸Be), ²⁰⁸Pb(¹²C, ⁸Be(g.s.)) and ²⁰⁸Pb(¹²C, ⁸Be(2.94 MeV)) have been determined by coincidence measurement of two or three correlated α-particles. Inclusive α-particle production cross sections were also measured at E_12c = 187 MeV. It is found that the inelastic process (¹²C, ¹²C¹→α + ⁸Be) does not contribute significantly to fast α-particle production but that the production of ⁸Be by projectile fragmentation is an important source of α-particles. At the highest bombarding energy (230 MeV) it appears that the ¹²C → 3α fragmentation reaction becomes more prominent at the expense of the ¹²C→α + ⁸Be fragmentation channel.     

Non-statistical effects in the 12C(12C, α)20Ne reaction near Ec.m. = 15 MeV

The ¹²C(¹²C, α)²⁰Ne reaction is studied near E_c.m. = 15 MeV. Angular distributions for three energies and excitation functions at θ_{lab = 30°} over an energy range E_c.m. = 14.5?15.4 MeV for about 20 levels in ²⁰Ne (E_ex = 0–13 MeV) are examined. The statistical analysis yields the results that a correlated resonance is present at E_c.m. = 14.75 MeV. A nonstatistical contribution to the reaction is also apparent when energy-averaged cross sections are compared with the Hauser-Feshbach model predictions. Strong population of the 0⁺₃ band in ²⁰Ne is observed.     

Structure of 13C from an R-matrix analysis of 12C + n scattering and reaction cross sections

Differential cross sections for ¹²C + n elastic and inelastic scattering and for the ²C(n, α) ⁹Be reaction, together with high resolution total cross-section data were analyzed by means of a multilevel multichannel R-matrix program to determineJ, π, and γ_λc for states in ¹³C up to E_x = 13.5MeV. Good overall fits to the data were obtained throughout this large energy range. Spin and parity assignments for thirteen states above E_x = 9.5MeV for which there had been either no previous J^π assignments or only tentative assignments have been made in this study. The present results are in good agreement with previous analyses and model calculations.     

Elastic scattering of 17, 18O on 12, 13C at Ec.m. = 12.6 – 14.0 MeV

The angular distributions of the elastic scattering of ^{17, 18}O on ^{12, 13}C were measured at c.m. energies between 12.6 to 14.0 MeV. A rise of the cross section at backward angles was observed. Standard optical-model fits were found to reproduce reasonably well the forward part of the cross section, but fail at backward angles. Possible contributions of first-order cluster exchange and compound-nucleus reactions are discussed. Excitation functions of various exit channels in the ¹⁸O + ¹²C system were measured at backward angles in the energy range of 12.0 to 14.8 MeV c.m. No significant correlation was found between any of these cross sections.     

Intermediate resonance of inelastic 12C + 12C scattering

The intermediate resonances observed in the inelastic ¹²C + ¹²C cross sections to the single and mutual 2₁⁺(4.43 MeV) excitations and the single 3₁^? (9.64 MeV) excitation are studied by the coupled-channel method with the use of the coupling interaction derived by the folding procedure between ¹²C and ¹²C. It is shown that the model is successful in reproducing the gross structures of the inelastic cross sections and especially the correlated resonance energies of the inelastic channels. The inelastic resonances are shown to be due to the molecular resonances in an adiabatic potential between two ¹²C, which reproduces correctly the coupled channel resonances.     

Alignment and resonances in 12C+12C inelastic scattering

Using the out-of-plane γ-ray particle coincidence method we have measured the spin alignment P_zz of excited ¹²C(2⁺) nuclei from ¹²C+¹²C inelastic scattering in the energy range 16 MeV ? E_cm ? 33 MeV.P_zz varies strongly as a function of energy and angle. The correlation of resonant structures in the cross section with maxima of the alignment is particularly clear in mutual inelastic scattering and in θ_cm = 90° single inelastic scattering.     

Resonant behaviour of the 16O-12C elastic scattering cross section

Resonances in the elastic scattering of ¹⁶O by ¹²C are reported at E_c.m. = 17.29 and 20.79 MeV, with respective J^π assignments of 11^? and 13^?. A 14⁺ spin assignment is shown to be more probable for the resonance at 22.79 MeV than a previous tentative assignment of 16⁺. A correlation is found between maxima of the total fusion cross section and the position of odd angular momentum resonances.     

Spins of resonances in the 12C + 12C system

By measuring angular distributions we have assigned J^π = 6⁺ to a resonance at E_c.m. = 7.50 ±0.05 MeV in the ¹²C + ¹²C system.     

12C+13C在库仑位垒以下能区的熔合截面测量

深垒下能区的12C+13C熔合截面测量对检验天体中熔合反应外推模型具有很重要的意义。目前在库仑位垒以下能区存在的各种测量结果,都利用了统计模型来修正得到熔合截面,但对于这些方法间的系统误差仍没有很好地研究。实验采用离线活度测量的方法,在E_c.m.=4.4～5.8 MeV能区内对12C+13C熔合截面进行测量。经Hauser-Feshbach统计模型对分支比的修正后,熔合总截面由24Na活度推导出。通过本实验数据与其它实验方法获得的数据进行比较,确定了统计模型的系统误差为14%。The study of fusion reactions of 12C+13C at the deep sub-barrier energies is very important for the test of predictive power of the extrapolation models for nuclear reactions for astrophysics. Until now, all the measurements below Coulomb barrier energies have to use the statistical model calculations to estimate the branching ratios to deduce the total fusion cross sections. However, the systematic uncertainty induced by the calculated corrections has not been studied well. In this experiment, the fusion cross sections of 12C+13C have been measured using an offline activity measurement in the range of E_c.m.=4.4 to 5.8 MeV. The total fusion cross sections have been deduced from the 24Na activities after correcting the branching ratios estimated with the Hauser-Feshbach statistical model. Through the comparison between our result and other data obtained with other methods, the systematic uncertainty of statistical model has been determined to be 14%.     

Unexpected interference patterns observed in the 12C(14N, 13N)13C reaction at energies close to the Coulomb barrier

The reaction ¹²C(¹⁴N, ¹³N)¹³C has been measured at 28, 32, 34 and 36 MeV beam energies. The energy dependence of the measured interference pattern cannot be reproduced by DWBA calculations which take account of the interference between proton and neutron transfer. A rather strong asymmetry of the angular distributions about θ_c.m. = 90° has been observed.     

Limitation to complete fusion in the reactions 12,13C+48Ti and 30Si+30Si

Excitation functions of the reactions ^{12, 13}C+⁴⁸Ti and ³⁰Si+³⁰Si were measured by in-beam γ-ray spectrometry in the energy ranges 20–60 MeV for the ^{12, 13}C induced reactions and 55–126 MeV for the ³⁰Si+³⁰Si reaction. Light-particle angular distributions were measured at 46 MeV and 47.5 MeV for the ¹³C and ¹²C induced reactions. Measurements of elastic scattering angular distribution and particle-γ coincidences were carried out for the system ¹³C+⁴⁸Ti at 46 MeV. The limitation to complete fusion detected for the system ³⁰Si+³⁰Si appears to be related to entrance channel effects and is well reproduced by a barrier penetration calculation using the KNS potential. The angular distribution measurements carried out for the ¹²C+⁴⁸Ti and ¹³C+⁴⁸Ti systems allowed to identify an incomplete fusion mechanism with emission of direct α-particles before the formation of a fully equilibrated system.