Low energy fusion of 12C + 12C and 16O + 16O systems

The adiabatic time-dependent Hartree-Fock method (ATDHF) is applied to the calculation of low energy fusion of ¹²C + ¹²C and ¹⁶O + ¹⁶O systems. The energy dependence of the results is in good agreement with experiment, while the order of magnitude is not correct. It is shown that the dynamical effects included in ATDHF are very important and cannot be neglected at the energies of astrophysical interest.     

Radiative pion capture in 12C and 16O

Radiative pion capture in ¹²C and ¹⁶O is investigated. An effective interaction Hamiltonian based upon the CGLN theory is employed. Capture rates in ¹²C and ¹⁶O from Is and 2p pionic orbits are calculated by using the nuclear model of Kamimura, Ikeda and Arima for the odd parity states of ¹²C, and that of Walker with strong ground state correlations, for the odd parity states of ¹⁶O. The results are compared with those of the 1p-1h nuclear model under the Tamm-Dancoff and random phase approximations of Gillet and Vinh Mau. Detailed examinations are made for the transitions to low-lying states with 1⁺ and 2⁺ for ¹²C and with 1^?, 2^? and 3^? for ¹⁶O by using the Cohen-Kurath and the Walker models, respectively. The results are in good agreement with the recent experimental data from Berkeley.     

The 12C(18O, α)26Mg and 12C(18O, 8Be)22Ne reaction

Excitation functions for α-emission leading to the ground and first excited states of ²⁶Mg and ⁸Be emission leading to the ground and first and second excited states of ²²Ne have been measured at several forward angles for E_c.m. = 15 to 22.4 MeV. There is little evidence for correlated structure. The angular distribution at 16.5 MeV for the α + ²⁶Mg(g.s.) channel is rather structureless while that for the ⁸Be+²²Ne(g.s.) channel appears to be dominated by a J = 13 contribution. Statistical model calculations indicate that much of the yield for both the α and ⁸Be exit channel is compound nuclear in origin, with some indication of a larger direct contribution for the ⁸Be channel at the lower end of the bombarding energy range.     

12C(7Li,t)16O and stellar helium fusion

The reaction ¹²C(⁷Li, t)¹⁶O has been studied at $\text{E(}{}^7\text{Li}\text{) = 34}\text{MeV}$ with the LASL tandem accelerator and QDDD magnetic spectrometer. Angular distributions to levels with E_x < 11 MeV have been obtained from 0° to 90°, including 0°. The results have been analyzed with finite-range distorted-wave Born approximation theory. The α-particle spectroscopic factors and reduced widths obtained are compared with those calculated with group theory (SU(3)) and other models. The analysis of data for the 7.1 and 9.6 MeV J^π = 1^? levels, which are of great importance in stellar helium buring, yields a ratio, R, of dimensionless reduced α-widths $\text{θ}{}^2{}_{\mathrm{<mtext>a</mtext>}}\text{(7.1}\text{MeV}\text{)}\text{θ}{}^2{}_{\mathrm{<mtext>a</mtext>}}\text{(9.6}\text{MeV}\text{)}\text{= 0.35b ± 0.13}$. The observed line width of the 9.6 MeV level (Γ_c.m. = 390 ± 60 keV) is less than the accepted value (Γ_c.m. = 510 ± 60 keV) and implies θ²_a(9.6 MeV) ≈ 0.6. These results as well as data for the 6.92 MeV J^π = 2⁺ and 10.35 MeV J^π = 4⁺ “α-cluster” states indicate 0.09 < θ²_a(7.1 MeV) < 0.33 with a mean value θ²_a(7.1 MeV) = 0.14 ± 0.04. The implication for stellar helium burning is discussed.     

Microscopic analysis of the 12C(α, γ)16O reaction

Electric transition probabilities in the ¹⁶O spectrum, and the ¹²C(α, γ_o,3¹⁶O capture cross sections are calculated with antisymmetric wave functions by the generator coordinate method. The influence of bound states on radiative capture is shown to be automatically included in the model. The reduced α-widths of the ¹⁶O bound states are discussed, and compared with previous theoretical and experimental estimates. The microscopic E2 capture cross sections to the O⁺₁ and 2₁⁺ states yield an astrophysical S-factor of 0.09 MeV · b at 0.3 MeV. An attempt to treat the El multipolarity by relaxing the long-wavelength approximation leads to a large underestimation of the γ-widths. Adopting the experimental γ- width and the theoretical reduced α-width of the 1₁^? state provides s_E1 = 0.30 MeV · b at 0.3 MeV.     

12C(7Li,t)16O和20Ne(d,6Li)16O反应的研究

本文把用于处理重离子引起的单粒子转移反应的Goldfarb-Buttle方法推广到多粒子转移反应。计算了¹²C(⁷Li,t)¹⁶O和²⁰Ne(d,⁶Li)¹⁶O反应,用了¹⁶O的全相干波函数,考虑了某些反冲因素,并将结果与实验作了比较。     

The reaction 14C(3He,n)16O and the coexistence model of 16O

The reaction ¹⁴C(³He, n)¹⁶O has been measured at a ³He bombarding energy of 25.4 MeV. The zero-degree differential cross section for the excitation of the three low lying 0⁺T = 0 states, at energies 0.0, 6.05 and 12.05 MeV are, respectively, 1.33 ± 0.10, 0.49 ± 0.10, and 0.50 ± 0.10 mb/sr These measured cross sections are in rough agreement with single-step zero-range DWBA calculations using an empirically determined ¹⁴C ground state wave function and in which the Brown and Green coexistence-model wave functions are used to describe the ¹⁶O 0⁺ states. The angular distribution of the transition to the ground state is measured between 0° and 32°.     

12C(12C, 8Be)16O angular distributions and excitation functions between 35 and 69 MeV bombarding energy

An array of eight detectors has been developed for identifying the particle unstable ⁸Be nucleus from nuclear reactions with high detection efficiency. Absolute cross sections have been measured for the reaction ¹²C(¹²C, ⁸Be_g.s.)¹⁶O to the ground state and to several excited states in ¹⁶O. Excitation functions at seven angles from 15° to 45° (lab) in 5° steps have been measured for bombarding energies between E¹²_C(lab) = 35 and 69 MeV. Excitation functions were obtained for the following states in the residual nucleus ¹⁶O which were found to be strongly populated: g.s.(0⁺); 6.1 MeV (0⁺, 3^?); 6.9 MeV (2⁺); 10.4 MeV (4⁺); 11.1 MeV (4⁺); 14.7 MeV (6⁺,…) and 16.3 MeV (6⁺,…). The energy range is covered in 250 keV (c.m.) steps; at certain energy ranges in ¹²⁵ keV or 50keV steps. All excitation functions exhibit a strong energy dependence of the cross section; pronounced gross structures with superimposed fine structures, similar to those observed for ¹²C+¹²C elastic and inelastic scattering at these energies, are observed. At 19.3 MeV, where resonant structures were observed in the reactions ¹²C(¹²C, p)²³Na, ¹²C(¹²C, n)²³Mg and ¹²C(¹²C, d)²²Na, no resonance is found for the reaction studied here. At 60, 61 and 63 MeV angular distributions have been measured in 1° and 2.5°(lab) angular steps. The excitation functions have been analyzed in terms of Ericson fluctuations and cross-correlation functions.     

在独立α集团模型下对敲出反应16O(p,pα)12C和16 O(α,2α)12C的研究

在独立α集团模型下，利用扭曲波冲量近似(DWIA)，计算了实验室系下入射能量为101.5MeV 的敲出反应¹⁶O(p，pα)¹²C和实验室系下入射能量分别为90Me V和140MeV 的敲出反应¹⁶O(α,2α)¹²C.得到的反应截面和谱因子与实 验数据基本符 合，比用壳模型的结果有了一定的改进，表明独立α集团模型能较好地描述α集团敲出反应 的机理. 关键词： α集团模型 敲出反应 反应截面 谱因子     

Microscopic study of the 12C + 16O system

An angular momentum projected microscopic calculation is performed for the ¹²C + ¹⁶O system with an effective nuclear force and the exact Coulomb interaction. The ¹²C wave function is projected on a 0⁺ state. Parametrizations of the Coulomb interaction between the nuclei are fitted. The L-projected energy curves present a quite complicated structure especially for the negative parity states. The role played by critical angular momenta is put into evidence. A generator coordinate calculation gives several bands of bound, quasibound and virtual states. Excellent agreement in energy and angular momentum is obtained with the 13.7 MeV (J = 9), 19.7 MeV (J = 14), 22.7 MeV (J = 15) and other resonances.     

The sub-Coulomb 12C + 12C resonances in a microscopic 12C+12C,α+20Ne, 8Be+16O cluster basis

The low-J resonances in the Coulomb barrier region of the ¹² C+¹²C system are investigated in the framework of a microscopic cluster model basis including ¹²C+¹²C, α+ ²⁰Ne, and su8 Be+ ¹⁶O fragment decompositions. Calculations are carried out in an orthogonality condition model approximation in which Pauli-forbidden components are properly excluded from the basis but in which the interaction among cluster fragments is approximated by a local potential, obtained from a gaussian NN interaction by a folding procedure leading to both spherical and Q · Q terms. Only minor adjustments of overall strength and fall-off parameters are introduced to gain a consistent picture of the low-energy spectrum in the separate rearrangement channels. The basis includes cluster relative motion excitations with oscillator quanta from 12 to 20 and is not quite rich enough to give a detailed quantitative comparison between theory and experiment. Predicted excitation energies are too high by ~ 3 MeV and predicted ¹²C partial widths are too small to indicate a well-developed surface-peaked molecular character; but it does appear possible to identify a 5 MeV region as the potential seat of the 0⁺, 2⁺, 4⁺ resonances. The number and approximate spacing of the resonance fine structure components are in agreement with experiment.     

Energy dependence of the 24Mg(16O, 12C)28Si reaction

Excitation functions for the reaction ²⁴Mg(¹⁶O, ¹²C)²⁸Si(g.s., 2⁺₁) were measured at 5°(lab) in the energy range 32 < E_c.m. < 49 MeV. Although the resonant structure, previously observed at lower energies, becomes progressively weaker, three new correlated maxima have been observed near E_c.m. = 37.5, 40.2 and 43.5 MeV. Angular distribution measurements at these energies yield spin assignments, from P²_j(cos θ) comparisons, of 27, 29 and 31, respectively. Attempts to find a consistent optical-model fit to the elastic scattering in the entrance channel and an exact finite-range DWBA fit to the four-nucleon transfer reaction in this energy range were unsuccessful. Such a failure is to be expected if strong couplings between the elastic channel and inelastic channels of either the initial or final system are important. The features of the resonance phenomena in the transfer reaction are discussed within a band crossing model framework.     

Four-nucleon transfer with the 32S(16O, 12C)36Ar reaction

Angular distributions have been measured for the ³²S(¹⁶O,¹²C)³⁶Ar reaction at 45.5 MeV leading to excited states between E_x, = 0 and 8 MeV. Experimental cross sections are compared with exact finite-range DWBA calculations in combination with extensive shell-model calculations, which include sd- and fp-shell configurations. Transitions to low-energy positive-parity states and bound negative-parity states are well reproduced. The calculations, however, fail to describe some high-energy positive-parity states. Calculations with a complete cluster expansion for the four transferred nucleons give about 50% larger cross sections, but can not explain the observed discrepancies. Possible interference of reaction processes other than direct α-transfer and special structure effects are discussed.     

Microscopic study of elastic 12C+16O scattering

The L=0 to 17 phase shifts are calculated microscopically for elastic ¹²C+¹⁶O scattering with a generator coordinate method. The experimental resonances are shown to belong to four different bands. Interpretations and spin assignments are suggested for several recently observed anomalies. A spin J=15 seems likely for the 22.8 MeV resonance. A missing J=13 resonance should be searched for between 17 and 18 MeV.     

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.     

Comparative study of the selectivity displayed by (6Li,d) and (16O, 12C) reactions

Four-particle-transfer processes induced by the (⁶Li, d) and (¹⁶O, ¹²C) reactions to strongly excited 0⁺ states are compared. Although the selectivity displayed by these reactions is similar, the corresponding relative cross sections are rather different. These results emerge naturally from a simple microscopic model.     

Search for resonances in 12C(9Be, α)17O

Excitation functions at 7° (lab) have been measured from E_c.m. = 5.1 to 11.4 MeV in approximately 114 keV steps for 15 groups of final states in ¹⁷O populated by the ¹²C(⁹Be, α) reaction. Statistical tests have been used to locate possible non-statistical structure in the excitation functions. Possible anomalies were found near E_c.m. = 6.3, 7.5, 8.9 and 9.7 MeV. Angular distributions were measured at E_c.m. = 9.20, 9.71 and 10.23 MeV for the three lowest excited states in ¹⁷O. The data have been compared with Hauser-Feshbach calculations in addition to the following reaction mechanisms: compound plus a single resonance, compound plus interfering resonances and compound plus direct reactions.     

Energy dependence of transition strengths extracted from 12C(τ, α) and 16O(τ, α)

The (τ, α) reaction on ¹²C and ¹⁶O has been studied at 24 and 28 MeV bombarding energy. Differential cross sections have been obtained and analysed with DWBA to yield relative spectroscopic factors. The comparison with results obtained at lower bombarding energies shows that the strengths of some anomalous shell-model-forbidden transitions decrease with energy. This agrees qualitatively with the prediction of a reaction model which assumes a cluster substitution mechanism to explain the anomalous (τ, α) transitions.     

Spectroscopy of A = 16 from 13C(6Li,t)16O

The ¹³C(⁶Li, t)¹⁶O reaction has been studied at 34 MeV. Selective population of narrow states is observed up to 21 MeV excitation in ¹⁶O. This reaction populates strongly both unnatural-and natural-parity states that have little or no ¹²C + α₀ width. The measured angular distributions are compared with Hauser-Feshbach and finite-range DWBA calculations. Reasonable agreement with the DWBA calculations is found for most of the states strongly populated. The widths of the narrow states populated in the 16–20 MeV excitation region are presented. Comparison of the present data with that from medium-energy inelastic scattering and other multiparticle transfer reactions is made.     

DWBA analysis of the reaction 12C(α, n)15O

Angular distributions of neutrons from the reaction ¹²C(α, n)¹⁵O(g.s.) have been measured at lab energies from 18.4 to 23.1 MeV and angles ranging from 0° to 130°, using a time-of-flight technique. The experimental curves generally show a forward peaking and a strong dependence on the incident energy. The data were compared with the angular distributions predicted by the distorted-wave theory of direct Nuclear reactions, and no agreement could be obtained when only a stripping mechanism was taken into account.