The4He(12C, γ)16O reaction at stellar energies

The capture reaction⁴He(¹²C, γ)¹⁶O (E _c.m.= 1.34–3.38 MeV) as well as the elastic scattering process⁴He(¹²C,¹²C)⁴He (E _c.m.=1.44–3.38 MeV) have been investigated with the use of an intense¹²C beam and a windowless and⁴He recirculating gas target system. The measurements involved two large NaI(T1) crystals in close geometry to an extended gas target, whereby angle-integrated γ-ray yields were obtained. A large area plastic detector was used for the suppression of time-independent background. A search for cascade γ-ray transitions was carried out by coincidence techniques. The measurement of absolute cross sections is also reported. Theoretical fits of the excitation function for the groundstate γ-ray transition requireE1 as well asE2 capture amplitudes, which are of equal importance at stellar energies. This result increases significantly the stellar burning rate of⁴He(¹²C, γ)¹⁶O and leads to¹⁶O as the dominant product at the end of helium burning in massive stars. The observed capture yield to the 6.92 MeV state is dominated by the direct capture mechanism and plays a small role at stellar energies.     

The 12C(α, γ)16O reaction and stellar helium burning

The cross section for the reaction ¹²C(α, γ)¹⁶O has been measured for a range of c.m. energies extending from 1.41 MeV to 2.94 MeV, by using ¹²C targets of high isotopic purity, large NaI(T1) crystals, and the time-of-flight technique for the suppression of prompt neutron background and time-independent background. Gamma-ray angular distributions were measured at c.m. energies of 2.18, 2.42, 2.56 and 2.83 MeV. By means of theoretical fits, which include the coherent effects of the 1^? states of ¹⁶O at 7.12 MeV, 9.60 MeV, and those at higher energies, the electric-dipole portion of the cross section at astrophysically relevant energies has been determined. A three-level R-matrix parametrization of the data yields an S-factor at E_c.m. = 0.3 MeV, S(0.3 MeV) = 0.14^+0.14_?0.12 MeV · b. A “hybrid” R-matrix optical-m parameterization yields S(0.3 MeV) = 0.08^+0.05_?0.04 MeV · b. This S-factor is of crucial importance in determining the abundances of ¹²C and ¹⁶O at the end of helium burning in stars.     

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.     

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.     

Nuclear reaction cross sections of 16O + 16O obtained by γ-ray detection

The partial production cross sections for reaction residues produced by the fusion of ¹⁶O with ¹⁶O have been measured at E_c.m = 9–30 MeV by detecting the characteristic γ-rays with a Ge(Li) detector. The dominant products are ²⁴Mg and ²⁷A1 corresponding to 2α and αp emission from the compound nucleus, respectively. The total γ-producing cross sections σ_R were also derived by summing the partial cross sections after correction for the observed (average) γ-ray angular distributions. The trend in the total cross sections is very similar to the trends derived from an optical model or a statistical-evaporation model calculation. The partial production cross sections were compared with other experimental results at 11.9 MeV and 30 MeV and with the results of the statistical-model calculation. It is concluded that the treatment of angular momentum in the calculation is inadequate for describing the partial cross sections. Structure in the partial and total cross section excitation functions is observed with minima occurring at E_c.m. = 27, 24, 20, 17.5, and possibly 15 MeV. Some of this structure is well established by the statistical accuracy of the data and most, but perhaps not all of it, is correlated in the various channels. This structure is compared with that observed in another experiment and some of its implications are discussed.     

Total reaction cross section for 12C + 16O below the Coulomb barrier

The energy dependence of the total reaction cross section, σ(E), for ¹²C + ¹⁶O has been measured over the range E_c.m. = 4–12 MeV, by detecting γ-rays from the various possible residual nuclei with two large NaI(Tl) detectors placed close to the target. This technique for measuring total reaction cross sections was explored in some detail and shown to yield reliable values for σ(E). Although the principal emphasis of this work was placed on obtaining reliable cross sections, a preliminary study has been made of the suitability of various methods for extrapolating the cross section to still lower energies. The statistical model provides a good fit with a reasonable value for the strength function, 〈γ²〉/〈D〉 = 6.8 × 10^?2, over the range E_c.m. = 6.5–12 MeV, but predicts cross sections which are much too large for E_c.m. < 6.5 MeV. Optical model fits at low energies are especially sensitive to the radius and diffuseness of the imaginary component of the potential and, since these are still poorly known at present, such extrapolations may be wrong by orders of magnitude. A simple barrier penetration model gives a moderately good fit to the data and seems to provide the safest extrapolation to lower energies at the present time. It is clear, however, that our knowledge of the heavy-ion reaction mechanism at low energies is incomplete, and that cross-section measurements at still lower energies are needed to establish the correct procedure for extrapolating heavy-ion reaction cross sections to low energies.     

Fragmentation of the total cross section in the reaction16O+208Pb

The fragmentation of the total reaction cross section was investigated for¹⁶O +²⁰⁸Pb atE _c.m.=84 MeV andE _c.m.=92 MeV. Total cross sections for the inelastic, transfer and fission channels were measured. The sum of the inelastic and transfer channels accounts for 30% of the total reaction cross section; the residual strength is found in a compoundfission process.     

On the resonant behavior of the16O+15N reaction

The ¹⁶ O+ ¹⁵ N reaction products have been studied by the γ-ray detection method in the CM energy range 15.5 to 36.1 MeV and by the kinematical coincidence method at energies ranging from E _CM =20.6 to 33.5MeV. The γ-ray yield excitation function of the ¹⁶O 3^? inelastic channel shows the existence of resonant structures. Two structures with ～ 1.6 MeV width are observed in the large angle elastic scattering excitation function, they are correlated with the resonances seen in the inelastic channel. Angular momentum assignments were made from the elastic backward angular distributions.     

The resonant behaviour of the heavy-ion reaction14C +16O

The¹⁴C+¹⁶O reaction has been studied by a kinematic coincidence technique at 17 incident energies ranging fromE _c.m.=21.05 to 32.1 MeV. Three broad resonances previously reported at approximately 23, 27 and 31 MeV were confirmed and observed in several channels. The evolution of the elastic angular distributions was correlated with these three resonances.     

9Be + 12C, 9Be + 16O,9Be + 19F reactions at energies below the barrier

The ¹⁶O + ⁹Be reactions have been studied from E_c.m. = 2.0 MeV to 5.1 MeV, an energy near the top of the Coulomb barrier. The cross section for the neutron transfer reaction ⁹Be(¹⁶O,¹⁷O¹ (0.87 MeV))⁸Be has been measured over this range by detecting the prompt 0.87 MeV γ-rays. The total fusion cross section has been determined from E_c.m. = 2.8 to 5.1 MeV by observing individual γ-ray transitions in the evaporation residues with a Ge(Li) detector, and then summing the separate yields. Direct processes are found to dominate the reaction yield below E_c.m. = 4 MeV. A comparison of the energy dependence of the fusion cross section for this reaction and the ¹²C + ¹³C reaction, which proceeds via the formation of the same compound nucleus, ²⁵Mg, reveals differences at sub-barrier energies. Optical model and incoming-wave boundary condition calculations are presented. Data have also been obtained for the near optimum Q-value neutron-transfer reactions ⁹Be(¹²C, ¹³C¹)⁸Be and ⁹Be(¹⁹F, ²⁰F)⁸Be, and these are discussed in terms of a simple model of sub-barrier direct reactions.     

Resonances and fluctuations in the 16O + 15N and 12C + 19F collisions

The search and study of quasi-molecular resonances in the ³¹P composite system populated via two entrance channels are performed with two different experimental techniques. The ¹⁶O + ¹⁵N reaction products have been studied by the γ-ray detection method at cm. energies ranging from 15.5 MeV to 36.1 MeV. Binary channels of the ¹⁶O + ¹⁵N and ¹²C + ¹⁹F collisions have been studied by using the kinematical coincidence method at 26 incident energies ranging from E_c.m. = 20.6MeV to 33.5MeV for the first system, and at energies corresponding to the same excitation energies of the composite system for the second system. The ¹⁶O + ¹⁵N reaction exhibits two prominent gross structures in the large angle elastic scattering excitation function correlated with the resonant structures observed in inelastic channel γ-ray yield measurements. Spin assignments were tentatively made for the two resonances. On the contrary, no such structures can be clearly established in the ¹²C + ¹⁹F system where only indications of non-correlated structures in various channels have been observed.     

Gross structure in γ-ray yields following the 16O + 12C reaction

The γ-ray yield of discrete transitions from evaporation residues formed in the reaction ¹⁶O + ¹²C has been measured between E_{c.m. = 6 and 31 MeV}. Data for a backed and self-supporting target were compared to check the consistency of the observed results. Channels in which α-particles are emitted carry most of the oscillatory structure which was previously observed for the total fusion cross section. Relative yields of the different evaporation channels can be reproduced by statistical model calculations. Optical model calculations with a parity-dependent exchange contribution reproduce the periodicity of the gross structure but underestimate the magnitude of the oscillations.     

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.     

Description of elastic scattering in the <Superscript>16</Superscript>O + <Superscript>16</Superscript>O and <Superscript>16</Superscript>O + <Superscript>12</Superscript>C systems

The objective of the present study was to describe more precisely experimental data on elastic scattering in the ¹⁶O + ¹⁶O system at E _lab = 124, 145, 250, 350, and 480 MeV and in the ¹⁶O + ¹²C system at E _lab = 132, 170, 181, 200, 230, 260, and 281 MeV. The role of exchange interaction in the region of backward angles is investigated. The coefficient of incompressibility of nuclear matter is estimated at K = 205 MeV ± 15%.     

The heavy-ion reaction channels of the system 16O + 16O

The reaction channels of the system ¹⁶O + ¹⁶O with outgoing heavy particles from lithium to magnesium have been measured using a ΔE-E telescope. Excitation functions from 49 to 65 MeV at θ_Lab = 30° and angular distributions from θ_Lab = 10° (20°) to 50° at E_Lab = 51.5 MeV are presented for the strong transitions. The excitation function of the ¹²C-²⁰Ne (4.25 MeV) channel shows a pronounced regular cross structure with peaks at 52 and 60 MeV. A selective excitation of certain states in the inelastic scattering and the ¹²C-²⁰Ne channel is observed; the yields of the other heavy-ion channels being weaker by at least one order of magnitude. An explanation of this phenomenon is given by considering the angular momentum matching between entrance and exit channels. Furthermore it is shown that no strong dependence of the cross sections on the transferred angular momentum or on the nuclear structure of the final states is observed. Possible implications of these results on the reaction mechanism are discussed.     

Intermediate width structures in the 12C(12C,8Beg.s.)16O reaction at E c.m. =20 to 30 MeV

The ¹²C(¹²C,⁸Be_g.s.)¹⁶O reaction cross section has been measured at center-of-mass energies between 20 and 30 MeV. Intermediate width structures have been observed for the reactions leading to the ground state and two doublets of states, 6.05/6.13 MeV and 6.92/7.12 MeV, in ¹⁶O. For the ⁸Be_g.s.+¹⁶O_g.s. channel the dominant angular momenta contributing to several structures have been deduced by the analysis of the excitation functions at selected center-of-mass angles. Correlations between the structures in the ⁸Be_g.s.+¹⁶O_g.s. channel and in other inelastic scattering channels in the E _c.m. = 30 MeV region are discussed. An interpretation of the resonances in terms of current structural models is given     

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 ?.     

Nonstatistical structures in the excitation functions of20Ne(16O,12C)24Mg and20Ne(16O,20Ne)16O reactions

The data on the excitation functions of²⁰Ne(¹⁶O,¹²C)²⁴Mg,²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(1.37, 2⁺),²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(4.12, 4⁺+4.24, 2⁺) +²⁰Ne(¹⁶O,¹²C^*(4.44, 2⁺))²⁴Mg,²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(6.01, 4⁺+6.43, 0⁺),²⁰Ne(¹⁶O,²⁰Ne)¹⁶O,²⁰Ne(¹⁶O,²⁰Ne^*(1.63, 2⁺))¹⁶O, and²⁰Ne(¹⁶O,²⁰Ne^*(4.25, 4⁺))¹⁶O reactions atθ _lab=13° fromE _c.m.=22.8 to 38.6 MeV have been subjected to a statistical analysis comprising of the calculations of the distribution of cross sections, deviation functions, cross-correlation functions, summed excitation functions, cross-channel correlation coefficients and coherence widths. The analysis confirms the existence of nonstatistical structures atE _c.m.=24.6, 27.8, 31.7 and 35.5 MeV, and identifies a new structure of the same nature atE _c.m. =25.6 MeV.     

Coupled-channels study of projectile and target excitation in the scattering of 6Li from 12C and 16O

Coupled-channels calculations are presented tor elastic and inelastic ⁶Li + ¹²C scattering at E_c.m. = 16 MeV and 20 MeV, and for ⁶Li + ¹⁶O at 18.7 MeV. Excitation of states within ⁶Li, ¹²C and ¹⁶O are treated with rotational, rotation-vibration and vibrational models only. The 3⁺⁶Li and 2⁺¹²C states are strongly coupled to the elastic scattering and reduce the strengths of both the real and imaginary potentials. The 3^?16O state reduces only the strength of the imaginary potential. All other states are weakly coupled and have little effect on each other or the potential. The data are reasonably well described, with there being some preference for the 3^? state in ¹²C to be K = 0. Excitation of the 0₂⁺ state in ¹²C requires a combination of β-vibration and monopole breathing-mode form factors. The deformation lengths found are in poor agreement with those deduced from electron or proton scattering.     

Spins of resonances in the 12C + 16O system

The spins of resonances appearing at 22 MeV c.m. entrance channel energy in the ¹²C + ¹⁶O system are determined. Several inelastic transitions are used and a value of J^π = 15^? is deduced. This value disagrees with a previous J^π = 14⁺ assignment based on elastic scattering, but agrees with the J^π = 15^? value predicted at this energy by a recent microscopic calculation of ¹²C + ¹⁶O scattering.