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.     

Selectivity of the 12C(18O, 16O)14C reaction

A study about the ¹²C(¹⁸O, ¹⁶O)¹⁴C two-neutron transfer reaction was performed at the Catania INFN-LNS laboratory at 84 MeV incident energy. The ¹⁶O ejectiles produced in the reactions were momentum analyzed and identified by the MAGNEX spectrometer. The Q-value spectrum of ¹⁴C shows several known bound and resonant states, in particular states with 2p-4h configuration respect to the ¹⁶O core. The integrated cross sections show an enhanced yield for the two-neutron transfer compared to the one-neutron transfer. These results are some experimental evidences that the (¹⁸O, ¹⁶O) reaction proceeds mainly by the direct transfer of the neutron pair, instead of a second order process.     

The K-matrix parametrization of the 12C(α, γ)16O cross section

The experimental data on the El part of the ¹²C(α, γ)¹⁶O cross section and the l = 1 phase shift of ¹²C(α, α)¹²C are analyzed in terms of a two-channel, two-level approximation of a modified K-matrix. The latter allows a unitary parametrization, avoids computing Coulomb wave functions and does not require introducing channel radii; at low energies, it differs very little from the conventional K-matrix. Simple results are obtained which allow the extrapolation of the ¹²C(α, γ)¹⁶O cross section to lower energies of astrophysical interest (E_α(c.m.) ≈ 300 keV). Our results are compared with those of other parametrizations and suggestions are made to improve the uncertainties resulting from the best data presently available.     

Measurement of the cascade transition via the first excited state of 16O in the 12C(alpha,gamma)16O reaction, and its S factor in stellar helium burning

Radiative alpha-particle capture into the first excited, J(pi)=0+ state of 16O at 6.049 MeV excitation energy has rarely been discussed as contributing to the 12C(alpha,gamma)16O reaction cross section due to experimental difficulties in observing this transition. We report here measurements of this radiative capture in 12C(alpha,gamma)16O for center-of-mass energies of E=2.22 MeV to 5.42 MeV at the DRAGON recoil separator. To determine cross sections, the acceptance of the recoil separator has been simulated in GEANT as well as measured directly. The transition strength between resonances has been identified in R-matrix fits as resulting both from E2 contributions as well as E1 radiative capture. Details of the extrapolation of the total cross section to low energies are then discussed [S6.0(300)=25(-15)(+16) keV b] showing that this transition is likely the most important cascade contribution for 12C(alpha,gamma)16O.     

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.     

On the Gross Structure of Fusion Cross Section for 16O+12C System

The gross structure appeared in the total fusion cross section for ¹⁶O+¹²C system is studied by using the LCNO theory and the folding model of the paritydependent potential.The experimental data of the fusion cross section,elastic scattering excitation functions and angular distributions for this system are well explained.     

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.     

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.     

Elastic alpha-12C scattering and the 12C(alpha,gamma)16O E2 S factor

Angular distributions of 12C(alpha,alpha)12C have been measured for E(alpha) = 2.6-8.2 MeV, at angles from 24 to 166, yielding 12 864 data points. R-matrix analysis of the ratios of elastic scattering yields a reduced width amplitude of gamma12 = 0.47 +/- 0.06 MeV(1/2) for the Ex = 6.917 MeV (2+) state in 16O(a = 5.5 fm). The dependence of the chi2 surface on the interaction radius a has been investigated and a deep minimum is found at a = 5.42(+0.16)(-0.27) fm. Using this value of gamma12, radiative alpha capture and 16N beta-delayed alpha-decay data, the S factor is calculated at E(c.m.) = 300 keV to be S(E2)(300) = 53(+13)(-18) keV b for destructive interference between the subthreshold resonance tail and the ground state E2 direct capture.     

Cluster knockout reactions

Cluster knockout reactions are expected to reveal the amount of clustering (such as that of α, d and even of heavier clusters such as¹²C, ¹⁶O etc.) in the target nucleus. In simple terms, incident medium high-energy nuclear projectile interacts strongly with the cluster (present in the target nucleus) as if it were existing as a free entity. Theoretically, the relatively softer interactions of the two outgoing particles with the residual nucleus lead to optical distortions and are treated in terms of distorted wave (DW) formalism. The long-range projectile–cluster interaction is accounted for, in terms of the finite range (FR) direct reaction formalism, as against the more commonly adopted zero-range (ZR) distorted wave impulse approximation (DWIA) formalism. Comparison of the DWIA calculations with the observed data provide information about the momentum distribution and the clustering spectroscopic factor of the target nucleus. Interesting results and some recent advancements in the area of (α, 2 α) reactions and heavy cluster knockout reactions are discussed. Importance of the finite-range vertex and the final-state interactions are brought out.     

On the nuclear interaction potential in the reactions with heavy ions

The interaction potential of heavy ions⁴He,⁶Li,¹²C and¹⁶O is constructed in the folding model. The density distribution of nuclear matter for these nuclei is calculated in the framework of the hyperspherical function method. For the calculation of the folding potentials we have employed the Skyrme nucleon-nucleon forces. The influence of several effects on the results of calculations is studied: the role of the three-body forces of the nucleon-nucleon interaction, dependence of the folding potential on the mass numbers of the colliding nuclei and the possibility of observing the monopole resonance in the ion inelastic scattering. Using our folding potential as a real part of the optical potential we have calculated the differential cross section of elastic scattering of⁶Li from¹²C at laboratory energy of lithium ionsT _L =90.0 MeV. Reasonable agreement with experiment is obtained.     

Electron-induced neutron knockout from 4He

The differential cross section for electron-induced neutron knockout in the reaction 4He(e,e(')n)(3)He has been measured for the first time with a statistical accuracy of 11%. The experiment was performed in quasielastic kinematics at a momentum transfer of 300 MeV/c and in the missing-momentum range of 25-70 MeV/c. The comparison of the data with theoretical calculations shows an impressive increase of the cross section resulting from final state interaction effects. Specifically, the p-n charge-exchange process dominates the cross section in this kinematical regime.     

Cross sections for the 11.08 (3+) and 11.096 MeV (4+) states in 16O by 12C(6Li,d) and 13C(6Li,t)

Particle and particle-γ measurements were performed to determine the cross sections for population of the 8.87 (2^?), 10.35 (4⁺), 11.08 (3⁺) and 11.096 MeV (4⁺) states in ¹⁶O by the ¹²C(⁶Li, d) and ¹³C(⁶Li, t) reactions in the energy range from 20—34 MeV. In general, statistical compound nuclear calculations correctly predict the magnitude of the cross sections of the unnatural parity states and underpredict those for the natural parity states. The population of the 10.35 MeV 4⁺ state in the ¹³C(⁶Li, t) reaction is correctly predicted by these calculations. These measurements support earlier claims that the large ¹²C(⁶Li, d) cross section to the 11.096 MeV 4⁺ state is a result of multistep processes.     

First direct measurement of the total cross-section of 12C(α,γ)16O

The total cross-section of ¹²C(α,γ)¹⁶O was measured for the first time by a direct and ungated detection of the ¹⁶O recoils. This measurement in inverse kinematics using the recoil mass separator ERNA in combination with a windowless He gas target allowed to collect data with high precision in the energy range E = 1.9 to 4.9 MeV. The data represent new information for the determination of the astrophysical S(E) factor.     

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.     

12C(alpha,gamma)16O: the key reaction in stellar nucleosynthesis

The angular distributions of gamma rays from the 12C(alpha,gamma)16O reaction have been measured at 20 energy points in the energy range E(cm) = 0.95 to 2.8 MeV. The sensitivity of the present experiment compared to previous direct investigations was raised by 1-2 orders of magnitude, by using an array of highly efficient ( 100%) Ge detectors shielded actively with BGOs, as well as high beam currents of up to 500 microA that were provided by the Stuttgart Dynamitron accelerator. The S(E1) and S(E2) factors deduced from the gamma angular distributions have been extrapolated to the range of helium burning temperatures applying the R-matrix method, which yielded S(300)(E1) = (76+/-20) keV b and S(300)(E2) = (85+/-30) keV b.     

Investigating the <Superscript>16</Superscript>O + <Superscript>12</Superscript>C reaction over a wide range of energies

The main aim of this work was to describe the reactions of elastic scattering of ¹⁶O + ¹²C over a wide range of energies in an optical model with an l-dependent core. We obtained a value for the compressibility coefficient that agreed with the one found from data on the giant monopole resonance. We considered the elastic transfer of an α particle to reproduce the cross section in the reverse hemisphere.     

Cross sections of the reactions16O(γ,x)13 N and16O (γ,x)11 C,and Yield of12C (γ, t) up to 55 MeV

Yield curves of the reactions¹⁶O (γ, x)¹¹C,¹⁶O (γ, x)¹³N and¹²C(γ, t) have been measured relative to¹²C(γ, n)¹¹C with bremsstrahlung. The cross section σ[¹⁶O(γ, x)¹¹C] has a shape similar to σ[¹⁶O(γ, t)] and shows a broad maximum near 38 MeV. Differences between σ[¹⁶O(γ, x)¹³ N] and σ[¹⁶O(γ, t)] point to a reaction mechanism via quadrupole absorption in¹⁶O. The yield of¹²C(γ, t) exceeds the¹⁶O(γ,t) yield by a factor of two.