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.     

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.     

The (18O,16O) reaction on even tin isotopes

The two-neutron transfer reaction^ASn(¹⁸O,¹⁶O)^A+2Sn has been measured for the isotopes A=112, 116, 118, 120, 122 and 124 at bombarding energies of 57 and 60 MeV together with the elastic scattering. Angular distributions have been analysed for the transitions to the ground state and to the first excited 2⁺ state. The observed ground state transition is strongly enhanced. The theoretical DWBA analysis is performed with a finite range 2n-transfer form factor including recoil correction. The calculated cross section reproduces the observed systematic change over all isotopes. The absolute cross sections are normalized by a factor of 4.7 and 7.5, depending on the two different sets of 2n-wave functions used in the analysis. The results confirm the prediction of the pairing model that the transition strengths of a neutron pair between the ground states of even tin isotopes are the same.     

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.     

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 β-delayed α-spectrum of 16N,and its role in defining the astrophysical cross section for 12C(α,γ)16O

It has proven to be very difficult to determine the astrophysically important cross section for ¹²C(α, γ)¹⁶O at the relevant energies (∼300 keV) from radiative capture measurements. The present paper summarizes a new measurement of the β-delayed α-spectrum of ¹⁶N that substantially improves our knowledge of the E1 α-capture cross section on ¹²C at 300 keV. The paper concludes with a brief discussion of the status of the total ¹²C(α, γ)¹⁶O cross section at 300 keV.     

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.     

Experimental determination of the total reaction cross section of the stellar nuclear reaction 16O + 16O

The total reaction cross section for ¹⁶O + ¹⁶O has been measured at six energies between E_c.m. = 6.8 and 11.9 MeV. Cross sections for the production of protons, alphas, neutrons, deuterons, ³¹S, ³⁰P, ¹²C(g.s.) + ²⁰Ne(g.s.) and the relative γ-yield were obtained with a variety of experimental methods. No ³H or ³He were found. All cross sections are normalized to ¹⁶O + ¹⁶O elastic scattering at θ_c.m. = 90°, which was measured separately with high precision between E_c.m. = 7.3 and 14.4 MeV. The elastic scattering and relative γ-yield of ¹²C + ¹²C were measured between E_c.m. = 3.9 and 7.5 MeV. The elastic scattering and neutron yield of ¹²C + ¹⁶O were measured between E_c.m. = 5.4 and 10.1 MeV.     

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.     

Light charged particle decay in the reaction7Li+16O

Angular distributions and excitation functions for the emission of a large number of proton, deuteron, triton, and-particle groups in⁷Li+¹⁶O reactions have been measured in the vicinity of the Coulomb barrier. Within the framework of the statistical reaction model, two approaches are presented that can reproduce the only weakly anisotropic shape of the angular distributions and the absolute cross section for those groups of ejectiles where contributions from direct reaction modes are small. When a standard Woods-Saxon potential deduced from elastic scattering is used, the entrance channel angular momentum distribution must be limited to values below critical angular momental _cr which are smaller than the grazing angular momental _gr if fusion is to be described. A global proximity potential with a parameter set that has been adjusted to reproduce the fusion reactions of a variety of p- and sd-shell nuclei yields very similar results when applied to⁷Li+¹⁶O. The proximity potential effectively introduces a similar angular-momentum limitation. This analysis proves the existence of a fusion cross section limitation and the importance of strong direct reaction modes (transfer and possibly inelastic processes) in⁷Li+¹⁶O reactions at energies close to and even below the Coulomb barrier. Another aspect of⁷Li+¹⁶O is addressed briefly. The resonance-like structure observed in the heavy-ion radiative capture reaction⁷Li(¹⁶O, ₀₊₁)²³Na atE _x (²³Na)=25.4 MeV is not observed in the particle decay channels investigated in the present work.The authors would like to acknowledge the help received from B. Bellenberg, B. Dechant, H. Hemmert, T. Krischak, E. Kuhlmann, H. Putsch, and C. Scholz during the experiments.     

The 12C(α, γ)16O cross section at stellar energies

The capture reaction ¹²C(α, γ)¹⁶O has been investigated at E = 0.94 to 2.84 MeV with the use of an intense α beam and implanted ¹²C targets of high isotopic purity. The studies involved NaI(Tl) crystals and, for the first time, germanium detectors. The measurement of absolute cross sections, γ-ray angular distributions and excitation functions is reported. A cross section of 48 pb is found at E = 0.94 MeV. The data provide information on the E1 and E2 capture amplitudes involved in the transition to the ground state as well as to excited states. The S-factor at stellar energies has been determined by means of theoretical fits. The results verify the previous report of a substantial higher S-value compared to the value recommended in 1975. The present uncertainty in the S-value as well as possible improvements are discussed. This S-value is of crucial importance to nuclear astrophysics.     

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.     

Angular distributions and forward recoil range distributions of residues created in the interaction of 12C and 16O ions with 103Rh

We have measured the angular distributions and the forward recoil range distributions of residues produced in the interaction of, respectively, 151, 228 and 402 MeV ¹²C ions with ¹⁰³Rh and the forward recoil range distributions of residues produced in the interaction of 303 MeV ¹⁶O ions with ¹⁰³Rh. These data have been successfully reproduced by a theory which assumes that the dominant mechanisms are complete and incomplete fusion of the projectile with the target and single nucleon transfers from the projectile to the target and predicts that, starting from an incident energy of about 250 MeV, a large fraction of the residues has a mass and charge very close to those of the target nucleus. This is because, at incident energies of a few hundred MeV, a large fraction of the kinetic energy of ¹²C and ¹⁶O is carried away by fast ejectiles which then leave behind the intermediate equilibrated nuclei with a rather small excitation energy and small forward linear momentum.     

The16O(α, γ)20Ne direct capture reaction at low energies

The¹⁶O(α, γ)²⁰Ne direct capture cross section has been calculated in a microscopically founded cluster model which reproduces simultaneously both the correct binding energies and the deformations of the²⁰Ne bound states. Theα+¹⁶O scattering states are derived from a microscopically derived local potential. The astrophysicalS-factor is found to increase linearly with energy in the energy rangeE _cm≈0.4–2 MeV and might therefore be determinable experimentally.     

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.     

Proton and alpha evaporation spectra in low energy 12C and 16O induced reactions

Proton and alpha particle spectra have been measured in the ¹²C+⁹³Nb and ¹²C+⁵⁸Ni reactions at E(¹²C)=40 and 50 MeV and in the ¹⁶O + ⁹³Nb reaction at E(¹⁶O) =75 MeV. The spectra are compared with the statistical model calculations. The shapes of the calculated spectra are in agreement with experimental data except for the alpha spectrum in the ¹²C + ⁹³Nb reaction at 40 MeV. The observed evaporation bump is at ∼2 MeV lower energy compared to the calculated one. This discrepancy could imply alpha particle emission from a deformed configuration before compound nucleus formation at this near Coulomb barrier beam energy.     

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.     

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°.     

A detailed study of the 12C + 16O fusion reaction at Ecm = 19 to 24 MeV

Excitation functions of evaporation residues following the ¹²C + ¹⁶O reaction are investigated at E_cm = 19 to 24 MeV. At the resonances which have been previously identified in the ¹²C(¹⁶O, ⁸Be)²⁰Ne two-body channel, an order of magnitude larger resonance cross section is observed in the fusion channel than that in the two-body one and is shared among a few evaporation residues (²⁰Ne, ²³Na and ²⁴Mg). Here the resonance cross section is defined as the resonance part of the cross section on a resonance in an excitation function. It is found that for each resonance the relative intensity of the resonance cross sections of these residues is fairly well explained by assuming that they are coming from the decay of a compound nuclear resonance. It indiates that these intermediate resonances have a large probability to proceed to the formation of a more complicated configuration prior to its decay into exit channels. However, the resonant enhancement in the fusion channel is found to be weak at three energies (E_cm = 19.7, 22.0 and 22.6 MeV), where prominent resonant structures have been observed in inelastic channels. These distinct situations may be attributed to the magnitude of level density of the compound nucleus.