Neutron branching in the reaction 12C + 12C

The cross section for the reaction ¹²C(¹²C, n)²³Mg has been measured in the energy range E_c.m. = 3.54?4.94 MeV by counting the delayed γ-rays from ²³Mg decays (half-life = 11.57 sec), and a theoretical model has been employed to extrapolate the results to threshold (E_c.m = 2.60 MeV). By combining these results with previous measurements of the reactions ¹²C(¹²C, p)²³Na and ¹²C(¹²C, α)²⁰Ne, the neutron branching ratio in the energy interval from threshold to 8 MeV is deduced, and a thermal average is computed that should be valid for use in astrophysical environments characterized by temperatures in the range (0.5–5) × 10⁹ °K. The neutron branching at temperatures appropriate to hydrostatic carbon burning in stars (T ≈ 109 °K) is found to be much smaller than previously estimated.     

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.     

Structures in the excitation functions for compound reactions in the12C+14C system

Excitation functions for the elastic scattering of¹²C on¹⁴C and the reactions¹⁴C(¹²C, α)²²Ne,¹⁴C(¹²C,t)²³Na and¹⁴C(¹²C,d)²⁴Na have been measured in the vicinity of the Coulombbarrier. Strong fluctuations of the differential cross sections as a function of incident energy are observed in the α-particle, triton and deuteron channels. The total yield in the three different channels shows correlated structures at energiesE _c.m.=6.8, 7.2 and 8.3 MeV. This phenomenon is similar to the structures observed in the¹²C+¹²C reactions and indicates the possible presence of resonances in the entrance channel.     

Gamma-ray yields from 12C + 13C reactions near and below the coulomb barrier

The γ-ray yields from low-lying transitions in heavy residual nuclei produced in the ¹²C+¹³C reaction have been measured from E_c.m. = 3.1 to 11.9 MeV using a Ge(Li) detector. Total cross sections for compound nucleus formation were deduced from the experimental data with the aid of the Hauser-Feshbach model. Several independent checks on this procedure are described. These tests verify the assumptions made in the analyses of this reaction and suggest that the deduced cross sections have an absolute uncertainty of ±30 %. The present experimental results for the ¹²C+¹³C reaction are qualitatively very different from those for the ¹²C+¹²C reaction and do not provide any striking evidence for either broad singleparticle resonances in the total reaction cross section or for narrow non-statistical (quasimolecular) resonances in summed cross sections for proton and for α-particle emission to bound states of ²⁴Na and ²¹Ne, respectively. The predictions of several optical models employing attractive nuclear potentials are compared to the data. None is successful in reproducing the measured cross sections over the entire range of bombarding energy. The predictions at low energies depend sensitively on the shape of the potential a few fm inside the region of the nuclear surface. A narrow, rapidly varying energy dependence of the γ-ray yields is observed, with a peak-to-valley ratio of typically 1.1. However, a statistical analysis shows that these fluctuations, and those observed in recent charged particle measurements of α-particle yields, are reasonably consistent with those expected from the formation and decay of strongly overlapping levels in the compound nucleus. Finally, several observations are made on the validity of certain approximations often made in statistical analyses of heavy-ion reactions.     

The12C+12C reaction at subcoulomb energies (I)

The reaction¹²C+¹²C has been studied in the energy rangeE _cm=2.45–6.15 MeV byγ-ray spectroscopy. Gamma-ray transitions from a large number of excited states in²⁰Ne,²³Na and²³Mg were observed, which show strong and rapid yield variations. When the influence of the Coulomb barrier is removed, these structures appear superimposed on a flat reaction yield, which does not show a strong increase at low energies, in contrast to previous work. These results obviate the need for the hypothesis of absorption under the barrier at least down toE _cm=2.45 MeV. The nuclear and astrophysical aspects of the data are discussed.     

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.     

The energy dependence of fusion in the 9Be+28Si system

The angular distributions of the energy spectra of the light charged particles (p, d and α) from the ⁹Be + ²⁸Si reaction have been measured in the energy range 12 ≦ E_lab ≦ 30 MeV. The particle evaporation spectra and the angular distributions were analyzed with a spin dependent statistical model. Angular distributions of ⁹Be ions elastically scattered on ²⁸Si have been measured at the energies 12 MeV, 17 MeV, 23 MeV and 30 MeV and were analysed, together with previously measured cross sections, with the optical model. The fusion cut-off angular momentum l_fus(E), the fusion cross section σ_fus(E) and the ratio σ_fus/σ_R^OM(E) were deduced. The excitation function for fusion was analyzed with the Glas and Mosel model. The parameters obtained from the fusion excitation function were compared with the corresponding ones from the ⁹Be + ²⁸Si optical-model interaction potential.     

Comparison of the fusion reactions12C+20Ne and16O+16O near the Coulomb barrier

The partial cross sections of heavy residual nuclei produced in the heavy ion fusion of¹²C+²⁰Ne have been measured atE _c.m.=6–15 MeV viaγ-ray spectroscopy with a Ge(Li) detector. Windowless and recirculating gas target systems have been used. The dominant residual nuclei are²⁴Mg,²⁷Al,²⁸Si,³⁰Si,³⁰P and³¹P, which arise from two- and three-body breakups in the exit channels. The observed excitation functions are smooth in their energy dependence and give no indications for the existence of pronounced resonance structures, in contrast to theoretical predictions. The Coulomb excitation of²⁰Ne served as an intrinsic calibration standard in the determination of absolute partial and total fusion cross sections. The same experimental set-up was also used in the reaction studies of¹⁶O+¹⁶O atE _c.m.=7–14 MeV, going through the same compound nucleus³²S at similar excitation energies. The observed energy dependence in the excitation functions is in good agreement with previous work. The total fusion cross section agrees fairly well with two sets of values reported previously, but deviates significantly from other reported absolute cross section values. The relative evaporation distributions of the residual nuclei are similar for both heavy ion reactions. However, the ratio of their total fusion cross sections deviates from model predictions and suggests that compound nucleus formation does depend on the microscopic structure of the colliding nuclei in the entrance channel. From the observed energy dependence of the above ratio, particularly at subcoulomb energies, geometrical effects in the entrance channel (due to deformed and spherical nuclei) appear to be weak. The astrophysical aspects of the data in the context of late stellar nucleosynthesis are discussed.     

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.     

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.     

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 reactions of 12C with 12C AT 293 MeV

Energy spectra, angular distributions, and elemental yield distributions have been measured for products Z = 1?9 produced in the reactions of ¹²C on ¹²C. A total reaction cross section 1170_?100⁺¹⁷⁰ mb was determined from the measured elemental cross sections and the principle of charge conservation. This total reaction cross section is about 250 mb less than the geometric cross section and agrees with the Glauber-model calculations of DeVries and Peng. The experimental energy spectra, angular distributions, and yield distributions were compared with those from model calculations for the statistical decay of the products of fusion and of incomplete fusion reactions. For both types of calculations, a modified version of the code LILITA was used. By comparing the data to model calculations, an upper limit of 75 mb for the fusion cross section was determined. That limit corresponds to an upper limit of L_crit for fusion of 10? in the sharp-cutoff approximation. The dominant reaction mechanisms appear to be incomplete fusion processes.     

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.     

Coupled-channels analysis of energy-dependent isospin violation in the 12C(d, α)10B(1.74 MeV,T = 1) reaction

We have studied the isospin non-conserving ¹²C(d, α)¹⁰B(1.74 MeV, 0⁺, T= 1) reaction at several incident energies of 9 ≦ E_d ≦ 16 MeV in terms of a coupled-channels method. The reaction processes involved in the present analysis are the successive single-nucleon pick-up processes as well as the inelastic scattering of deuterons from ¹²C. It is assumed that the isospin violation should occur in the intermediate mirror cluster states of ³He + ¹¹B and t + ¹¹C, due to the Coulomb interaction. The calculation reproduces fairly well the observed features of the reaction, i.e. the decreasing cross section with increasing incident energy, and the variation of the angular distribution. We also note that the calculation shows the energy-dependent localization of isospin violation in the angular momentum space, i.e. a specifically narrow localization at the lower incident energies studied and its broadening at the higher energies. This fact is associated with the variation of the angular distribution from a forward-backward symmetry at the lower incident energies to a forward peak at the higher energies.     

Fusion cross sections for 10,11B+12C at sub-Coulomb energies

Total fusion cross sections for the ¹⁰B + ¹²C and ¹¹B + ¹²C reactions have been determined over a 5 MeV (c.m.) energy range extending to ≈ 3 MeV below the Coulomb barrier. Absolute γ-ray yields for specific transitions in the de-excitation of the heavy products following compound nucleus decay were measured using a Ge(Li) detector. Statistical model calculations of the decay modes of the compound nucleus have been used to deduce, from the γ-ray data, cross sections for single proton, neutron and α-particle emission, and to determine total cross sections for compound nucleus formation. No evidence has been found for sub-Coulomb resonances in either reaction. The total reaction cross sections are compared with optical model calculations using different parameter sets and the observed trend in the very low energy cross sections is discussed relative to other reactions in the same mass region.     

Non-statistical structures in12C(15N,4He)23Na reaction

The data on the? _lab=7° excitation functions of¹²C(¹⁵N,⁴He)²³Na reaction betweenE _cm=9.42 and 17.33 MeV for 28 states upto an excitation energy of 8.940 MeV in²³Na have been subjected to statistical analysis. In addition to statistical fluctuations, the results of the analysis indicate the existence of non-statistical structures atE _cm=10.66, 10.93, 11.38, 12.62, 13.16, 15.32 and 16.18 MeV.     

12C+12C fusion reactions near the Gamow energy

The fusion reactions 12C(12C,alpha)20Ne and 12C(12C,p)23Na have been studied from E=2.10 to 4.75 MeV by gamma-ray spectroscopy using a C target with ultralow hydrogen contamination. The deduced astrophysical S(E)* factor exhibits new resonances at E< or =3.0 MeV, in particular, a strong resonance at E=2.14 MeV, which lies at the high-energy tail of the Gamow peak. The resonance increases the present nonresonant reaction rate of the alpha channel by a factor of 5 near T=8x10(8) K. Because of the resonance structure, extrapolation to the Gamow energy EG=1.5 MeV is quite uncertain. An experimental approach based on an underground accelerator placed in a salt mine in combination with a high efficiency detection setup could provide data over the full EG energy range.     

Alpha-particle unstable states in12C

Alpha particle unstable states in¹²C have been investigated using the three reactions¹⁴N(d, α′)¹²C,¹⁴N(d, α′α)⁸Be and¹²C(α, α′)¹²C. Excitation cross sections and angular distributions have been measured for the reactions¹⁴N(d, α′) at 52 MeV and¹²C(α, α′) at 90 MeV. For a few angle pairs the α-decay of excited states in¹²C have been observed in a¹⁴N(d, α′α) correlation measurement. The reactions selectively excite onlyT=0 states. A previously undetected level with a large α-decay width (Γ=1.2 MeV) has been observed at 15.62 MeV excitation. This level shows up clearly in both reactions and is further distinguished from the nearby 14.08 state in the correlation measurement because of the distinctly different energy distributions of the decay products. On the basis of a particle angular distributions the 15.62 MeV level was assigned spin and parity 4⁺ and the level at 14.08 was assigned 3^?. The latter differs from the value suggest by earlier work. Comparison with DWBA calculations indicates that angular distributions of all other prominent levels are in agreement with their earlier assignments. Two levels at 19.20 and 20.30 MeV (both Γ?0.4 MeV) and three further levels at 21.81, 22.7 and 24.24 MeV also decay predominantly by α-emission.     

Remeasurement of the low-energy cross section for the 15N(p, α0)12C reaction

The cross section for the ${}^{15}\text{N(p}\text{, α}{}_0\text{)}{}^{12}\text{C}$ reaction has been measured at θ_lab = 135° over the proton energy range 93 ≦ E_p ≦ 418 keV. The results are in good agreement with the less precise but much earlier measurements of Schardt, Fowler and Lauritsen (1952). An analysis of the present data in terms of a two-level calculation including the 338 keV (1^?) and 1028 keV (1^?) resonances determines a zero-energy intercept for the astrophysical S-factor of S(0) = 78 ± 6 MeV · b.     

Selective population of the lowest-lying negative parity states in23Na in the12C(12C,p)23Na reaction

The¹²C(¹²C,p)²³Na reaction was investigated in the vicinity of the Coulomb barrier. The lowest-lying negative parity states in²³Na were found to be preferentially populated at energies for which correlated resonances exist in the excitation functions of theα, p, n andγ exit channels of the¹²C+¹²C reaction. If these negative parity states are assumed to consist of ap _1/2 hole coupled to a²⁰Ne quartet state, this selectivity can be explained with the existence ofα-particle doorway states.