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.     

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.     

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.     

Fusion, resonances and scattering in12C+12C reaction

The variation of fusion cross-section (σJ_fus) with energy in the¹²C+¹²C collision is linked to the underlying resonance phenomenon through the behavior of reaction cross-section (σ) of which σ_fus is taken as a part. The calculation of σ_fus is done through an energy-dependent imaginary potential in the optical model potential (OMP). Through dispersion relation, such an imaginary potential gives rise to energy-dependent real potential which is incorporated in the OMP. In our calculation, a form of potential for the nuclear part which has a soft repulsive in-built core is introduced based on similar works done earlier. The calculated results of σ_fus are used to explain the oscillatory structure, astrophysical S-factor and the decreasing trend at higher energies of the experimental σ_fus data in the case of¹²C+¹²C system with remarkable success. The potential used for fusion calculation is tested for fitting elastic scattering data at some energies and is found good in forward angles. Further improvement of the fitting of these data is obtained by incorporating a coupling potential in the surface region. About twenty resonances are observed in our calculation in the specific partial waves and some of them are found close to the experimentally identified resonances in¹²C+¹²C reaction. Thus, we provide an integrated and comprehensive analysis of fusion, resonance and scattering data in the best studied case of¹²C+¹²C reaction within the framework of optical potential model.     

Spin alignment in12C+12C inelastic scattering

The spin alignment P_zz of¹²C(2 ₁ ⁺ ) produced in¹²C+¹²C inelastic scattering at bombarding energies in the region of known resonances between E_cm=18.5 and 32.8 MeV has been determined with a γ-ray detector positioned in the direction of the scattering normal. The values obtained in the centers of three resonances as well as those obtained off-resonance are spread over a range between ?.05 and +.80 with no clear indication in favour of simple pictures of molecular resonances.     

Detailed energy dependence of the elastic and inelastic12C +12C scattering between 5 and 10 MeV/nucleon

Excitation functions for¹²C+¹²C elastic and inelastic scattering to 2⁺ level have been measured over the energy range 30–60 MeV (cm) by 250 keV steps using the kinematical coincidence method. The intermediate structure resonances disappear aboveE _cm=35 MeV while the broad and irregular structure becomes a general feature of the interaction at higher energies.     

Tensor polarization of 12C[2+ 1] in the 16O(13C,12C)17O reaction at 50 MeV

The ¹⁶O(¹³C,¹²C)¹⁷O reaction at 50 MeV has been investigated using the kinematical coincidence method. Polarization tensors t ₂₀ and t ₄₀ of ¹²C[2⁺ ₁] for the quantization axis taken along the direction of propagation have been measured by analyzing the energy spectrum of ¹²C[2⁺ ₁], modulated by the effect of γ ray emission. The deduced t ₄₀ values significantly deviate from zero, contrary to the prediction of the distorted-wave Born approximation theory based on one-step p shell neutron stripping without spin-dependent interactions. The phenomenological spin–orbit interaction necessary to reproduce the magnitude of measured t ₄₀ is found to be much larger than the folding model prediction. It is shown that the experimental polarization tensors as well as the cross sections can be reproduced by introducing multi-step processes involving excitations in ¹²C and ¹³C without introducing spin-dependent interactions. Received: 2 August 1999 / Revised version: 3 February 2000     

On spectral temperatures of negative pions produced in d 12C, 4He12C, and 12C12C collisions at 4.2 A GeV/c

The experimental transverse momentum distributions of negative pions produced in d ¹²C, ⁴He¹²C, and ¹²C¹²C collisions at 4.2 A GeV/c were analyzed in the framework of Hagedorn Thermodynamic Model. The spectral temperatures of π ^? mesons as well as their relative contributions to the total multiplicity of π ^? mesons were extracted from fitting the p _t spectra by two-temperature Hagedorn function. The results were compared systematically with the earlier results obtained from analysis of non-invariant center-of-mass energy spectra of negative pions produced in the analyzed collisions.     

Resonant effects in the12C+12C→8Be gs +16O gs reaction aroundE cm=32.5 MeV

The¹²C+¹²C→⁸Be _gs +1¹⁶O _gs reaction has been studied at c.m. energies of 27.9, 32.5 and 35.0 MeV. The energy dependence of the cross section is consistent with a resonant behaviour like the one observed for two¹²C nuclei excited in a very deformed state in the final channel. The angular distributions for the two reactions show also a similar oscillatory behaviour. The analysis suggests that the reaction proceeds through the formation of an intermediate state with a complex nature, involving largely deformed configurations as well as almost spherical ones.     

Gammadecay of quasimolecular resonances in the12C+12C system

We have studied the heavy-ion radiative capture reaction¹²C(¹²C,γ)²⁴Mg forE _cm =4.7–6.0 MeV. Transitions to the ground-, first and unresolved second and third excited states in the final nucleus²⁴Mg have been observed with cross sections as low as 1 nb/sr. Forγ ₁ two strong resonance-like structures at 4.9 and 5.0 MeV were found correlated in energy with established 2⁺ resonances. Statistical model calculations cannot account for the observed yield. The branching ratioΓ _γ /Γ associated with theγ ₁ decay channel of the 5 MeV resonance was estimated to be 1.1·10^?5 yielding aγ-ray strength of 0.8 eV. The experimental result is in agreement with calculations based on the generator coordinate method where broad barrier resonances are viewed as short lived states of quasimolecular nature.     

Dynamic polarization potential of 12C+12C system at molecular-resonance energies

The nuclear reaction dynamics leading to the formation of recently discovered resonance in the mutual-0₂ ⁺ channel of the ¹²C+¹²C inelastic scattering around E _c.m.≃ 32 MeV is studied in terms of the dynamic polarization potential (DPP) induced by the channel coupling among various excited states in ¹²C. The microscopic 3α cluster-model wave functions are used to generate the ¹²C−¹²C diagonal and coupling potentials in the double-folding model. It is found that DPP for the 0₂ ⁺+ 0₂ ⁺ channel is an unusually strong attractive potential which even exceeds the zeroth-order folding-model potential of this channel around the nuclear surface region and that the strong coupling between the 0₂ ⁺ and 2₂ ⁺ states is predominantly responsible for the unusual DPP in this channel. The effective potential, the sum of the original folding-model potential and the attractive DPP, is found to generates resonance states in the same energy region as that of the resonance states generated by the original folding-model potential but the former states are found to be higher-nodal states having four additional radial nodes. Similar but more moderate property of DPP is also found in the entrance (elastic) channel. These results suggest that the reaction dynamics of generating the resonance in the ¹²C(0₂ ⁺) +¹²C(0₂ ⁺) channel may rather differ from that of the simple crossing of the zeroth-order molecular band generated by the potentials in the entrance and exit channels suggested by the standard band-crossing model. Received: 17 December 1998 / Revised version: 1 March 1999     

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.     

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.     

Measurement of spin-alignment of excited12C2+ nuclei in interactions of16O with12C usingγ-decay in flight

Measuring energy spectra of nuclei afterγ-decay of excited states in flight the spin alignment of¹²C₂₊ states has been measured. Inelastic scattering,¹⁶O(¹⁶C,¹²C₂₊)¹⁶O and the reaction¹²C(¹⁶O,¹²C₂₊)¹⁶O leading to¹²C₂₊ (4.43 MeV) state have been studied. Characteristic line shapes of the¹²C₂₊ peak were observed using a Q3D magnetic spectrometer. The magnetic substate (m-states) population has been deduced from the spectra as function of reaction angle. A comparison of the measuredm-state population with reaction models shows that the first reaction is consistent with inelastic scattering although discrepancies remain. Discrepancies are also obtained if the reaction¹²C(¹⁶O,¹²C₂₊)¹⁶O is interpreted using a FRDWBA transfer calculation. At least 1/3 of the cross section can be attributed toα-transfer. A calculation which couples transfer and inelastic scattering channels seems to be necessary.     

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.     

Time-dependent Hartree-Fock calculation of 12C + 12C with a realistic potential

We have used a realistic single-panicle K-matrix model to compute the head-on scattering of ¹²C + ¹²C at incident projectile lab energies of 3.2, 6.4, 12.8, 19.2, 25.6, 32, 51.2 and 64 $\text{MeV}\text{nucleon}$, above the Coulomb barrier, in the time-dependent Hartree-Fock approximation. Direct and exchange Coulomb forces as well as spin-orbit forces are included. A large deformed harmonic oscillator basis is used. Spatial density and current distributions at various times are shown. The outgoing energy is found to be E₀ = 0.8E_in?28 (MeV), in the c.m. system. Fusion and fully relaxed scattering are observed at low energy. Some compression is seen at higher energies but no shock waves can be detected. Consequences for heavy-ion reactions are discussed.     

Energy dependence of 12C+12C single-neutron transfer cross sections

The one-neutron transfer reaction induced by 25, 35 and 50 MeV/nucleon ¹²C beams on a ¹²C target has been studied. The observed angular distributions for the ¹³C_g.s-¹¹C_g.s. final state agree in shape and magnitude with predictions of the exact finite- range distorted wave Born approximation. Above roughly 30 MeV/nucleon, the angel integrated cross section falls off with an approximately exponential slope in accordance with the expectations of the reaction dynamics at high bombarding energies.     

Cluster Model Analysis of Pion Elastic and Inelastic Scattering from 12C

Angular distributions of differential cross sections for the ¹²C(π ^±, π ^±)¹²C and ¹²C(π ^±, π ^±)¹²C^* reactions at pion kinetic energy ranging from 50 to 260 MeV have been analyzed with the 3α-particle model of ¹²C. The model provides good fits to a wide range of data. Differential cross sections for inelastic transitions to the (2^?+?; 4.44 MeV) and (3^???; 9.64 MeV) states in ¹²C are computed and the deformation lengths δ ₂ and δ ₃ are extracted. It is found that the extracted deformation lengths are sensitive to the nuclear model used and similar to the corresponding values found with other probes and nuclear models.