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.     

Potential resonant screening effects on stellar 12C + 12C reaction rates

The ¹²C + ¹²C fusion cross-sections show a resonant behavior down to the lowest energies accessible so far in the laboratory. If this tendency continues into the astrophysical energy range, the stellar ¹²C + ¹²C reaction rates have to be corrected for resonant screening effects, in addition to the conventional screening corrections. We estimate the resonant screening effects in the weak electron screening limit for hydrostatic burning and white-dwarf environments. Received: 24 May 2002 / Accepted: 31 July 2002 / Published online: 7 November 2002 RID="a" ID="a"e-mail: langanke@ifa.au.dk Communicated by J. ?yst?     

Angular distribution measurement for ~(12)C fragmentation via ~(12)C + ~(12)C scattering at 100 MeV/u

The angular distributions and energy spectra of~(11)B,~(10)B,and~9Be fragments of~(12)C in the angular range from 1.0°~to 7.5°~at 100 Me V/u were obtained via~(12)C+~(12)C scattering.Detailed comparisons are presented between the experimental data and the modified antisymmetrized molecular dynamics(AMD-FM),binary intranuclear cascade model(BIC)and Liege intranuclear cascade model(INCL++).The experimental angular distributions and energy spectra are well reproduced by the AMD-FM calculations but fail to be reproduced by the physical models installed in the Geant4 program,including the BIC and INCL++models.     

A study of the 26Mg(12C, 12B)26Al charge-exchange reaction

The reaction ²⁶Mg(¹²C, ¹²B)²⁶A1(5⁺, 3⁺) has been studied using a beam of 102 MeV of ¹²C. Shell-model, microscopic direct model and finite-range coupled reaction channel (CRC) calculations including recoil effects, have been performed, for comparison with the experimental data. DWBA calculations were performed for the intermediate states of interest in the ¹¹B + ²⁷Al and in the ¹³C + ²⁵Mg channels and these results were also compared with the experimental ones. The dominant reaction mechanism for ²⁶Mg(¹²C, ¹²B)²⁶Al(5⁺, 3⁺) appears to be the sequential mode.     

The 12C+24Mg elastic scattering: An example of anomalous transparency at coulomb barrier energies

Fifteen complete angular distributions of the elastic scattering of ¹²C+²⁴Mg were measured at energies around the Coulomb barrier (E_cm = 10.67–16 MeV). The angular distributions are strongly oscillating and could be well described by an optical potential family, whose real part was determined without continuous ambiguity. The imaginary part of this optical potential is very shallow. At four energies the inelastic scattering angular distributions leading to the 2⁺ state of the ²⁴Mg were also measured and analysed with coupled-channels calculations. The volume integrals of the optical potentials used in the coupled-channels calculations present the threshold anomaly in their energy dependence, with a clear Q-value dependence.     

Investigation of quasimolecular states in 24Mg* through the analysis of the angular dα correlations in the 12C(14N, d)24Mg(α)20Ne reaction

Theoretical analysis of the differential cross sections and angular correlation functions in the ¹²C(¹⁴N, d)²⁴Mg*(α)²⁰Ne reaction at the energy of the incident nitrogen ions E _lab=29–42 MeV is performed in the models of the direct transfer of ¹²C cluster and the compound nucleus. Amplitudes of the reduced widths for the excited quasimolecular states like ¹²C ? ¹²C* in the ²⁴Mg nucleus are obtained. The effect of various states of the relative motion of nuclei in the ¹²C + ¹²C* configuration on the angular dα-correlation functions is studied.     

A Common Optical Potential for ~4He+~(12)C at Intermediate Energies

A common optical potential for ~4He+~(12)C at intermediate bombarding energies,which is essential in analyzing exotic nuclei with ~4He clusters,is obtained based on the Sao Paulo potential.Among systematic optical potentials for ~4He+~(12)C,this potential has the merit of using a fixed imaginary part of the Woods-Saxon form.By opticalmodel calculations,this potential reproduces the experimental elastic scattering angular distributions of ~4He+~(12)C well within the energy range of 26A-60 A MeV.It is also applied successfully in calculations of the breakup reactions of ~6Li+~(12)C and ~6He+~(12)C with a three-body continuum discretized coupled-channel method.     

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.     

Rotational band of 12C + 12C gross-structure resonances and its representation by a double-minimum optical potential

A detailed phase shift analysis of ¹²C + ¹²C elastic data from E_cm = 5.5 to 33 MeV has revealed a pronounced sequence of gross structure resonances. They appear to form a rotational band from l = 0 to at least 16ħ, and are the dominant structural feature of the ¹²C + ¹²C reaction. The resonances are parametrized by a Breit-Wigner analysis and are simulated by shape-resonances in an optical potential with a secondary minimum at large radius. They are discussed in terms of shape-isometric doorway states in ²⁴Mg.     

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.     

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.     

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.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

The breakup of24Mg into16O and8Be

The breakup of²⁴Mg into¹⁶O and⁸Be fragments has been studied using the reactions¹²C(²⁴Mg,¹⁶O⁸Be)¹²C and¹²C(²⁰Ne,¹⁶O⁸Be)⁸Be. In the latter case, discrete states are observed near 24–28 MeV of excitation in²⁴Mg and the yield from this reaction is an order of magnitude greater than that of the former. This implies the excited configuration populated in²⁴Mg is favoured by the transfer of an alpha-particle and would therefore suggest an association with a 4-particle 4-hole configuration. This suggests a link with the octupole stabilised deformed minimum which appears in Nilsson-Strutinsky calculations of the potential energy surface in²⁴Mg, and also with theα —¹⁶O —α structure predicted in cranked cluster model calculations. In the excitation spectrum no states appear above 31 MeV indicating a possible band termination in disagreement with recent results using the¹⁶O+¹²C reaction. These results are discussed in terms of the Harvey model.     

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.     

Coupled-channel fusion and inelastic scattering calculations for 18O + 44Ca and 12C + 48Ti

Fusion and inelastic scattering coupled-channel calculations are carried out for the systems ¹⁸O + ⁴⁴Ca and ¹²C + ⁴⁸Ti. Comparison between ¹²C + ⁴⁸Ti and ³²S + ²⁴Mg sub-barrier fusion cross-section enhancement is made using simple analytical expressions. The distribution of the angular momentum absorbed by the compound nucleus is discussed in a quantum-mechanical coupled-channel model.     

Observation of the nuclear rainbow scattering for12C+12C atE Lab =300 MeV

The elastic and inelastic scattering of¹²C on¹²C has been measured in the angular range between 2.8° and 70.4° in the c.m. system atE _Lab =300 MeV. Optical model calculations have been performed with Woods-Saxon and folded potentials, the ground state and the first 2⁺-state were coupled in the calculations. The large cross sections of the elastic scattering at large angles is related to the nuclear rainbow scattering, which is centered at about 56°. This requires a potential depth of 100 MeV at a distance of 3 fm, the fit to the data is sensitive down to this region. The calculations with the folded potential show a better agreement with the data than those with the Woods-Saxon shape. The total reaction cross section of 1,420 mb, obtained from the optical model analysis, corresponds to the geometrical value; no transparency is observed.