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.     

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.     

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.     

Optical potential for 12C + 28Si scattering

¹²C + ²⁸Si elastic scattering angular distributions are smooth functions, relatively easily fit by optical potential predictions, at laboratory bombarding energies, E_1ab, within ≈ 10 MeV of the Coulomb barrier (i.e. up to E_1ab ≈ 27 MeV). Between E_1ab = 27 and 36 MeV the angular distributions show pronounced oscillatory structure which is not easily fit with an optical potential. No optical potential has been found to give a very good account of all the angular distributions simultaneously; the best simultaneous fit to all the data was achieved with a surface-transparent potential whose real and imaginary well depths are energy dependent.     

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.     

A search for resonant two-step α-exchange in 6Li + 12C scattering

Excitation functions for ¹²C(⁶Li, ⁶Li)¹²C (gs, 4.43 MeV) have been measured at 10 angles (40° ? θ_cm ? 160°) over the energy range 20 MeV < E_lab < 36 MeV. A single anomaly of width Γ ≈ 800 keV is observed at E_lab = 22.8 MeV. The results casts doubts on the resonant two-step α-exchange mechanism suggested to occur in this system.     

Angular correlation studies of intermediate width structures in 16O + 12C

An angular correlation technique has been utilized to study the spins of several intermediate width resonances in the inelastic scattering of ¹⁶O + ¹²C in the range 19 ? E_cm ? 23 MeV. An analysis of the correlations and previously reported angular distributions strongly indicates that interpretations of these structures in terms of a single rotational band are inadequate.     

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.     

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.     

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.     

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.     

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.     

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.     

Phenomenological analysis of the 24Mg(12C, α)32S resonant reaction studied at low incident energy

The ²⁴Mg(¹²C, α)³²S reaction has been studied in the region of the Coulomb barrier. Three angular distributions for the α-particle groups populating the ground and first-excited 2⁺ state of ³²S have been measured spanning the apparent resonant structure observed at E_c.m = 14.20 MeV. Regge-pole and phase-shift analyses suggest a spin assignment of 8 for the corresponding resonance at E_x = 30.51 MeV in ³⁶Ar.     

Alignment and resonances in 12C+12C inelastic scattering

Using the out-of-plane γ-ray particle coincidence method we have measured the spin alignment P_zz of excited ¹²C(2⁺) nuclei from ¹²C+¹²C inelastic scattering in the energy range 16 MeV ? E_cm ? 33 MeV.P_zz varies strongly as a function of energy and angle. The correlation of resonant structures in the cross section with maxima of the alignment is particularly clear in mutual inelastic scattering and in θ_cm = 90° single inelastic scattering.     

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.     

Sub-coulomb energy 12C + 10, 11B and 14N + 10B fusion cross sections

Total fusion cross sections have been measured for the following reactions and energy intervals: ¹²C + ¹⁰B, E_c.m. = 2.10–5.38 MeV; ¹²C + ¹¹B, E_c.m. = 2.10–5.99 MeV; ¹⁴N + ¹⁰B, E_c.m. = 2.64–5.97 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by two large NaI detectors. No resonance structure was observed in the three reactions. The elastic scattering excitation function was also measured at θ_c.m. = 90.4° for ¹²C + ¹⁰B over the energy range E_c.m. = 3.18–6.82 MeV. Optical model potentials were found which could consistently describe both the fusion and elastic scattering data.