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.     

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.     

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.     

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.     

Reaction rate of 24Mg(p,γ)25Al

The proton-capture reaction on ²⁴Mg has been investigated in the bombarding energy range of E_p=0.2–1.7 MeV. Resonance properties (strengths, branching ratios and lifetimes) of low-energy resonances have been measured. From the experimental results, accurate proton partial widths, γ-ray partial widths and total widths (Γ_p, Γ_γ, and Γ) have been deduced. The present experimental information establishes the ²⁴Mg+p reaction rates over the temperature range T=0.02–2.0 GK with statistical uncertainties of 5% to 21%. Our recommended reaction rates deviate from previous estimates by 18% to 45%. Based on our results, we can rule out the recent suggestion that the total width of the E_R=223 keV resonance has a significant influence on the reaction rates. We also discuss several effects that might give rise to systematic uncertainties in the reaction rates. The astrophysical implications for hydrogen burning of ²⁴Mg at low stellar temperatures are presented.     

Alpha chain states in 4N-nuclei

We review the experimental evidence for alpha chain states in 4N-nuclei. Bloch-Brink cranked cluster model calculations suggest that such states should exist in all light A=4N nuclei. Recently a strong resonance has been observed in the¹²C(¹²C,¹²C(O ₂ ⁺ ))¹²C(O ₂ ⁺ ) reaction at 33 MeV which has been taken as evidence of a 6-α chain state in²⁴Mg. The angular distributions show strong peaks at 90° due to the simultaneous excitation of several nearly degenerate resonances with a range of L-values. We review our analysis of these data and present the results of calculations for the widths of resonances in hyperdeformed nuclei. We demonstrate that such resonances may have relatively narrow widths despite their high excitation energies. We surmise that the 33 MeV resonance in¹²C+¹²C scattering has a chain state structure.     

Spectroscopy of highly excited states in29Si

Particleγ-ray coincidences have been measured in the²⁸Si (d,pγ) reaction at 6.5 and 7 MeV bombarding energy, in the²⁶Mg (α,nγ) reaction at 12, 14 and 15 MeV, and in the²⁷A1 (τ,pγ) reaction at 9 MeV. Theγ-decay has been observed for all bound states of²⁹Si and for 56 unbound states up to 12,960 KeV excitation energy. Particleγ-ray angular correlations were measured in the²⁸Si (d,pγ) reaction at 6.5 MeV and in the²⁶Mg (α,nγ) reaction at 12 MeV. Spin (-parity) assignments or restrictions were obtained for nearly all bound states and some high-spin states above the binding energy. The assignment of mirror levels in²⁹Si and²⁹P has been extended to 8.2 MeV excitation energy. The excitation energies of 41 positive-parity states are reproduced by shell model calculations. The possible existence of aK ^π=5/2⁺ band with prolate deformation is discussed.     

Study of the structure of16O above 25 Mev by the reaction13C(τ, α)12C*(γ15.1)

The nucleus¹⁶O has been investigated within the excitation range of 25–32 MeV by means of the reaction¹³C(τ, α)¹²C^* _15.1(γ)¹²C. Excitation functions for the 15.1 MeVγ-rays, taken for bombarding energiesE _τ=2.6–12 MeV at 0? and 90?, exhibit some marked structures with widths of 0.5 to 1 MeV. As the (τ, α)-reaction leads to the 15.1 MeV,T=1 state, levels in¹⁶O underlying these structures should have largeT=1 components. Angular distributions of theα-particles coincident to the 15.1 MeVγ-rays show patterns typical for a direct process and are, therefore, compared with DWBA calculations.     

Investigation of backward α-particle scattering in 24Mg and 28Si through α-γ angular correlations

Alpha-gamma angular correlations have been measured for the reaction ²⁴Mg(α, α'γ) in the energy range 15.50 to 17.00 MeV in steps of 300 keV and for ²⁸Si(α, α'γ) from 15.00 to 16.20 MeV in steps of 200 keV to provide energy averaged results. The scattered α-particles were detected for lab angles θ_α = 115°–178° in a multidetector arrangement. The coincident γ-rays were observed with a Ge(Li) detector placed at 90° in the reaction plane. Data were obtained for the 1st, 2nd and 3rd excited states of ²⁴Mg and for the 1st, 2nd, 3rd and 4th excited states of ²⁸Si. The absolute doubledifferential cross sections were analysed with Hauser-Feshbach calculations. The analyses show that compound nuclear processes are responsible for the rise of backward α-scattering in ²⁴Mg(α, α'γ)²⁴Mg and ²⁸Si(α, α'γ)²⁸Si at the energy studied.     

The structure of27Al

Gamma decay modes and spin assignments of levels in²⁷Al have been investigated by proton-γ-ray angular correlation measurements in the²⁴Mg(α, pγ) reaction at 14.2, 15 and 15.6 MeV bombarding energy and byγ-ray angular distribution measurements on the E_p=1820, 2114, 2293 and 2574 keV resonances of the²⁶Mg(p, γ) reaction. Unique spin assignments were obtained as follows: I=3/2 for the 5827 keV state, I=5/2 for the 6115, 6465, 6765, 7577, 7721, 8097, 8136, 8324 keV states, I=7/2 for the 5433, 6533, 7413, 8037, 8442, 8586 keV states, I=9/2 for the 5418, 6512, 6713, 7997 keV states, I=11/2 for the 5500, 6948, 7400, 8396 keV states. The level scheme and electromagnetic properties of levels are compared with the results of shell model calculations which use the complete configuration space of the 0d_5/2-1s_1/2-0d_3/2 shell and the unifieds-d shell Hamiltonian. The agreement is good to excellent and extends into the region of high level density above 7 MeV excitation energy. The total B(M1↑) below 8.5 MeV excitation energy is evaluated, using published resonance fluorescence and (e, e′) data, and quenching relative to the free-nucleon predictions is reexamined. Evidence in favour of a prolate ground state deformation of²⁷Al and implications of this work for the astrophysically interesting²⁶Al(p, γ) reaction are discussed.     

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.     

Phase shift analysis of elastic proton scattering by12C

Angular distributions of the polarization and cross section in¹²C (p,p)¹²C were measured at 24 energies between 9.95 and 10.90 MeV. A phase shift analysis of the data was carried out. The results show four resonances in¹³N atE _x =11.40, 11.64, 11.67 and 11.82 MeV with spins 5/2⁺, 5/2^?, 3/2^? and 3/2⁺.     

High-spin states in 34CI

High-spin yrast states in ³⁴Cl have been studied with the reactions ³¹P(α, nγ)³⁴Cl at E_α = 11.7?16.3 MeV and ²⁴Mg(¹²C, pnγ)³⁴Cl at E(¹²C) = 32–35 MeV. Ambiguities in the ³⁴Cl level scheme for levels at E_x = 4.82 and 5.32 MeV have been resolved through combination of threshold measurements with the ³¹P + α reaction and gamma-gamma coincidence and E_γ-measurements with the ²⁴Mg + ¹²C reaction. Gamma-gamma coincidence and in-beam γ-γ angular correlation experiments have been performed employing a Compton-suppression spectrometer with a solid angle of 120 msr.Unambiguous spin-parity assignments of J^π = 6^?, 5⁺ and 7⁺ to the ³⁴Cl levels at E_x = 4.74, 4.82 and 5.32 MeV, respectively, are obtained.Previously unreported levels of high spin are found at E_x = 7.25 and 7.80 MeV with J^π = (9⁺) and (8⁺); τ_m = 200 ± 70 fs and 100 ± 70 fs, respectively. Excitation energies, mean lives, branching ratios and multipole mixing ratios are reported. The experimental results are compared with large-scale shell-model calculations. The high-spin yrast levels can be characterized by a rather simple shell-model structure.     

Fluctuations in12C+24Mg elastic and inelastic scattering

The data on the ϑ_c.m.=180° excitation functions of¹²C+²⁴Mg,¹²C* (4.43 MeV)+²⁴Mg and¹²C+²⁴Mg*(1.36 MeV) from 12.27 to 22.80 MeV, 16.53 to 27.47 MeV, and 11.33 to 26.40 MeV(c.m.) respectively have been subjected to statistical analysis. The effect of averaging interval, employed for data reduction, on the coherence widths as obtained from the autocorrelation function has been studied. The fluctuating features of the cross-sections turn out to be consistent with the statistical model expectations.     

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.     

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.     

Hydrogen burning of 24, 25, 26Mg in explosive carbon burning

The absolute resonance strengths of the ^24–26Mg(p, γ)^25–27Al reactions have been studied. The absolute values S_c.m.=1.03 ± 0.11, 2.3 ± 0.2 and 2.2 ± 0.2 eV for the frequently used standard resonances at E_p=823, 434 and 454 keV in the reactions ^24–26Mg(p, γ)^25–27Al, respectively, have been determined. In addition, absolute values for use as standards were determined for the 684 keV ²⁵Mg(p, γ)²⁶Al and 840 and 1966 keV ²⁶Mg(p, γ)²⁷Al resonances. New relative values were determined for the strengths of the if²⁵Mg(p, γ)²⁶Al resonances at ifE_{p = 0.3–1.7 MeV} and the ²⁶Mg(p, γ)²⁷Al resonances at E_p = 0.3–2.1 MeV. The resonance energies and total widths obtained in the present work are also given. The branching ratios and angular distributions of the γ-rays used in the absolute strength determinations were obtained in the same set-up as the absolute strength measurement. Using the revised resonance strengths, the astrophysical reaction rates of hydrogen burning of ^24–26Mg in explosive carbon burning in the stellar temperature region of T = (0.1–5.0) × 10⁹ K are compared with Hauser-Feshbach calculations. The present reaction rates are also discussed in the frame of the MgAl cycle.     

Electron scattering studies of magnetic isovector transitions in 12C at high momentum transfer

The inelastic electron scattering cross sections for the M1 transition to the 15.11 MeV (1⁺, T = 1) level and for the M2 transition to the 16.58 MeV (2^?, T = 1) level in ¹²C have been measured in the momentum transfer region q = 0.4–3.0 fm^?1, with emphasis on precise data at high momentum transfers. Additionally, a broad state near 15.4 MeV excitation has been observed and its excitation energy and natural width have been established as 15.44 ± 0.04 MeV and 1.5 ± 0.2 MeV, respectively. The Fourier-Bessel technique for determining the Mλ transition current density has been applied to the M1 and M2 transitions. Particular attention has been paid to the Coulomb corrections required to deduce the PWBA form factors. The M1 radiative width is Γ_γ0 = 38.5 ± 0.8 eV.     

High-spin states of 26Mg populated in the 12C(18O, α) reaction

The structure of ²⁶Mg has been investigated by means of the ¹²C(¹⁸O, α) reaction. Several previously unknown states were populated between excitation energies of 0 to 16 MeV. Excitation functions were measured for 126 states for bombarding energies between 43.2 and 45.9 MeV in 300 keV steps at a lab angle of 7°. The experimental energy averaged differential cross sections were compared with statistical model calculations and good agreement was obtained for the states whose spins and parities were previously established. The statistical model calculations were used to suggest the spins and parities for the rest of the states. In particular, candidates for 6⁺ and 8⁺ states were interpreted as members of three rotational bands in ²⁶Mg: the ground-state band, the K = 2⁺ band based on the 2.938 MeV 2⁺ state, and a K = 0⁺ band based on the 3.588 MeV 0⁺ state. Back bending of the yrast band is observed and it is suggested that it may be due to band crossing of the ground-state and first excited K = 0⁺ bands.