Fusion cross section for 13C + 13C at low energies

The energy dependence of the fusion cross section has been measured over the range E_c.m. = 3.05–6.88 MeV by detecting the γ-rays from residual nuclei in a 4π geometry. Analyzing the 1.37 MeV photopeak, originating from ${}^{24}\text{Mg}\text{1.37}\text{MeV}\text{→}\text{g.s. transition}$, the cross sections for ²⁴Mg+2n channel were also deduced. The measured fusion cross sections have been compared with those for ¹²C + ¹²C and ¹²C + ¹³C systems and found to be significantly different. For ¹³C+¹³C the fusion cross sections agree with the standard optical-model prediction down to the lowest measured energies, while for ¹²C + ¹²C and ¹²C + ¹³C they are, at the lowest energies, too low. It is suggested that the unpaired valence nucleons facilitate fusion at energies well below the Coulomb barrier.     

Fusion and neutron-transfer cross sections for 13C + 10B and 13C + 11B reactions at subbarrier energies

The cross sections for the ¹⁰B(¹³C, ¹²C)¹¹B neutron-transfer reaction, leading to the ¹¹B 4.45 and 6.74 MeV and ¹²C 4.44 MeV excited states, and for ¹³C + ¹⁰B fusion have been measured by the characteristic and total γ-ray yield methods, respectively, over the energy (c.m.) interval 2.4–5.8 MeV. For ¹³C + ¹¹B, with no transfer reactions present, the fusion cross sections have been measured between E_c.m. = 2.3 and 6.4 MeV. The fusion cross sections for ¹³C + ¹⁰B and ¹³C + ¹¹B are found to be almost equal and slightly enhanced with respect to those for ¹²C + ¹⁰B and ¹²C + ¹¹B.     

16O, 24, 26Mg, 28Si, 32S, 40Ca(α, 12C) and multi-α-cluster transfer reactions

The (α, ¹²C) reaction has been studied on a variety of nuclei, A = 16 to 40, at E_α = 90.3 MeV. The data indicate a rapid fall-off of cross sections with increasing target mass, approximately as A_t^{?5 ± 1}. This and other systematics are used to estimate cross sections for multi-α-cluster transfer reactions in heavy nuclei and suggest σ_T < 10^?34 cm² consistent with present experimental limits. The data for ²⁴Mg(α, ¹²C)¹⁶O has been studied in more detail and indicates a selective population of final states including ¹⁶O g.s., with oscillatory angular distributions in some instances. Finite-range distorted-wave Born approximation calculations for direct ⁸Be pickup have been performed utilizing cluster overlap amplitudes obtained with zero-order SU(3) wave functions. The calculations are in qualitative, and often quantitative, agreement with shapes and absolute magnitudes of the measured angular distributions although the cross sections for certain α-cluster states (2⁺, E_x ≈ 7 MeV; 4⁺, E_x ≈ 10.3 MeV) are greatly overestimated with this model. Other more complicated mechanisms, such as successive α-transfer, cannot be excluded. The systematics of the calculated ⁸Be cluster overlaps and the calculated and measured (α, ¹²C) cross sections are investigated, and implications for multi-α-cluster transfer reactions are discussed.     

No pre-critical enhancement observed in 13C(π+, γ)13N(g.s.) at q ≅ 2mπ

The cross section and angular distribution for the reaction ¹³C(π⁺, γ)¹³N(g.s.) have been measured from 37 to 85° in the laboratory, at a pion energy of 115.5 MeV. The observed cross section ranges from 320 to 660 $\text{nb}\text{sr}$. These results do not show the large magnitude and wide-angle peaking expected if pre-critical effects due to nascent pion condensation were present. In addition, the observed cross section is less than one-half of the predictions of available theoretical calculations which do not include the pre-critical effect. Data on the reaction ¹H(π^?, γ)n at T_π = 116.6 MeV were also obtained for calibration purposes. These data agree with expectations based on knowledge of the inverse reaction and previous measurements.     

Structure of 13C from an R-matrix analysis of 12C + n scattering and reaction cross sections

Differential cross sections for ¹²C + n elastic and inelastic scattering and for the ²C(n, α) ⁹Be reaction, together with high resolution total cross-section data were analyzed by means of a multilevel multichannel R-matrix program to determineJ, π, and γ_λc for states in ¹³C up to E_x = 13.5MeV. Good overall fits to the data were obtained throughout this large energy range. Spin and parity assignments for thirteen states above E_x = 9.5MeV for which there had been either no previous J^π assignments or only tentative assignments have been made in this study. The present results are in good agreement with previous analyses and model calculations.     

Four-nucleon transfer with the 32S(16O, 12C)36Ar reaction

Angular distributions have been measured for the ³²S(¹⁶O,¹²C)³⁶Ar reaction at 45.5 MeV leading to excited states between E_x, = 0 and 8 MeV. Experimental cross sections are compared with exact finite-range DWBA calculations in combination with extensive shell-model calculations, which include sd- and fp-shell configurations. Transitions to low-energy positive-parity states and bound negative-parity states are well reproduced. The calculations, however, fail to describe some high-energy positive-parity states. Calculations with a complete cluster expansion for the four transferred nucleons give about 50% larger cross sections, but can not explain the observed discrepancies. Possible interference of reaction processes other than direct α-transfer and special structure effects are discussed.     

Intermediate resonance of inelastic 12C + 12C scattering

The intermediate resonances observed in the inelastic ¹²C + ¹²C cross sections to the single and mutual 2₁⁺(4.43 MeV) excitations and the single 3₁^? (9.64 MeV) excitation are studied by the coupled-channel method with the use of the coupling interaction derived by the folding procedure between ¹²C and ¹²C. It is shown that the model is successful in reproducing the gross structures of the inelastic cross sections and especially the correlated resonance energies of the inelastic channels. The inelastic resonances are shown to be due to the molecular resonances in an adiabatic potential between two ¹²C, which reproduces correctly the coupled channel resonances.     

Time-dependent Hartree-Fock calculations for 14N + 12C reactions

We present Time-Dependent Hartree-Fock calculations for the massasymmetric system ¹⁴N + ¹²C in the range 20 ? E_cm ? 114. A simplified effective interaction of the Skyrme form has been used and the orbital angular motion of the ions has been treated in the rotating frame approximation. The overall magnitude of the calculated fusion cross-section is in agreement with experiment. The calculated differential cross section for direct inelastic reaction products is proportional to ${}^1\text{sin θ}$. This is in contrast to the exponential decrease observed experimentally.     

The photoneutron cross section in 13C

The photoneutron cross section in ¹³C was measured using bremsstrahlung from an electron synchrotron operated in energy sweeping mode. Neutrons were detected by a multi-BF₃-counter detection system. Decorrelated cross-section ordinates were calculated directly using a modified Leiss-Penfold analysis. The cross section from threshold to 25 MeV shows detailed structure, some nine maxima, in agreement with recent continuum shell-model calculations.     

Charged pion photoproduction from 10B and 13C

Positive and negative pion photoproduction cross sections from ¹⁰B and ¹³C leading to the ground state of the residual nucleus have been calculated in the plane-wave and distorted-wave impulse approximations. The results are compared with experiment and with other theoretical calculations. While a large discrepancy is observed between experiment and theory in the case of negative pion photoproduction from ¹³C, fair agreement is obtained between experiment and the plane-wave calculations in all other reactions. It is found that in all reactions studied, except in the case of positive pion production from ¹³C, the inclusion of the pion-wave distortions moves the theory away from the experimental points. It is also found that the photopion differential-cross-section calculations show a sensitivity to the nuclear wave function different from that predicted by the electron scattering form-factor calculations.     

Resonant behaviour of the 16O-12C elastic scattering cross section

Resonances in the elastic scattering of ¹⁶O by ¹²C are reported at E_c.m. = 17.29 and 20.79 MeV, with respective J^π assignments of 11^? and 13^?. A 14⁺ spin assignment is shown to be more probable for the resonance at 22.79 MeV than a previous tentative assignment of 16⁺. A correlation is found between maxima of the total fusion cross section and the position of odd angular momentum resonances.     

Mass distributions of fusion products in reactions between 19F and 12C

Nuclear reactions between ¹⁹F and ¹²C target nuclei were studied at beam energies of 50, 63.2 and 76 MeV. Reaction products in the mass range from A = 11 to 31 emitted in forward direction (4°–20°) were identified with a time-of-flight telescope. Mass distributions of the fusion products were obtained. Their characteristic structure is interpreted as a consequence of the superposition of nucleon and α-particle emission. Qualitative conclusions are drawn on the relative intensities of the different decay modes of the compound nucleus. Fusion cross sections and estimates of the contribution of direct channels to the total reaction cross section are discussed.     

The compound nucleus reaction 12C(11B, 2α) 15N

Energy spectra and differential cross sections of nitrogen products formed in the reaction 28 MeV ¹¹B + ¹²C have been measured using a ΔE?E counter telescope. The energy spectra are smooth and therefore indicate that the nitrogen products were formed by a compound nucleus mechanism, via the formation and decay of the compound nucleus ²³Na. The experimental results are compared with statistical model calculations and good agreement is obtained. This result provides further evidence for the importance of the compound nucleus mechanism in heavy ion reactions with light nuclei and also gives added validity to the statistical model for light compound systems.     

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.     

Analyzing power measurements for the 13C(p,d)12C reaction at 200 and 400 MeV

Cross sections and analyzing powers for the ¹³C($\text{p}$,d) reaction have been measured at 200 and 400 MeV to the 0⁺, ground state and 2⁺, 4.44 MeV state of ¹²C. While the cross sections are rather structureless, DWBA calculations in exact finite range account well for both the magnitude and shape of the angular distributions. On the other hand, the measured analyzing powers are in serious disagreement with the DWBA calculations.     

Unexpected interference patterns observed in the 12C(14N, 13N)13C reaction at energies close to the Coulomb barrier

The reaction ¹²C(¹⁴N, ¹³N)¹³C has been measured at 28, 32, 34 and 36 MeV beam energies. The energy dependence of the measured interference pattern cannot be reproduced by DWBA calculations which take account of the interference between proton and neutron transfer. A rather strong asymmetry of the angular distributions about θ_c.m. = 90° has been observed.     

The excitation function of the 13C(α, n)16O reaction and its astrophysical application

Neutron-liberating reactions as well as neutron absorbing processes play important parts in the synthesis of elements in a star and in the different phases of its life sequence. Thus the ¹³C(α, n)¹⁶O reaction is of interest for instance in connection with processes such as hydrostatic and explosive burning, as well as in the synthesis of oxygen and other light elements. A good knowledge of the energy dependence of the cross section of the alpha-carbon reaction is evidently of importance. In the present work the neutron yield from a thick ¹³C target was measured for α-particles in the energy range 0.60 to 1.15 MeV with a sensitive 4π neutron detector. Stellar temperatures between 3.5 and 9.2 × 10⁸ K are involved in this energy region. The observed neutron yield curve was used to determine astrophysical cross section factors S(E) as well as parameters for the 1.056 MeV resonance. Starting from these quantities, an expression for the mean lifetime of ¹³C nuclei interacting with helium was derived.     

The (p, π±) reactions on 12,13C at 200 MeV

Angular distributions from the (p, π^±) reactions have been measured at 200 MeV on ¹²C and ¹³C leading to discrete final states in the residual nuclei. A comparison of the cross sections is made between transitions to isobaric analog and non analog final states. Differences between the (p, π⁺) and (p, π^?) reactions are found in the shape and magnitude of the differential cross section as well as in the energy variation.     

Photodisintegration of 13C

The nucleon decay of the photoresonance in ¹³C is analyzed using bound-state shell model and R-matrix theory. Total and partial photo cross sections, branching ratios, final state population, and nucleon emission spectra are considered and compared with available data.     

Scattering and reactions of 14C + 14C and 14C + 14C

We have studied elastic scattering, inelastic scattering and several transfer channels of the systems ¹⁴C + ¹⁴C and ¹⁴C + ¹²C over a wide range of energies up to E_c.m. = 35 eMeV and 32 MeV, respectively. The reaction channels were identified by means of kinematic coincidences between solid-state detectors, γγ coincidences were measured to determine cross sections for mutual inelastic scattering of ¹⁴C + ¹⁴C.Pronounced regular gross structures, similar to those found for ¹⁶O + ¹⁶O, are observed in the elastic excitation function of ¹⁴C + ¹⁴C at θ_c.m. = 90°, The angular distributions measured at the energies of the maxima and an optical-model analysis suggest that one or a few surface partial waves dominate the scattering behaviour. Correlated structure of narrower width is found in the inelastic channels and, to a lesser degree, in the transfer channels which appear with rather small cross sections.In ¹⁴C + ¹²C elastic scattering the gross structures are strongly fragmented, in contrast to ¹⁴C + ¹⁴C but similar to ¹²C + ¹²C. While the ¹²C(2⁺) excitation is very weak, the observed strengths of the ¹⁴C(3^?) excitation and of neutron transfer point to a substantial role of these channels as coupling partners to the elastic configuration and to their influence on the elastic scattering behaviour. A correlated intermediate structure is observed near 23.5 MeV, where a dominance of l = 18 is suggested by the elastic scattering angular distribution. This unexpectedly high l-value exceeds l_graz at this energy by at least two units of ?.