Fusion cross-section measurements for the 13C+13C reaction

Absolute γ-ray yields from characteristic low-lying levels in nuclei produced in the ¹³C+ ¹³C reaction have been measured from E_c.m. = 4.0 to 15.8 MeV using an intrinsic germanium detector. Statistical-model calculations of the decay modes of the compound nucleus have been used to deduce absolute cross sections for the production of the observed residual nuclei and to determine the fusion cross section. Consistency checks on the adopted procedure lead to an estimated absolute uncertainty of ± 15 % on the deduced cross sections. Over the energy range covered, no striking evidence has been found for either broad single-particle resonances or for narrow non-statistical resonances in the cross sections for individual channels. Comparisons are made with optical-model calculations of the reaction cross section and with different expressions for the fusion cross section.     

Gamma-ray yields from 12C + 13C reactions near and below the coulomb barrier

The γ-ray yields from low-lying transitions in heavy residual nuclei produced in the ¹²C+¹³C reaction have been measured from E_c.m. = 3.1 to 11.9 MeV using a Ge(Li) detector. Total cross sections for compound nucleus formation were deduced from the experimental data with the aid of the Hauser-Feshbach model. Several independent checks on this procedure are described. These tests verify the assumptions made in the analyses of this reaction and suggest that the deduced cross sections have an absolute uncertainty of ±30 %. The present experimental results for the ¹²C+¹³C reaction are qualitatively very different from those for the ¹²C+¹²C reaction and do not provide any striking evidence for either broad singleparticle resonances in the total reaction cross section or for narrow non-statistical (quasimolecular) resonances in summed cross sections for proton and for α-particle emission to bound states of ²⁴Na and ²¹Ne, respectively. The predictions of several optical models employing attractive nuclear potentials are compared to the data. None is successful in reproducing the measured cross sections over the entire range of bombarding energy. The predictions at low energies depend sensitively on the shape of the potential a few fm inside the region of the nuclear surface. A narrow, rapidly varying energy dependence of the γ-ray yields is observed, with a peak-to-valley ratio of typically 1.1. However, a statistical analysis shows that these fluctuations, and those observed in recent charged particle measurements of α-particle yields, are reasonably consistent with those expected from the formation and decay of strongly overlapping levels in the compound nucleus. Finally, several observations are made on the validity of certain approximations often made in statistical analyses of heavy-ion reactions.     

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.     

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.     

Partial breakdown of the evaporation model and possible preequilibrium α-particle emission in heavy-ion fusion reactions

Relative cross sections for residual nuclei following fusion reactions were measured by γ-ray spectroscopy in the reactions ⁵²Cr+ ¹²C at 56.00 MeV and ⁴⁸Ti+ ¹⁶O at 57.74 MeV, in which the common “compound nucleus” ⁶⁴Zn was excited at the same energies and the relative distributions of the entrance spins were nearly identical. It is shown that ratios of the measured cross sections in both entrance channels can be precisely determined experimentally and are insensitive to small changes of the parameters in calculations based on the evaporation model. Using these particular quantities, we have shown that the evaporation process is not the sole mechanism producing the observed residues, especially those resulting from α-particle emission. The assumption of preequilibrium α-particle emission at high channel spins is shown to reproduce the present data fairly well.     

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.     

Measurement of the 11B(11B, 10Be)12C proton transfer reaction at low energies

Differential cross sections for the ¹¹B(¹¹B,¹⁰Be)¹²C proton transfer reaction leading to the ¹⁰Be(g.sO+¹²C(4.43 MeV) $\text{(Q = 0.289}\text{MeV}\text{)}\text{and}{}^{10}\text{(3.37}\text{MeV}\text{) +}{}^{12}\text{C}\text{(g.s.) (Q = 1.36}\text{Me V}\text{)}$ final channels have been measured at E_c.m. = 5.5 MeV by coincident detection of the ¹⁰Be and ¹²C nuclei. The integrated cross sections for the ¹⁰Be + ¹²C(4.43 MeV) channel have been obtained for incident energies between E_c.m. = 2.66 and 3.64 MeV from the yields of the 4.43 MeV γ-ray emitted in the ¹²C 4.43 MeV → g.s. transition. The cross-section magnitudes compare well with the DWBA calculations. The sub-barrier transfer cross sections exhibit an unusual energy dependence: their ratio to the total reaction cross section is decreasing with decreasing incident energy.     

Boron+boron sub-Coulomb energy total reaction cross sections

Total reaction cross sections have been measured for the following reactions and energy intervals: ¹¹B+¹¹B, E_c.m. = 1.56–3.65 MeV; ¹⁰B+¹¹B, E_c.m. = 1.61–3.94 MeV; ¹⁰B+¹⁰B, E_c.m. = 1.84–3.66 MeV. Absolute cross sections were extracted from the prompt γ-rays emitted by the various residual nuclei and measured by large NaI detectors. The absolute accuracy of the method is thoroughly discussed and tested via a measurement of the ¹²C+¹²C reaction. For all three boron cases measured neither intermediate nor giant type resonances were observed. The cross sections are well described by optical model calculations based on lowenergy ¹¹B+¹¹B elastic scattering parameter sets.     

Isomeric cross sections for the (n, 2n) reaction on 82Se, 81Br,and 45Sc at 15.1 MeV

Activation techniques have been used to measure the cross sections at 15.1 MeV neutron energy for the following reactions: ⁸²Se(n, 2n)^81m+gSe, ⁸¹Br(n, 2n)^80m+gBr, and ⁴⁵Sc(n, 2n) ^44m+gSc. Isomeric cross-section ratios were evaluated by applying the method of least squares to the time behavior of γ-ray activity following the ground-state decay of each isomeric pair. The absolute cross section σ_m for the formation of the metastable state was measured by the mixed-powder method with the ²⁷Al(n, α)²⁴Na reaction as the monitor. The cross section σ_g for the formation of the ground state was then determined by using the isomeric cross-section ratio. The sum of σ_m and σ_g for each reaction is compared with the theoretical value obtained from calculations based on the statistical model for the formation of a compound nucleus and its subsequent emission of neutrons.     

Excitation functions of191+193Ir,197Au(6Li,xn+yp) compound nuclear reactions at ELi=48–156 MeV

Excitation functions of the compound nuclear reactions^191+193Ir,¹⁹⁷Au(⁶Li,xn+yp) forx =3–13 andy=0–2 have been investigated by means of in-beamγ-ray spectroscopy at the 156 MeV⁶Li beam of the Karlsruhe Isochronous Cyclotron. The beam energy has been varied in the range of 48 to 156 MeV in steps of about 10 MeV by Be-absorber foils in the external beam line. Absolute cross sections have been determined by normalizing the measuredγ-ray intensities to the production cross sections ofK- X-rays in the target. The experimental excitation functions are discussed on the basis of predictions of the preequilibrium (hybrid) model. While in most cases the theoretical calculations fairly well reproduce energy position and shapes of the curves, strong discrepancies in the absolute scale of the cross sections are observed. The theoretical predictions overestimate the (⁶Li,xn) cross sections by a factor of about 6. Conspicuous anomalies have been detected when comparing the (⁶Li, xn+1(2)p) reactions with (⁶Li,xn) reactions. The reactions with emission of one or two protons are considerably enhanced. The discrepancies and anomalies observed are tentatively explained by the influence of direct reaction channels as the⁶Li break-up, which experimentally proved to be the dominant contribution to the total reaction cross section. The enhancement of the reactions with emission of protons may be a consequence of transfer reactions into highly excited states combined with compound nucleus formation thus implying a cluster effect in preequilibrium emission process.     

Total reaction and transfer cross sections for 11B + 9Be and 13C + 9Be reactions at low energies

The total reaction cross sections for ¹¹B + ⁹Be and ¹³C + ⁹Be have been measured by the total γ-ray yield method over the energy intervals E_c.m. = 1.4–4.4 MeV and E_c.m. = 2.0–5.2 MeV, respectively. The cross sections for the neutron transfer reactions ¹¹B(⁹Be, ⁸Be)¹²B, leading to the ¹²B 0.953 and 1.674 MeV states, and ¹³C(⁹Be, ⁸Be)¹⁴C, leading to the ¹⁴C 6.094, 6.728 and 6.902 MeV states, have been obtained from the yields of the characteristic γ-rays. The α-transfer reaction ¹¹B(⁹Be, ⁵He)¹⁵N, leading to many unresolved ¹⁵N states, has been observed with large cross section. There is, however, no evidence for the ¹³C(⁹Be, ⁵He)¹⁷O transfer process in the ¹⁷O + nα channels. This different behaviour of the ¹¹B + ⁹Be and ¹³C + ⁹Be systems seems to indicate that the α-transfer reaction at sub-barrier energies is not a direct transfer process, and that it probably occurs via molecular state formation.     

14N fusion with 13C and 16O at sub-barrier energies

Total fusion cross sections for the ¹⁴N+¹²C and ¹⁴N+¹⁶O reactions have been measured in the c.m. energy ranges 3.6–9.2 MeV and 5.6–12.6 MeV, respectively. Cross sections are also reported for important individual exit channels which were studied by observing discrete γ-ray transitions in the evaporation residues with a Ge(Li) detector. Excitation functions reveal no evidence of intermediate structure in these reactions. The fusion cross sections for ¹⁴N induced reactions on ¹²C, ¹⁴N and ¹⁶O are compared with an IWB calculation using recently published semi-empirical parameters for the real ion-ion interaction potential. Such a comparison supports the view that low-energy fusion studies may be sensitive probes of the nuclear potential in the interior of the interaction barrier.     

55Mn(n,n'γ) cross-section studies for En = 1.0–3.6 MeV

Absolute ⁵⁵Mn(n, n′γ) γ-ray production cross sections have been measured for 19 transitions from levels up to and including the 2429 keV state in ⁵⁵Mn over the energy range E_n = 1.0–3.6 MeV. Angular distributions were also measured for 6 of the transitions. Branching ratios were extracted and total inelastic neutron cross sections were inferred for these ⁵⁵Mn excited states. The measured and inferred cross sections are compared with calculated cross sections using the statistical compound nucleus theory.     

High-spin states in 58Ni

High-spin states of ⁵⁸Ni were investigated via the study of in-beam γ-ray induced by the compound reaction ⁴⁸Ti(¹²C, 2n)⁵⁸Ni between 26 and 48 MeV. The energies and decay modes of these levels were determined from the analysis of γ-γ coincidence measurements at 35 MeV. The most intense lines in the ⁵⁸Ni γ-ray spectrum correspond to a cascade to the ground state, through levels at 1.454, 2.459, 3.619 and 4.381 MeV, also fed in other reactions, and by two previously unknown levels at 5.125 and 5.662 MeV; the spin assignments based on the present study are (apart from the ground state) 2, 4, 4, 5, 6 and 7 respectively for these levels. The first three were already known and the last three are new. The mixing ratios for the transitions between these levels are also determined. We observe also the same cascade in the reaction ⁵⁶Fe(α, 2n)⁵⁸Ni at an incident energy 18–24 MeV. Comparisons with other reactions, previous studies and recent shell-model calculations are presented.     

Comparison of cross sections for C + O reactions in the second regime of complete fusion

Kinetic energy spectra, angular distributions, and elemental yield distributions have been measured for the ¹² C + ¹⁶ O, ¹² C + ¹⁸ O and ¹³ C + ¹⁷ O reaction products over an energy range from 2 to 7 times the Coulomb barrier energy. A careful kinematic analysis of the evaporation residues and comparisons with statistical-model calculations show that fusion proceeds with full momentum transfer followed by a statistical decay of the compound nucleus. The competition between complete fusion process and peripheral reactions in the ¹² C + ¹⁶ O system is less important than for the ¹² C + ¹⁸ O and ¹³ C + ¹⁷ O reactions. The unexpectedly high ¹² C + ¹⁶ O complete fusion cross sections are related to the possible occurrence of a superdeformation of the ²⁸ Si compound nucleus.     

Cross section measurements for the 9Be+9Be System at subbarrier energies

The total reaction cross section and the characteristic y-ray cross sections have been measured for the ⁹Be+ ⁹Be reaction in the energy range E_cm = 1.4–3.4 MeV, detecting the prompt γ-rays emitted by the various residual nuclei with two Nal detectors in nearly 4π geometry and with a germanium detector, respectively. The differential elastic cross sections for the same system have also been measured at e_c.m.= 2.2, 2.7 and 3.2 MeV. The cross sections calculated with the “standard” and the proximity optical model potentials, which describe well the total reaction cross sections of the light nuclei, agree with the ⁹Be + ⁹Be elastic-scattering data, but underpredict the total reaction cross section by a factor of 2 to 3. The characteristic γ-ray measurements show that all two-particle emission channels, nα ¹³C, nn¹⁶O, np¹⁶N and αα¹⁰Be are enhanced by about that factor, while the single-particle emission channel, p¹⁷N, is not enhanced.     

Alpha-cluster break-up and reaction mechanism in (p, α) reactions on light nuclei

The differential cross sections for the ¹¹B(p, α)⁸Be and ²³Na(p, α)²⁰Ne reactions were measured at bombarding energies between 6 and 24 MeV. The observed angular distributions can be divided into two domains: at low energies the shapes vary rapidly with incident energy indicating a compound nucleus reaction ; at higher energies rather stable diffraction patterns are seen exhibiting a direct reaction mechanism and DWBA calculations are able to describe the shapes. The change from one region to the other is rather abrupt and this behaviour seems typical for reactions having an α-like compound nucleus. The energy at which this change occurs corresponds to an excitation energy in the compound nucleus of about 20 MeV above the α-threshold.     

Mass yield distributions of target fragments from the reactions of iron with 135 MeV/nucleon 12C and 80 MeV/nucleon 16O ions

Cross sections for the production of target fragments in the reactions of iron with 135 MeV/nucleon ¹²C and 80 MeV/nucleon ¹⁶O ions have been measured by off-line γ-ray spectroscopy. Through these data, the mass yield distributions have been obtained. The result of the experiment for the reaction with 135 MeV/nucleon ¹²C ions is compared with theoretical calculations using the fusion-fragmentation model and the GEMINI code for sequential binary decay, following a calculation with the fireball model. Reveived: 24 March 1999 / Revised version: 16 July 1999     

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.     

Absolute residue cross sections for 46–50Ti + 13C reactions at 36, 46 and 56 MeV

Absolute cross sections for nuclei produced in the reactions ^46–50Ti + ¹³C at 36, 46 and 56 MeV (lab) were measured. Complete identification in mass and atomic number for the evaporation residues was obtained by means of in-beam γ-ray spectroscopy techniques. In the entire energy range, an overall satisfactory account of the observed product nuclei is given by the predictions of the fusion-evaporation model. Direct channels like inelastic scattering and n-transfer appear to be noticeable and contribute ~ 15 % to the total cross section.