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.     

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.     

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.     

Measurements of elastic scattering for 7Be, 7Li + 9Be systems and fusion cross sections for 7Li + 9Be system

Elastic scattering angular distributions have been measured for ⁷Be + ⁹Be system at E_lab = 17, 19 and 21 MeV in the angular range θ_cm=26^○–58°, and for ⁷Li + ⁹Be system at E_lab= 15.75, 24 and 30 MeV. An optical model (OM) analysis of these data have been carried out. For the ⁷Li + ⁹Be system fusion cross sections were obtained at E_lab = 15.75, 24 and 30 MeV by measuring the α-evaporation spectra from the compound nucleus at backward angles. The measured α-evaporation spectra were reproduced by the statistical model calculations and fusion cross sections were extracted therefrom. The ratios of the experimental fusion cross sections to the total reaction cross sections (obtained form OM analysis) were found to be rather small. This result suggests that break-up process has a strong influence on fusion process leading to a reduction in fusion cross section.     

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.     

Spectroscopy of 13Be

Six quasi-stationary states of ¹³Be populated in the ¹⁴C(¹¹B,¹²N) ¹³Be reaction at E_lab = 190 MeV are reported. A Q-value = −39.60(9) MeV and a mass excess, M.E.= 33.95(9) MeV, have been found for the lowest observed spectral line. The ground state is unstable with respect to one-neutron emission by 0.80(9) MeV. Excitation energies of 1.22(10), 2.10(16), 4.14(12), 5.09(14) and 7.0(2) MeV have been obtained for the observed spectral lines.     

Alpha transfer at sub-coulomb energies in the 9Be + 16O reaction

From a detailed comparison of the sub-Coulomb-barrier cross sections for the ⁹Be + ¹⁶O and ¹²C + ¹³C reactions, it is demonstrated that there is a strong α-transfer in the channel ⁹Be + ¹⁶O→²⁰Ne¹ + ⁵He, in accord with the near optimum Q-value for the α-transfer.     

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.     

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.     

Mechanism of the 12C(11B,15N)8Be reaction and 8Be + 15N optical-model potential

Angular distributions of the ¹²C( ¹¹B, ¹⁵N) ⁸Be reaction were measured at the energy E_lab(¹¹B) = 49 MeV for the transitions to the ground and 2.94 MeV (2⁺) excited state of ⁸Be and to the ground and 5.270 MeV (5/2⁺) + 5.299 MeV (1/2⁺), 6.324 MeV (3/2^-), 7.155 MeV (5/2⁺) + 7.301 MeV (3/2⁺), 7.567 MeV (7/2⁺) excited states of ¹⁵N. The data were analyzed by the coupled-reaction-channel method. The elastic, inelastic scattering and one- and two-step transfers were included in the coupling scheme. The data of the ¹²C( ¹¹B, ⁸Be) ¹⁵N reaction at E_cm = 9.4-17.8 MeV known from the literature, were also included in the analysis. The mechanism of the ¹²C( ¹¹B, ¹⁵N) ⁸Be reaction and the optical-model potential parameters for the ¹⁵N + ⁸Be channel were deduced. The energy dependence of the optical-model parameters for the ¹⁵N + ⁸Be channel was obtained.     

Proton polarization and differential cross section for the (3He,p) reaction on 6Li and 9Be at 14 MeV

Angular distributions of the proton polarization and the differential cross section have been measured for the reaction (³He, p) initiated by 14 MeV incident ³He particles and proceeding to the ground and the first excited states of the final nuclei ⁸Be and ¹¹B. Large polarization values were observed, especially for the ⁹Be(³He, p)¹¹B reaction leading to both the ground and the first excited states in ¹¹B. The experimental results have been analysed in terms of a two-nucleon transfer spindependent distorted-waves theory using finite-range formalism and including corrections due to the non-locality of the optical potentials. A proper coherent summation over L and S, whenever necessary was included in the DWBA calculations of the polarization and the differential cross section as implied by the presence of the spin-orbit terms in the optical-model potentials used to generate the distorted waves.     

Comparison of 7Li , 7Be + 9Be elastic scattering in the coupled-reaction-channels approach

The data for the ⁷Li + ⁹Be and ⁷Be + ⁹Be elastic scattering at the energies E _lab(⁷Li) = 15.75 , 24, 30, 34, 63 and 130MeV and E _lab(⁷Be) = 17 , 19 and 21MeV were analyzed within the optical model and coupled-reaction-channels method. The elastic and inelastic scattering, reorientation of ⁷Li , ⁷Be and ⁹Be as well as most important transfer reactions were included in the coupled-channels scheme. The resulting ⁷Li and ⁷Be potentials are very similar and have the same energy dependence. The real potential for recently derived ⁸Be + ⁹Be scattering potentials is very similar to that for ⁷Li , ⁷Be but the imaginary part of the ⁸Be one has a much greater strength at longer range.     

The energy dependence of fusion in the 9Be+28Si system

The angular distributions of the energy spectra of the light charged particles (p, d and α) from the ⁹Be + ²⁸Si reaction have been measured in the energy range 12 ≦ E_lab ≦ 30 MeV. The particle evaporation spectra and the angular distributions were analyzed with a spin dependent statistical model. Angular distributions of ⁹Be ions elastically scattered on ²⁸Si have been measured at the energies 12 MeV, 17 MeV, 23 MeV and 30 MeV and were analysed, together with previously measured cross sections, with the optical model. The fusion cut-off angular momentum l_fus(E), the fusion cross section σ_fus(E) and the ratio σ_fus/σ_R^OM(E) were deduced. The excitation function for fusion was analyzed with the Glas and Mosel model. The parameters obtained from the fusion excitation function were compared with the corresponding ones from the ⁹Be + ²⁸Si optical-model interaction potential.     

Interaction of loosely bound radioactive 7Be and stable 7Li with 9Be

Quasielastic scattering angular distributions have been measured for the ⁷Be + ⁹Be system at E _lab = 17 , 19 and 21MeV in the angular range $ \theta_{{cm}}^{}$ = 24^° - 57^° . An optical model (OM) analysis of these data has been carried out in order to extract optical potential parameters and reaction cross-sections. One-proton stripping cross-sections were also measured for this system at E _lab = 19 and 21MeV. These transfer angular-distribution data were compared with the finite-range distorted-wave Born approximation (FRDWBA) calculations. For the ⁷Li + ⁹Be system quasielastic scattering angular distributions were measured and emitted light charged particles were detected at E _lab = 15.75 , 24.00 and 30.00MeV in the angular range $ \theta_{{cm}}^{}$ = 7^° - 70^° . Fusion cross-sections were obtained by reproducing the measured $ \alpha$ -evaporation spectra from the compound nucleus at backward angles with the statistical model calculations. The ratios of the experimental fusion cross-sections to the total reaction cross-sections (obtained from OM analysis) were found to be small. This result suggests that the break-up process has a strong influence on the fusion process leading to a reduction in the fusion cross-section.     

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.     

Fusion around the barrier in 11,9Be +209Bi

The ⁹Be +²⁰⁹Bi fusion cross sections were measured in the range 37.5 MeV ≤ E _lab ≤ 45.0 MeV at the Munich Tandem via the observation of ground state α-decay of the evaporation residues. Fusion cross sections of ²⁰⁹Bi with the “halo”¹¹Be unstable projectile in the region around the Coulomb barrier were deduced from an experiment done with the same technique at the RIKEN Ring Cyclotron. Above the Coulomb barrier the ¹¹Be cross sections are larger than the ⁹Be ones in agreement with theoretical predictions based on the larger ¹¹Be halo radius. Also below the barrier these theories foresee the same behavior in disagreement with the experimental results, since the two cross sections are rather similar. Received: 2 April 1998     

Photoproduction of π+ from9Be

The reaction⁹Be(γ, π ⁺)⁹Li has been studied with bremsstrahlung in the energy range 100–800 MeV employing the radioactivity method. The cross section curve deduced is compared with an impulse approximation calculation including a volume and a surface production model. In the energy region 200–300 MeV the experimental cross section, approximately 7 (μb, is best reproduced by the surface production model with a cut-off parameterr ₀ equal to 2.8 fm, i.e. somewhat larger than the r.m.s. radius of⁹Be.     

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.     

Structure of neutron-rich Be and C isotopes

The structure of neutron-rich beryllium isotopes has been investigated using different heavy-ion-induced transfer reactions. In neutron transfer reactions, the population of final states shows a strong sensitivity to the chosen core nucleus, i.e., the target nuclei ⁹Be or ¹⁰Be, respectively. Molecular rotational bands up to high excitation energies are observed with ⁹Be as the core due to its pronounced 2α-cluster structure, whereas only a few states at low excitation energies are populated with ¹⁰Be as the core. For ¹¹Be, a detailed investigation has been performed for the three states at 3.41, 3.89, and 3.96 MeV, which resulted in the most probable spin-parity assignments 3/2⁺, 5/2^?, and 3/2^?, respectively. Furthermore, we have studied particle-hole states of ¹⁶C using the ¹³C(¹²C, ⁹C)¹⁶C reaction and found 14 previously unknown states. Using the ¹²C(¹²C, ⁹C)¹⁵C reaction, five new states were observed for ¹⁵C.     

Total reaction and fusion cross sections at sub- and near-barrier energies for the system 7Li + 28Si

Fusion cross sections are extracted for the ⁷Li$ + $²⁸Si system, via reaction cross section and transfer measurements at sub- and near-barrier energies ( E _lab = 5.7 to 14MeV). The energy evolution of transfer to reaction cross section ratios is determined with the aid of CDCC calculations, which subsequently allows the deduction of fusion cross sections at sub- and near-barrier energies. It is shown that fusion can be well represented in a BPM context. Fusion cross sections are compared for the systems ⁷Li$ + $²⁸Si and ⁶Li$ + $²⁸Si, the latter studied previously, and are found to exhibit different strengths. Last, the direct channels determined at 13MeV, are found to be dominated by a 2n -transfer mechanism.