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.     

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.     

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.     

Predictions for cross sections of light proton-rich isotopes in the ~(40)Ca + ~9Be reaction

The cross sections for Z=10–19 with isotopes T_z=-3/2 to-5 in the 140A Me V~(40)Ca+~9Be projectile fragmentation reaction have been predicted.An empirical formula based on the correlation between the cross section and average binding energy of an isotope has been adopted to predict the cross section.The binding energies in the AME16,WS4,and the theoretical prediction by the spherical relativistic continuum Hartree-Bogoliubov theory have been used.Meanwhile,the fracs parametrization and the modified statistical abrasion-ablation model are also used to predict the cross sections for the proton-rich isotopes.The predicted cross sections for the T_z=-3 isotopes are close to 10~(-10)mb,which hopefully can be studied experimentally.In addition,based on the predicted cross sections,Z=14 is suggested to be a new magic number in the light proton-rich nuclei with T_z-3/2,for which the phenomenon is much more evident than it is from the average binding energy per nucleon.     

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.     

Nuclear reaction cross sections of 16O + 16O obtained by γ-ray detection

The partial production cross sections for reaction residues produced by the fusion of ¹⁶O with ¹⁶O have been measured at E_c.m = 9–30 MeV by detecting the characteristic γ-rays with a Ge(Li) detector. The dominant products are ²⁴Mg and ²⁷A1 corresponding to 2α and αp emission from the compound nucleus, respectively. The total γ-producing cross sections σ_R were also derived by summing the partial cross sections after correction for the observed (average) γ-ray angular distributions. The trend in the total cross sections is very similar to the trends derived from an optical model or a statistical-evaporation model calculation. The partial production cross sections were compared with other experimental results at 11.9 MeV and 30 MeV and with the results of the statistical-model calculation. It is concluded that the treatment of angular momentum in the calculation is inadequate for describing the partial cross sections. Structure in the partial and total cross section excitation functions is observed with minima occurring at E_c.m. = 27, 24, 20, 17.5, and possibly 15 MeV. Some of this structure is well established by the statistical accuracy of the data and most, but perhaps not all of it, is correlated in the various channels. This structure is compared with that observed in another experiment and some of its implications are discussed.     

Studying the reactions of deuteron interaction with <Superscript>9</Superscript>Be nuclei at low energies

Data on elastic and inelastic scattering, and the reactions of few-nucleon transfers in the interaction between the nuclei of deuteron and ⁹Be at energies of around 10 MeV/nucleon, are analyzed. A theoretical analysis is performed using the double-folding potential model with the wave function of the ground state of the ⁹Be nucleus, constructed in the three-cluster α + α + n-approximation. Calculations of the cross section of elastic scattering for the reaction d + ⁹Be using the calculated folding potential are preformed using the optical model. The resulting optical potential is used to analyze cross sections of transfer reactions and inelastic scattering in the context of the distorted waves method. A comparative analysis of the experimental data and theoretical calculations is performed.     

Absolute cross section of the3He(α,γ)7Be reaction

The absolute cross section σ(E) of the³He(α, γ)⁷Be reaction has been measured fromE _c.m. =195 to 686 keV. The studies employed both a supersonic jet gas target and an extended gas target, and were carried out by the observation of the prompt capture γ-ray transitions as well as the⁷Be residual nuclei. The absolute cross sections deduced from the capture γ-rays are in good agreement with most previous work and remove a discrepancy with other earlier work. In comparison, the σ(E) values obtained from the⁷Be residual nuclei are systematically higher, suggesting a small production of additional⁷Be by contaminant reactions.     

Statistical giant resonance effects in heavy-ion radiative capture

Heavy-ion radiative capture has been observed in the two reactions ⁹Be(¹²C, γ)²¹Ne and ¹⁶O(⁷Li, γ)²³Na for c.m. energies between 3 and 9 MeV. High-energy γ-rays populating levels up to 4.7 MeV in the final nuclei were detected with a large volume, anticoincidence-shielded NaI spectrometer. Peak cross sections for individual transitions in both reactions were found near 60 nb/sr. For ⁹Be + ¹²C all excitation functions were rather smooth with a broad bump around E_c.m = 5–6 MeV. Statistical model calculations were in good agreement with the data suggesting that perhaps as much as half of the GDR strength in ²¹Ne is statistical. More structure was found in ¹⁶O + ⁷Li superimposed on still sizeable statistical yield. Previous measurements of the same reaction were found to be partially in error.     

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.     

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.     

Characteristics of elastic proton scattering from <Emphasis Type="Italic">A</Emphasis> = 9 Li,Be, and C isobars

Differential cross sections and analyzing powers (A _y ) for elastic proton scattering from ⁹Be at 220 MeV and 1.0 GeV and from ⁹Li and ⁹C at 60 and 700 MeV/nucleon are calculated in the context of the Glauber diffraction theory with the three-body wave functions for the ⁹Be, ⁹Li, and ⁹C nuclei described by the α + α + n, ⁷Li + n + n, and ⁷Be + p + p models. Comparison with the available experimental data is made, which allows some conclusions about the quality of the model wave functions.     

Nuclear rainbow in elastic scattering of <Superscript>9</Superscript>Be nuclei

A systematic investigation of the elastic scattering of the ⁹Be nucleus, which is among themost loosely bound stable nuclei was performed.Differential cross sections for elastic ⁹Be + ¹⁶O scattering were measured at a c.m. energy of 47.5 MeV (beam of 132-MeV ¹⁶O nuclei). Available data at different energy values and data for neighboring nuclei were included in our analysis. As a result, the very fact of rainbow scattering was reliably established for the first time in systems involving ⁹Be. In addition, the analysis in question made it possible to identify Airy minima and to determine unambiguously the nucleus-nucleus potential with a high probability.     

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.     

Triton emission in the interactions of fast neutrons with nuclei

Cross sections have been measured for the formation of tritium in the interactions with Li, Be, B, C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, Ca, V, Co, As, Y, La, Pr, Tb, Ho and Tl of fast neutrons produced via break-up of 53 MeV deuterons on a Be target (E_n = 11.5–43.5 MeV; I_max at 22.5 MeV; FWHM = 15.8 MeV). The activation technique in combination with vacuum extraction and low-level gas phase β^? counting of tritium was employed. Furthermore, cross sections were measured for isotopes of the elements Ne, Mg, Ar, Ca, Ti, Cr, Fe, Ni, Zn, Ge, Se, Zr, Mo, Pd, Te, Ba, Pr, Dy, W, Tl and Pb by γ-ray spectroscopic analysis of the radioactive reaction products. A comparison of the two sets of cross sections shows that for nuclei with A > 40 the emission of three single particles (lp2n) is much more probable than the emission of a bound tri-nucleon (³H). The cross-section data obtained via tritium counting show that the (n, t) cross sections for the lightest nuclei are exceptionally large, probably due to direct interactions, and the process competes with other modes of de-excitation; for elements with Z > 20, on the other hand, the cross section is low (< 0.25 % ofσ_n.e.) and practically constant, showing thereby that in the medium and heavy mass regions the probability of emission of a triton is relatively independent of the target nucleus. A comparison of the cross-section systematics at E_n = 14.6 MeV and for the neutron spectrum described above is presented; the trends are somewhat similar.     

Cross section measurements for the forward elastic scattering of 13 MeV 6,7Li and 24 MeV 16O from 9Be, 12C, 16O and 28Si

Absolute elastic cross sections have been measured at 12.45°, 16.45°, 20.45° and 28.0° for targets of ⁹Be, ¹²C, ¹⁶O, ²⁸Si and ¹⁹⁷Au being bombarded by beams of 13 MeV ^6,7Li and 24 MeV ¹⁶O. The reliability of a method previously proposed for low mass multielemental analysis [1,2] depends to some extent on the precision and accuracy of the cross sections reported here. The ¹⁶O-beam reactions, except the ¹⁶O + ⁹Be reaction, are found to be consistent with the Rutherford predictions. This allows us to obtain target thickness independent cross sections with uncertainties of approximately 7% for the reactions initiated with ^6,7Li beams. Most of these cross sections are found to be non-Rutherford. Comparisons made with previous investigations give strong support to the cross section values obtained in this work.     

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.     

Triton-emission cross sections with 30 MeV d(Be) break-up neutrons

Triton-emission cross sections were measured for Al, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Nb, Mo, Ag, Ta, Tl, Pb and Bi with a 30 MeV d(Be) break-up neutron spectrum characterized by a multiple-foil activation technique. The accumulated tritium was separated by vacuum extraction and measured by low-level gas-phase β^? counting. The systematic trend in the cross sections is somewhat similar to that in the 53 MeV d(Be) break-up neutron spectrum; apart from some initial decrease as a function of Z, the cross section is almost constant over the entire range of Z = 22 to 83. The magnitudes of the cross sections lie between those with 14 MeV neutrons and 53 MeV d(Be) break-up neutrons. Hauser-Feshbach calculations show that the statistical model describes the triton-emission cross sections for nuclei in the (2s, ld) shell within a factor of 2; for the heavier nuclei, however, the calculated cross sections are much smaller than the experimental values.     

The neutron continuum from the9Be+α reaction

Spectra of the low energy neutron continuum between 0.1 and 2.4 MeV from the Be+α reaction were measured at 5.01, 5.44, 6.37 and 7.44 MeV bombarding energies and different angles of neutron emission. The intensity is strongly peaked in the forward direction and the neutron distributions show maxima between 0.3 and 0.6 MeV. The results are consistent with the assumption that the continuum is due to the sequential decay⁹Be(α, α′)⁹Be*→⁸Be+n. The shape and magnitude of the continuum from a²⁴¹Am-Be(α,n) source were determined as well.     

S-matrix approach for description of refraction and absorption effects in9Be elastic scattering

A newS-matrix model was employed for analysing cross sections of⁹Be elastic scattering by¹²C,¹⁶O,²⁶Mg,²⁷Al,⁴⁰Ca,⁶⁰Ni and¹⁹⁷Au nuclei at 158 MeV. The results obtained are compared with those of optical model.