Fusion excitation functions near and below the Coulomb barrier for symmetric and asymmetric medium-mass systems

Fusion excitation functions for the systems ¹²C + ^{46, 48, 50}Ti, ^{28, 30}Si + ³⁰Si and ¹⁸O + ⁴⁴Ca have been determined at energies near and below the Coulomb barrier. Inelastic excitation functions for the targets ^{48, 50}Ti and ⁴⁴Ca have been also measured in the same energy range. The absolute cross sections were obtained by in-beam γ-ray spectroscopy technique using a rotating target. Fusion cross sections ranging in magnitude from ～ 0.3 mb to ～ 1300 mb were determined with an accuracy of 10–20%. The fusion excitation functions are analysed in the frame of a semiclassical barrier-penetration model. From the analysis, the height, the radius and the curvature of the fusion barrier for the different systems are extracted. The fusion cross sections are compared with the calculations performed using different heavy-ion potentials. The enhancement of the cross sections at sub-Coulomb energies can be reproduced with a one-dimensional barrier-penetration model taking into account the zero-point motion of the surface of the reaction partners. The fusion cross section of the system ¹⁸O + ⁴⁴Ca is well reproduced by quantum-mechanical calculations, introducing a new degree of freedom taking into account the formation of a neck during the fusion process.     

Elastic, inelastic scattering and fusion of the 14N +59Co system at energies close to the coulomb barrier

Elastic and inelastic scattering differential cross sections were measured in the energy range 30 MeV ≤ E _lab ≤ 55 MeV, for the ¹⁴N +⁵⁹Co system. Ambiguities of the optical potential derived from the analysis of the elastic scattering data were removed by performing calculations at the radius of sensitivity and by comparison with the available fusion cross section data. A simultaneous analysis of the three mechanisms was performed by coupled channel calculations, and a unique energy independent nuclear potential was found to be able to fit the data. Discussions and comparisons concerning the optical model, the threshold anomaly, full and approximated coupled channel calculations are presented. Received: 6 February 1997 / Revised version: 1 August 1997     

Fusion cross section for the system6Li+28Si atE ∼ 36 MeV

The fusion cross section for the system⁶Li+²⁸Si has been measured atE∼36 MeV. Combining this with the data available at lower energies, the nucleus-nucleus real potentials have been determined for a range of interaction distances.     

Energy dependence of optical-model parameters for the interaction of 6Li and 7Li Ions with 28Si nuclei at low energies

The results of a joint analysis of experimental data (angular distributions for scattering and total reaction cross sections) are presented for the case of the interaction of ^6,7Li ions with ²⁸Si nuclei at energies between 7.5 and 32 MeV. The respective calculations were performed on the basis of a deformed potential of the optical model by using the SPI-GENOA code. The energy dependences of the parameters of the macroscopic optical model and the total cross section for the (^6,7Li+²⁸Si) reactions were obtained over the energy interval from 7.5 to 32 MeV. The calculated angular distributions and total reaction cross sections are in good agreement with experimental data.     

Near-barrier transfer in16O +144, 154Sm

The production of nitrogen and carbon fragments in the reactions induced by¹⁶O on¹⁴⁴Sm and¹⁵⁴Sm targets was studied at two bombarding energies (65 MeV and 72 MeV) around the interaction barrier. The measured angular distributions exhibit the characteristic behaviour of direct transfer reactions, and theQ-value spectra are typically centered at the values predicted by kinematic selectivity. The comparison between fusion and charged-particle transfer cross sections shows that whereas fusion is the most important process at the highest bombarding energy, transfer reactions become comparable or even dominant (as in the¹⁴⁴Sm case) at near-barrier energies. The different transfer probabilities observed for the two systems are analyzed in terms of nuclear deformation.     

Measurement and interpretation of heavy ion fusion excitation functions

Fusion excitation functions for ³²S induced reactions on ²⁴Mg, ²⁷Al, ⁴⁰Ca and ⁵⁸Ni are reported at incident ³²S ion energies of 65 to 132.5 MeV. Measurements were made using counter-telescopes with beams from Van de Graaff accelerators. From these data barrier heights and radii for fusion are extracted. These results are interpreted in terms of the nuclear diftuseness, and the nuclear attractive potentials at the fusion radii are deduced. Relative density overlaps at the fusion radius are estimated from electron scattering density distributions. Several parameterizations for the fusion radii and barrier heights are presented. Fusion cross sections are compared with reaction cross sections based on elastic scattering measurements coupled with optical model analysis. It is found that for the systems investigated, 90±10 % of the reaction cross section results in fusion.     

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.     

Refractive scattering and reactions,comparison of two systems:16O+16O and20Ne+12C

Elastic, inelastic scattering as well as one-neutron transfer channels have been measured over a wide angular range for systems¹⁶O+¹⁶O at the incident energy of 350 MeV and²⁰Ne+¹²C at 390 MeV, respectively, using the Q3D magnetic spectrometer. In both cases differential cross sections have been measured down to about 50 nb/sr (or d/d _R10^–4) at large angles. For the¹⁶O+¹⁶O system refractive contributions are found at the level of these cross sections, whereas in the²⁰Ne+¹²C case a steeper decrease of the differential cross section with the angle is observed and the refractive contribution can not be determined. The elastic scattering data have been analyzed using standard Woods-Saxon potentials and potentials calculated in different versions of the double-folding model. Some properties of these potentials are tested in the calculations for inelastic scattering and one-neutron transfer within the DWBA. With the refractive pattern observed for the¹⁶O+¹⁶O system, the scattering and transfer data are found to be sensitive to the interaction potential at small internuclear distances down to about 2.5 fm.It should be acknowledged that part of the folding analysis reported here was done while one of the authors (D.T.K.) was staying at the Institute for Theoretical Physics, University of Tübingen. We also thank Prof. H. Clement and H. Abele for numerous discussions and contributions and Prof. G.R. Satchler for helpful comments on the use of the DWBA code PTOLEMY.     

Elastic scattering for the system 11Be + 209Bi at Coulomb barrier energies

The elastic scattering process for ¹¹Be ions impinging on a ²⁰⁹Bi target was studied in the energy range around the Coulomb barrier. The angular distributions of the ¹¹Be scattered particles were analyzed within the optical model framework in order to evaluate the reaction cross section, which turned out to be much larger than the fusion one, especially in the sub-barrier region. The comparison with the system ⁹Be + ²⁰⁹Bi showed that the reaction cross section is larger for the reaction ¹¹Be + ²⁰⁹Bi in the energy range around the Coulomb barrier, while they are rather similar at higher bombarding energies. This result suggests that direct processes related to the ¹¹Be halo structure and lower binding energy are more relevant at near-barrier energies.     

Correlations between nucleon transfer and fusion at near-barrier energies for the systems32S +100,101Ru and33S +90,91,92Zr

Transfer reactions at two near-barrier energies for the systems³²S +^100,101Ru have been studied. Differential cross sections have been extracted for a large variety of channels, with a set-up yielding good mass, nuclear charge and energy resolutions. A steeper decrease of the measured angular distributions at backward angles with respect to the prediction of a semiclassical theory is interpreted as a loss of transfer flux feeding more complex channels and/or fusion. Coupled channels calculations, which use the transfer form factors derived from the experiment, reproduce the fusion cross sections at sub-barrier energies. Multi-nucleon transfer seems to play an essential role for the fusion process, as evidenced by the found strong correlations. A systematic comparison is made with the systems³³S +^90,91,92Zr, which have been the object of a previous experimental study with the same set-up.     

12C + 7Li Reaction measurements and the 12C(7Li,t)16O reaction

A measurement of the residues from the ¹²C + ⁷Li reaction has been obtained for ⁷Li energies from 10 to 38 MeV. From these measurements the fusion cross sections and critical angular momenta for the ¹²C + ⁷Li system have been deduced. Cross sections for the ⁷Li(¹²C, t)¹⁶O reaction have been obtained for ¹²C energies from 54 to 62 MeV at θ_lab = 2.7°. The critical angular momenta obtained from the fusion cross sections have been used to perform Hauser-Feshbach calculations for the ¹²C(⁷Li, t)¹⁶O reaction. These calculations have been compared to measured angular distributions over a wide energy range. By comparing the fusion cross sections required by the Hauser-Feshbach calculations to fit the ¹²C(⁷Li, t)¹⁶O(8.87 MeV) reaction and the measured residue cross section it is estimated that at least 80 % of the measured residues are fusion products. The calculations also indicate that direct processes dominate the population of many ¹⁶O levels at forward angles and the 10.35 MeV state at backward angles. The necessity for using a critical angular momentum in Hauser-Feshbach calculations is discussed.     

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.     

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     

Isotopic effects in the 7Li + 10, 11B elastic and inelastic scattering

Angular distributions of the ⁷Li + ¹⁰B elastic and inelastic scattering were measured at the energy E _lab (¹⁰B) = 51 MeV (21 MeV c.m.). These and previously measured ⁷Li + ¹⁰B elastic-scattering data known at the ⁷Li-beam energies 24 MeV (14.1 MeV c.m.) and 39 MeV (22.94 MeV c.m.) were analyzed within the optical model and coupled-reaction channels method to determine the energy dependence of the parameters of the scattering potential and find the difference of these parameters from that of ⁷Li + ¹¹B scattering. It was found that the ⁷Li + ¹¹B potential parameters fail to describe the ⁷Li + ¹⁰B scattering data. The biggest difference is observed between the depths of the imaginary potentials that describe these scatterings.     

离线γ技术测量重离子熔合复合核平均角动量

使用离线γ测量技术在质心系25.0—40.5MeV的能区测量了¹²C+⁹³Nb熔合反应产生的二中子和三中子蒸发道的激发函数。由于在相同的激发能下,蒸发道的相对截面比与复合核的角动量有很强的依赖关系,应用统计蒸发程序(CASCADE),从二中子和三中子蒸发道的截面中提取不同能量下的复合核平均角动量和熔合截面。同时从能很好地拟合熔合激发函数的简单耦合道模型(CCFUS)计算中提取复合核的平均角动量。两种方法得到的复合核平均角动量随入射能量的变化相自洽,表明耦合道模型 关键词：     

Comparison of the fusion reactions12C+20Ne and16O+16O near the Coulomb barrier

The partial cross sections of heavy residual nuclei produced in the heavy ion fusion of¹²C+²⁰Ne have been measured atE _c.m.=6–15 MeV viaγ-ray spectroscopy with a Ge(Li) detector. Windowless and recirculating gas target systems have been used. The dominant residual nuclei are²⁴Mg,²⁷Al,²⁸Si,³⁰Si,³⁰P and³¹P, which arise from two- and three-body breakups in the exit channels. The observed excitation functions are smooth in their energy dependence and give no indications for the existence of pronounced resonance structures, in contrast to theoretical predictions. The Coulomb excitation of²⁰Ne served as an intrinsic calibration standard in the determination of absolute partial and total fusion cross sections. The same experimental set-up was also used in the reaction studies of¹⁶O+¹⁶O atE _c.m.=7–14 MeV, going through the same compound nucleus³²S at similar excitation energies. The observed energy dependence in the excitation functions is in good agreement with previous work. The total fusion cross section agrees fairly well with two sets of values reported previously, but deviates significantly from other reported absolute cross section values. The relative evaporation distributions of the residual nuclei are similar for both heavy ion reactions. However, the ratio of their total fusion cross sections deviates from model predictions and suggests that compound nucleus formation does depend on the microscopic structure of the colliding nuclei in the entrance channel. From the observed energy dependence of the above ratio, particularly at subcoulomb energies, geometrical effects in the entrance channel (due to deformed and spherical nuclei) appear to be weak. The astrophysical aspects of the data in the context of late stellar nucleosynthesis are discussed.     

Transfer reactions at high energy and ambiguities in heavy-ion potentials

The smaller impact parameters that contribute to transfer reactions between heavy ions at high energies make them more sensitive to different types of optical potentials than is the case at lower energies. This may allow one to distinguish between potentials that otherwise generate similar elastic scattering cross sections within the limited angular region over which typical elastic data are available. We cite as evidence results for nucleon transfers induced by¹⁸O +²⁸Si at 352 MeV which rule out surface transparent potentials.     

Comparison of one and two-neutron transfer near the coulomb barrier for the27Al(18O,16O)29Al,27Al(180,17O)28Al and27Al(13C,12C)28Al reactions

Total reaction cross sections for the transfer reactions²⁷Al(¹⁸O,¹⁶O)²⁹Al,²⁷Al(¹⁸O,¹⁷O)²⁸Al and²⁷Al(¹³C,¹²C)²⁸Al are reported for center-of-mass energies between 13 and 20 MeV for¹⁸O projectiles and between 11 and 17.5 MeV for¹³C projectiles. The reaction products,²⁹Al and²⁸Al, beta decay to²⁹Si and²⁸Si, respectively, and the subsequentγ decays of²⁹Si and²⁸Si were measured. Due to the relatively long beta decay half lives, data were taken in a beam-off mode, resulting in very clean spectra. Total cross sections were calculated and compared with a theoretical model for barrier penetration proposed by C.Y. Wong. Differences between¹⁸O induced one and two-neutron total transfer reaction cross sections are discussed.     

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.