Exploiting barrier distributions to investigate breakup effects in the fusion of 9Be+208Pb

The availability of precisely measured fusion excitation functions have allowed the determination of experimental fusion barrier distributions. This concept is utilised in ⁹Be+²⁰⁸Pb reaction, to reliably predict the expected complete fusion cross-sections. However, the measured cross-sections are found to be only 68% of those predicted. The large cross-sections observed for incomplete fusion products support the interpretation that this suppression of fusion is caused by ⁹Be breaking up into charged fragments before reaching the fusion barrier.     

Fusion near the threshold: A comparative study of the systems 40Ar + 112, 116, 122sn and 40Ar + 144, 148, 154Sm

Fusion excitation functions for the systems ⁴⁰Ar + ^{112, 116, 122}Sn and ⁴⁰Ar + ^{144, 148, 154}Sm have been determined, covering cross sections ranging from several hundred mb down to the μb level. The data show a pronounced correlation of the subbarrier behaviour with low-energy collective properties of the nuclei involved and are well reproduced by simplified coupled-channel calculations coupling fusion to inelastic channels. The possibilities of parameterizing the data in terms of a simple dynamic barrier-fluctuation phenomenon are discussed and result in the prediction of remarkably diffuse partial-wave distributions above the barrier. This is shown to be important for the analysis of deexcitation phenomena following fusion reactions.     

Near-barrier transfer and fusion of the systems33S +90,91,92Zr

Double differential cross sections of all prominent transfer channels have been measured in the systems³³S +^99,91,92Zr at two energies close to the nominal Coulomb barrier. In addition the fusion excitation functions of these systems have been measured below and around the barrier. The angular- andQ-distributions of the most important transfer reactions have been analysed in the framework of a simple semiclassical formalism. Particularly the two-nucleon transfer angular distributions exhibit strong multi step coupling effects which manifest themselves in reduced cross sections at large angles corresponding to close distances. From the angular distributions at forward angles, where a single step character of the transfer reaction can be assumed, approximate form factors have been extracted employing a first order perturbation theory. Within the uncertainties of a schematic coupled channels calculation the isotopic differences of the sub-barrier fusion enhancement can be understood on the basis of the isotopic differences of the transfer form factors andQ-values.     

Evaporation residue excitation functions for 35Cl induced reactions of 112, 120Sn and 141Pr

Evaporation residue excitation functions have been measured for ³⁵Cl ions up to 170 MeV (lab) on targets of ^{112, 120}Sn and ¹⁴¹Pr. These values are combined with previously reported fission excitation functions to give fusion excitation functions. Classical analysis of these results yield fusion barriers and fusion radii. Earlier results are confirmed: as the target atomic number increases the required density penetration at the fusion barrier increases. The percentage of the reaction cross section undergoing fusion monotonically decreases as the targets go from ²⁷Al to ¹⁴¹Pr. The nuclear contribution to the fusion barrier deduced from these measurements is compared with several model predictions and is found to be in satisfactory agreement with the models due to Bass and Krappe and Nix.     

Fusion excitation function measurements for the 16O+58Ni and 16O+62Ni systems

High precision fusion excitation functions have been measured for the ¹⁶O+⁵⁸Ni and ¹⁶O+⁶²Ni systems from which fusion barrier distributions have been evaluated. Coupled-reaction-channels (CRC) calculations, which describe elastic and quasi-elastic scattering, also satisfactorily reproduce the fusion cross sections and barrier distributions. The small value of Z₁Z₂ in this case leads to barrier distributions with relatively little structure. However, in conjunction with the detailed elastic scattering data for these systems, this allows us to elucidate the role of previously ignored states in ¹⁶O in pushing the entire distribution to lower energies. These shifts are consistent with derived magnitudes of polarization potentials for both systems.     

Heavy-ion fusion at low energies

Through precision measurements of fusion cross sections at energies close to the Coulomb barrier and through the application of the method of “experimental barrier distributions” which these permit, many recent advances have been made in our understanding of the dynamical processes occurring during a heavy-ion collision. It is now clear that the target and projectile reach one another in superpositions of states which correspond to different orientations for rotational nuclei or to different induced deformations for vibrational nuclei. The creation of a neck of neutron matter has also long been postulated and by studying the isotopic dependence of the fusion reaction, some recent results in the ¹⁰Ca+^90,96Zr systems appear to confirm this result. For large Z ₁ Z ₂ a type of extra-push effect can arise from the same inelastic entrance-channel effects which enhance the fusion of lighter systems, though this will be absent in cases where the enhancement arises from neutron transfers. The existence of different barriers will of course influence all other reaction channels. Fusion simply allows one to visualise the barriers most easily, since for this process, the total cross section is an incoherent sum of the contributions from all relevant eigenchannels. Some effects in other channels have already been observed. Other possible effects will be discussed. These include; the exploitation of the lowest-energy barrier to produce exotic evaporation residues and strongly deformed high-spin states at low excitation energy.     

Excitation functions of <Superscript>6</Superscript>Li incomplete fusion reactions with Pt nuclei

Experimentally determined excitation functions of the transfer reactions producing ^194–199Au and ^197m Hg isotopes during the interaction of ⁶Li with Pt nuclei are presented. An analysis of the experimental data as compared to EMPIRE-2.18 model calculations and experimental results on the d + ^natPt and α + ^natPt reactions allow determination of the interaction channels of d- and α-clusters in ⁶Li with the target nucleus. The results from model calculations of the reaction cross sections appear considerably lower than the experimental data. This discrepancy in describing the reactions with weakly bound nuclei is probably associated with the incomplete consideration of various interaction channels in the EMPERE-2.18 software. It is clear that a complete understanding of the interaction pattern in these processes requires consideration of the direct channels of ⁶Li nucleus cluster transfer during ⁶Li breakup near the Coulomb barrier.     

Fusion-fission of light nuclear systems

Considerable interest has been devoted to fusion reactions between light heavy ions specially between weakly bound ones, due to the anomalous decrease of the fusion cross sections when compared to the total reaction cross section in the energy region around the barrier [1–4]. While the exact nature of the process responsible for the fusion cross section limitation at barrier energies is still unclear, this study shows an inhibition of the yield as the system mass decreases, resulting from the progressive increase of the barrier height and decrease of the effective barrier radius [3]. Furthermore, extensive efforts have been made recently in the study of energy-damped binary yields from light heavy-ion collisions [2,4]. Based on the substantial amount of data accumulated so far, it is now generally accepted and supported by the transition state model [4], that the observed yields arise mostly from a fusion-fission process. Data on complete fusion, fusion-fission and ‘elastic fission’ for the ⁹Be, ^10,11B+^10,11B; ^16,17,18O + ^10,11B; ¹⁹F+¹²C; ^6,7Li+⁹Be, ¹²C reactions among others, are presented. For the loosely bound nuclei it was found that the severe fusion cross section limitation is due to a low survival probability of the weakly bound nuclei until the instant of the collision [1].     

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.     

Complete and incomplete fusion studies in7Li and16O induced reactions on51V by measurement of excitation functions and recoil ranges

Excitation function and mean projected recoil ranges of nuclei produced in the⁷Li and¹⁶O induced reactions on⁵¹V target were measured by conventional stacked foil and thick-target thick-recoil-catcher technique for bombarding energiesE ≤ 50.0 MeV for⁷Li ions andE ≃ 60.0-96.0 MeV for the¹⁶O ions. The measured recoil ranges are converted to momentum transfer. The momentum transfer information was used to get clues about some aspects of the interaction such as complete and incomplete fusion reaction mechanism which correspond to full and reduced momentum transfer respectively. The measured excitation functions are compared with the calculation based on the statistical model which describes only equilibrium decay of the compound nucleus using the CASCADE code. The comparison of the CASCADE code with the measured excitation functions for the residue radioisotopes⁵¹Cr and⁵⁴Mn for the⁷Li +⁵¹V system indicates the reaction mechanisms is complete fusion of⁷Li with the target nucleus⁵¹V. Similarly the comparison of the CASCADE code with the measured excitation functions of the residue radioisotopes for the system¹⁶O +⁵¹ V indicates that the four reaction mechanisms (i) complete fusion of¹⁶O, (ii) incomplete fusion of¹²C, (iii) incomplete fusion of⁸Be and (iv) incomplete fusion of⁴He respectively with the target might be contributing to reaction cross sections.     

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 and sub-barrier fusion in 40Ca + 90, 96Zr

The two systems ⁴⁰Ca + ^90,96Zr have been studied by measuring nucleon transfer reactions at two energies near the Coulomb barrier, thus complementing the available sub-barrier fusion cross-sections. Angular distributions for various transfer channels have been determined. Significantly larger neutron transfer cross-sections are found for the target ⁹⁶Zr that exhibits the larger enhancement in the sub-barrier fusion cross-sections. All data have been analyzed with a new model for heavy-ion collisions that calculates simultaneously transfer cross-sections, fusion excitation functions and barrier distributions. The model gives a good account of both transfer and fusion data. Received: 2 May 2002 / Accepted: 4 June 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: montagnoli@pd.infn.it, Fax +39049 8277102, Tel. +39049 8277117. RID="b" ID="b"On leave from the China Institute for Atomic Energy, 102413 Beijing, China. Communicated by C. Signorini     

Investigation of the influence of incomplete fusion on complete fusion of <Superscript>12</Superscript>C-induced reactions at ≈ 4–7.2 MeV/nucleon

In this paper, we present the results of our investigation of reaction dynamics leading to incomplete fusion of heavy ions at moderate excitation energies, especially the influence of incomplete fusion on complete fusion of ¹²C -induced reactions at specific energies ≈ 4–7.2M eV/nucleon. Excitation functions of various reaction products populated via complete and/or incomplete fusions of a ¹²C projectile with ⁹³Nb, ⁵⁹Co and ⁵²Cr targets were measured at several specific energies ≈ 4–7.2 MeV/nucleon, using a recoil catcher technique, followed by off-line γ-ray spectrometry. The measured excitation functions were compared with theoretical values obtained using the PACE4 statistical model code. For representative non-α-emitting channels in the ¹²C + ⁹³Nb system, the experimentally measured excitation functions were, in general, found to be in good agreement with the theoretical predictions. However, for α-emitting channels in the ¹²C + ⁹³Nb, ¹²C + ⁵⁹Co, and ¹²C + ⁵²Cr systems, the measured excitation functions were higher than the predictions of the theoretical model code, which may be credited to incomplete fusion reactions at these energies. An attempt was made to estimate the incomplete fusion fraction for the present systems, which revealed that the fraction was sensitive to the projectile energy and mass asymmetry of the entrance channel.     

Dynamics of low-energy heavy-ion fusion

Preliminary data on the fusion of ³⁶S+⁹⁶Zr are reported; the excitation function near the barrier is intermediate between those of ⁴⁰Ca+^90,96Zr. The peculiar role of the strong 3⁻ octupole vibration of ⁹⁶Zr is pointed out, in addition to the couplings to neutron transfer channels with positive Q-values. Recent data on ⁴⁰Ca+¹²⁴Sn are also shown; for that system the fusion barrier distribution is wide without separated peaks, similar to the case of ⁴⁰Ca+⁹⁶Zr. Simplified coupled-channel calculations have been performed, including surface vibrations and sequential neutron pick-up channels, with form factors that fit the single- and multi-nucleon transfer data for ⁴⁰Ca+¹²⁴Sn. A good agreement with the data is found.     

Effect of nuclear-reaction mechanisms on the population of excited nuclear states and isomeric ratios

Experimental data on the cross sections for channels of fusion and transfer reactions induced by beams of radioactive halo nuclei and clustered and stable loosely bound nuclei were analyzed, and the results of this analysis were summarized. The interplay of the excitation of single-particle states in reaction-product nuclei and direct reaction channels was established for transfer reactions. Respective experiments were performed in stable (⁶Li) and radioactive (⁶Не) beams of the DRIBs accelerator complex at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, and in deuteron and ³Не beams of the U-120M cyclotron at the Nuclear Physics Institute, Academy Sciences of Czech Republic (?e? and Prague, Czech Republic). Data on subbarrier and near-barrier fusion reactions involving clustered and loosely bound light nuclei (⁶Li and ³He) can be described quite reliably within simple evaporation models with allowance for different reaction Q-values and couple channels. In reactions involving halo nuclei, their structure manifests itself most strongly in the region of energies below the Coulomb barrier. Neutron transfer occurs with a high probability in the interactions of all loosely bound nuclei with light and heavy stable nuclei at positive Q-values. The cross sections for such reactions and the respective isomeric ratios differ drastically for nucleon stripping and nucleon pickup mechanisms. This is due to the difference in the population probabilities for excited single-particle states.     

基于双核模型对超重元素合成机制的研究

在双核模型基础上，考虑了熔合与准裂变的竞争，通过数值法求解主方程，计算了⁵⁰Ti，⁵⁸Fe+²⁰⁸Pb，²⁰⁹Bi这4个反应系统通过冷熔合反应合成超重元素的激发函数，得到了与实验比较符合的结果.计算了不同入射能量时各角动量分波对熔合概率和超重核存活概率的影响以及对蒸发剩余截面的贡献.这些结果对进一步理解超重核的合成机制有重要意义. 关键词： 超重元素 双核模型 熔合反应 蒸发剩余截面     

Empirical and theoretical fusion barriers for1H and4He: Connections to evaporation from hot nuclei

Fusion excitation functions for¹H and⁴He have been compared to a one-dimensional, barrier-penetration model. In contrast to fusion for heavier nuclei this simple model is completely adequate, except for the statically deformed targed²³³U. Empirical barrier heights are obtained and compared to those from two theoretical nuclear potentials. These empirical barriers (from cold reactants) are used as input for calculating evaporation spectra that arise from hot nuclear emitters. The excess of observed low-energy¹H and⁴He emission signals information content concerning distortions of the hot nuclei.     

Fusability and fissionability in 86Kr-induced reactions near and below the fusion barrier

Evaporation-residue excitation functions for the reactions ⁸⁶Kr + ^70,76Ge, ^92,100 Mo, ^99,102,104 Ru have been measured using activation methods and the velocity filter SHIP. The data span the region from well below the fusion barrier up to, and beyond, the energy where limitation by fission competition takes place. The data are shown to be compatible with the concept of complete fusion followed by the statistical decay of the equilibrated compound nucleus. Information on both the fusion probability at and below the fusion threshold and the fissionability of the compound nuclei formed, is extracted. The model dependence of the extracted fission barriers is discussed in detail. In analogy to studies involving lighter projectiles, strong correlations between the low-energy nuclear-structure properties of the nuclei and the subbarrier fusion probability are found. A relative shift of the fusion barrier to higher energies, that increases with the number of valence neutrons in the target nuclei, is observed.     

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.