Heavy ion reactions around the Coulomb barrier

The angular distributions of fission fragments for the 32S+184W reaction near Coulomb barrier energies are measured. The ex perimental fission excitation function is obtained. The measured fission cross sections are decomposed into fusion-fission, quasi-fission and fast fission contributions by the dinuclear system (DNS) model. The hindrance to completing fusion both at small and large collision energies is explained. The fusion excitation functions of 32S+90,96Zr in an energy range from above to below the ...     

Elastic and inelastic scattering of 58Ni +90,94Zr

Pure elastic and inelastic scattering cross sections have been measured for the systems ⁵⁸Ni +^90,94Zr at energies near the Coulomb barrier where not only quasi-elastic and fusion but also deep-inelastic process come into play. Coupled channels calculations including both projectile and target inelastic excitations can successfully explain the elastic and inelastic scattering angular distributions with an energy-independent semi-empirical bare potential. The calculation reproduces also the sum of the total quasi-elastic, fusion and deep-inelastic cross sections. Received: 14 September 1998 / Revised version: 21 October 1998     

Elastic scattering and fusion cross-sections in 7Li + 27Al reaction

With an aim to understand the effects of breakup and transfer channels on elastic scattering and fusion cross-sections in the ⁷Li + ²⁷Al reaction, simultaneous measurement of elastic scattering angular distributions and fusion cross-sections have been carried out at various energies (E _lab?=?8.0–16.0 MeV) around the Coulomb barrier. Optical model (OM) analysis of the elastic scattering data does not show any threshold anomaly or breakup threshold anomaly behaviour in the energy dependence of the real and imaginary parts of the OM potential. Fusion cross-section at each bombarding energy is extracted from the measured α-particle evaporation energy spectra at backward angles by comparing with the statistical model prediction. Results on fusion cross-sections from the present measurements along with data from the literature have been compared with the coupled-channels predictions. Detailed coupled-channels calculations have been carried out to study the effect of coupling of breakup, inelastic and transfer, channels on elastic scattering and fusion. The effect of 1n-stripping transfer coupling was found to be significant compared to that of the projectile breakup couplings in the present system.     

Influence of breakup on elastic and α-production channels in the ~6Li+~(116)Sn reaction

The effects of breakup reactions on elastic and α-production channels for the ~6Li+~(116)Sn system have been investigated at energies below and near the Coulomb barrier. The angular distributions of α-particle production differential cross sections have been obtained at several projectile energies between 22 and 40 MeV. The measured breakup α-particle differential cross sections and elastic scattering angular distributions have been compared with the predictions of continuum-discretized coupled channels(CDCC) calculations. The influence of breakup coupling has also been investigated by extracting dynamic polarization potentials(DPP) from the CDCC calculations. From the predictions of CDCC calculations the relative importance of the nuclear, Coulomb, and total breakup contributions have also been investigated. The nuclear breakup couplings are observed to play an important role in comparison to the Coulomb breakup for the direct breakup mechanisms associated in the reaction of ~6Li projectile with ~(116)Sn target nuclei. The influence of strong nuclear breakup coupling exhibits suppression in the Coulomb-nuclear interference peak. The direct breakup cross sections from the CDCC calculations under-predict the measured α-particle differential cross sections at all energies. This suggests that the measured α particles may also have contributions from other possible breakup reaction channels.     

Angular momentum and cross sections for fusion with weakly bound nuclei: breakup,a coherent effect

Results for the cross section and average angular momentum for complete fusion at energies around the Coulomb barrier are presented for 7Li with 165Ho. Comparison of the cross sections with a one-dimensional barrier penetration model, using a potential consistent with the measured elastic scattering, showed a reduction above the barrier and an enhancement below it. An increase in the measured average angular momentum, , above the barrier and its consistency with that obtained from the fusion excitation function for weakly bound nuclei, is reported. These results together with a reanalysis of existing data conclusively demonstrate that the effect of breakup on fusion is coherent, like coupling to any nonelastic channel.     

Strong coupling effects in near-barrier heavy-ion elastic scattering

Accurate elastic scattering angular distribution data measured at bombarding energies just above the Coulomb barrier have shapes that can markedly differ from or be the same as the expected classical Fresnel scattering pattern depending on the structure of the projectile, the target or both. Examples are given such as ¹⁸O + ¹⁸⁴W and ¹⁶O + ^{148, 152}Sm, where the expected rise above Rutherford scattering due to Coulomb-nuclear interference is damped by coupling to the target excited states, and the extreme case of ¹¹Li scattering, where coupling to the ⁹Li + n + n continuum leads to an elastic scattering shape that cannot be reproduced by any standard optical model parameter set. An early indication that the projectile structure can modify the elastic scattering angular distribution was the large vector analyzing powers observed in polarised ⁶Li scattering. The recent availability of high-quality ⁶He, ¹¹Li and ¹¹Be data provides further examples of the influence that coupling effects can have on elastic scattering. Conditions for strong projectile-target coupling effects are presented with special emphasis on the importance of the beam-target charge combination being large enough to bring about the strong coupling effects. Several measurements are proposed that can lead to further understanding of strong coupling effects by both inelastic excitation and nucleon transfer on near-barrier elastic scattering. A final note on the anomalous nature of ⁸B elastic scattering is presented as it possesses a more or less normal Fresnel scattering shape whereas one would a priori not expect this due to the very low breakup threshold of ⁸B . The special nature of ¹¹Li is presented as it is predicted that no matter how far above the Coulomb barrier the elastic scattering is measured, its shape will not appear as Fresnel like whereas the elastic scattering of all other loosely bound nuclei studied to date should eventually do so as the incident energy is increased, making both ⁸B and ¹¹Li truly “exotic”.     

Partial fusion of a weakly bound projectile with heavy target at energies above the Coulomb barrier

Partial-fusion cross-sections for the systems ⁶Li + ²⁰⁸Pb, ⁹Be + ²⁰⁹Bi have been determined. The effect of breakup on fusion for weakly bound projectiles ⁶Li and ⁹Be incident on ²⁰⁸Pb or ²⁰⁹Bi targets has been discussed comparing experimental fusion cross-section excitation functions to those evaluated with a semi-classical approach. It is shown that complete fusion of a weakly bound projectile with heavy target is reduced, whereas the breakup process has very little influence on the total-fusion cross-section for some of the studied systems at energies above the Coulomb barrier.     

Coulomb-nuclear interference in the scattering of 3He and α-particles by 122,124Te, 124Sn and 114Cd

Angular distributions and excitation functions of the elastic and inelastic scattering of ³He and α-particles by ^122,124Te, ¹²⁴Sn and ¹¹⁴Cd at incident energies around the Coulomb barrier were measured. The experimental results were analyzed in the framework of the optical model and DWBA taking into account the interference between nuclear and Coulomb excitation. Nuclear and charge deformation parameters were deduced.     

Near-barrier quasi-elastic cross sections and barrier distribution of 32S+90,96Zr

Quasi-elastic cross sections have been measured for ³²S+^90,96Zr with high accuracy near the Coulomb barrier at backward angles and the barrier distributions are extracted from them. We find that barrier distribution of ³²S+⁹⁶Zr is flat and extends to low energies. The sub-barrier fusion cross sections are strongly enhanced because of such barrier distribution. Compared with the reaction of ³²S+⁹⁰Zr, ³²S+⁹⁶Zr has stronger neutron transfers up to the six-neutron pickup, which is due to the positive Q values of neutron transfers in the latter. This indicates that the neutron transfer may play a role in the enhancement of sub-barrier fusion for ³²S+⁹⁶Zr.     

Elastic and inelastic scattering of 16O and 12C by 24Mg near the Coulomb barrier

Angular distributions for ¹⁶O + ²⁴Mg and ¹²C + ²⁴Mg elastic and inelastic (2⁺, 1.37 MeV state in ²⁴Mg) scattering have been measured at energies spanning the Coulomb barrier. Apart from the structure typical of strong destructive Coulomb-nuclear interference, the data exhibit some additional specific features. Coupled channel calculations were performed, along with DWBA calculations to analyse the data using fixed coupling strengths deduced from the results of Coulomb excitation work. The importance of higher-order effects such as reorientation, is demonstrated.     

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.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

Elastic scattering and total reaction cross section for the He + Al system

The elastic scattering of the radioactive halo nucleus ⁶He on ²⁷Al target was measured at four energies close to the Coulomb barrier using the RIBRAS (Radioactive Ion Beams in Brazil) facility. The São Paulo Potential (SPP) was used and its diffuseness and imaginary strength were adjusted to fit the elastic scattering angular distributions. Reaction cross-sections were extracted from the optical model fits. The reduced reaction cross-sections of ⁶He on ²⁷Al are similar to those for stable, weakly bound projectiles as ^6,7Li, ⁹Be and larger than stable, tightly bound projectile as ¹⁶O on ²⁷Al.     

Surface Diffuseness Anomaly in 16O+208Pb Quasi-elastic Scattering at Backward Angle

The quasi-elastic scattering excitation function of the doubly magic ^16O＋^208 Pb system at a backward angle is measured at sub-barrier energies with high precision. The diffuseness parameters extracted from both the singlechannel and the coupled-channels calculations give almost the same value a = 0.76 ± 0.04 fro. The results show that the coupling effect is negligible for the spherical system. The obtained value is smaller than the extracted value from the fusion excitation function, but larger than the value of a -- 0.63 fm, which is from the systematic analysis of elastic scattering data.     

Fission of238U induced by136Xe for energies close to the Coulomb barrier

Excitation functions and angular distributions have been measured for fission of²³⁸U induced by¹³⁶Xe ions with bombarding energies between 4.5 and 5.9 MeV/N. Structures expected theoretically as characteristic for Coulomb fission have not been observed. The Q-value of ?(7.5±1.0) MeV measured for bombarding energies below 4.7MeV/N, however, appears to be compatible with inelastic scattering (e.g. Coulomb excitation) rather than subcoulomb transfer followed by fission. The total kinetic energy of deep inelastic events at 5.9 MeV/N is consistent with the current knowledge about mass diffusion, but also (for the highest excitation energies) with a fast fission process in the presence of the projectile.     

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.     

IWB analysis of scattering and fusion cross sections for the 12C+12C, 13C+16O and 16O+16O reactions for energies near and below the Coulomb barrier

Calculations are presented of the elastic scattering and fusion cross sections for the astrophysically interesting reactions ¹²C+¹²C, ¹²C+¹⁶O and ¹⁶O+¹⁶O. The calculations are performed using the incoming wave boundary condition (IWB) and a real ion-ion interaction potential. The results are compared with the available experimental data for the energy region near and below the Coulomb barrier. With values of two adjustable potential parameters (the radial position of the l = 0 barrier and the diffuseness) determined by fitting elastic scattering data, good agreement is obtained for the average energy dependence of the ¹²C+¹²C and ¹²C+¹⁶O fusion cross sections. In the case of ¹⁶O+¹⁶O, both the calculated absolute magnitude and the energy dependence of the fusion cross section are inconsistent with the data and this discrepancy is 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 fusion of heavy nearly symmetric systems

Excitation functions in the vicinity of the Coulomb barrier have been measured for the formation of evaporation residues in¹⁰⁰Mo-induced fusion reactions with^{90, 92, 96}Zr,^{92, 96, 98, 100}Mo,¹⁰⁴Ru and¹¹⁰Pd as well as for the system⁹⁶Zr+⁹⁶Zr. From these data the fusion probability in central collisions was extracted covering a range of 4 orders of magnitude. At the fusion barriers expected from systematics we find that the fusion probability is suppressed by one to three orders of magnitude. It is rising very gradually at higher energies and reaches for the heaviest systems saturation only at energies as high as 30 MeV above the barrier. The observed hindrance of the fusion process increases roughly with the growing Coulomb repulsion between the collision partners, but there is also a distinct influence of their individual nuclear structure. The data are compared to the extra-push model, the surface-friction model and the diabatic fusion model. A parameterisation of the extra-push energy and its fluctuation in terms of a macroscopic quantity like the Coulomb repulsion combined with a microscopic quantity characterizing the nuclear structure is proposed. As a byproduct of this work a new alpha emitter,¹⁹¹Po, could be identified. Its half-life is (15.5 _–2.5 ⁺⁶ ) ms, the alpha energy is (7314±20) keV.