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     

Scattering of 11Be halo nucleus from 209Bi at the Coulomb barrier

The scattering of the radioactive, weakly bound, halo nucleus ¹¹Be from ²⁰⁹Bi has been studied at 40MeV beam energy. The measurement performed with a low-intensity and a large-emittance secondary beam could be made using an extremely compact, large solid angle (∼ 2π sr) detecting set-up, based on 8 highly segmented Si telescopes. The ^{11, 9}Be scattering angular distributions, as well as their relative reaction cross-sections, resulted to be rather similar. This may suggest that at Coulomb barrier energies the halo structure and the very small binding energy of the ¹¹Be projectile have no big influence on the reaction dynamics.     

Measurement of fusion cross section with neutron halo nuclei

Fusion cross sections of ¹¹Be, ¹⁰Be and ⁹Be have been measured on ²⁰⁹Bi target at 30–70 MeV. Due to the neutron halo effect of ¹¹Be, a large enhancement or suppression of the fusion cross section around the Coulomb barrier was theoretically predicted. Comparing the excitation function of ¹¹Be with ¹⁰Be at near the Coulomb barrier region, no significant difference has been observed.     

Reaction mechanisms in collisions induced by halo and/or weakly bound radioactive nuclei around the barrier

In this paper a brief review of the status of theory and experiments concerning the study of reaction mechanisms, in particular fusion, with halo and loosely bound nuclei at energies around the Coulomb barrier is made. The data of the reactions ^4,6He+⁶⁴Zn and ¹³N+⁹Be are discussed in more detail.     

Fusion-fission reactions induced by 6He-ions

The experimentally measured excitation functions for the fission and 4n evaporation channels are presented for the ⁶He + ²⁰⁹Bi reaction. The secondary ⁶He beam was produced using the special beam line (Q4DQ-spectrometer) of the U400M accelerator at FLNR, JINR. The comparison of the obtained experimental data with similar results for the ⁴He + ²⁰⁹Bi reaction shows that in the case of the ⁶He + ²⁰⁹Bi reaction a significant enhancement of the cross-section is observed for energies above the barrier. In order to get an agreement between the experimental data and the theoretical calculations it is necessary to reduce the Coulomb barrier by 15-20% , which corresponds to an increase of the parameter r₀ of the nuclear potential up to 1.5-1.6 fm. Received: 1 May 2001 / Accepted: 4 December 2001     

Transfer, breakup, and fusion reactions of 6He with 209Bi near the Coulomb barrier

The fusion of ⁶He with a ²⁰⁹Bi target displays a large enhancement at energies near to and below the Coulomb barrier. Recently, a ⁴He group of remarkable intensity, which dominates the total reaction cross-section, has also been observed in the near-barrier interaction of the same system. It is argued that this transfer/breakup channel acts as a doorway state to fusion. Received: 1 May 2001 / Accepted: 4 December 2001     

Variation of total kinetic energy and mass distributions in the fusion-fission reaction of 16O,19F + 209Bi at near barrier energies

Fission fragment mass and energy distributions and their correlations have been measured for the ¹⁶O and ¹⁹F + ²⁰⁹Bi reactions over a wide range of excitation energies ( E ^* = 30-50 MeV). It is observed that in the case of ¹⁶O + ²⁰⁹Bi reaction, the average total fragment kinetic energy, <TKE> is nearly independent of the bombarding energy. However, in the case of ¹⁹F + ²⁰⁹Bi reaction, the average total kinetic energy of the fission fragments shows a peaking behaviour near the barrier. The variation in <TKE> at near barrier energies in the ¹⁹F + ²⁰⁹Bi system seems to be correlated with corresponding strong variation in the variance of the fragment mass distribution. The present results may imply certain dynamical effects leading to compact scission configurations in the fission of ¹⁹F + ²⁰⁹Bi system at near barrier bombarding energies. Received: 9 April 2001 / Accepted: 26 May 2001     

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.     

Interaction at the barrier in the systems 9, 10, 11Be + 209Bi: Well-established facts and open questions

The experimental data relative to the interaction for the systems ^{9, 10, 11}Be + ²⁰⁹Bi at the Coulomb barrier are critically discussed and compared also with present theories. The break-up (BU) of the two loosely bound projectiles, ^{9, 11}Be, seems to influence the fusion process by “hindering” the fusion cross-sections; but, contrary to expectations, the ¹¹Be halo structure has no influence, since no “enhancement” is evident from the existing data. Attempt to describe simultaneously all the ⁹Be + ²⁰⁹Bi system data: fusion, elastic scattering and BU, within a coupled-channel (CC) approach is only partly successful. It is important, from a theoretical viewpoint, to include in the CC formalism as well as possible the BU process both to continuum states as well as to unbound resonances. More accurate and well-focused experiments are also necessary to pin down this problem. Received: 1 May 2001 / Accepted: 4 December 2001     

Does break-up affect 9Be +209Bi fusion at the barrier?

The ⁹Be +²⁰⁹Bi fusion cross sections were measured in the 36.0 MeV ≤ E_lab≤ 50.0 MeV range, down to 0.6 mb, with high accuracy via in-beam detection of the ground state α-decay of the evaporation residues produced. The elastic scattering cross sections around 150° and 135° were also obtained with moderate angular resolution. The cross sections below the barrier are reproduced by coupled channel calculations which include only one break-up channel with a moderate strength and a phenomenological renormalization of the potential depth. These simple calculations overestimate the cross sections above the barrier most likely due to the fact that the ⁹Be break-up process becomes much stronger. The barrier distributions extracted do not have evident break-up signature since they show one-barrier structure. Received: 22 February 1999 / Revised version: 26 March 1999     

Nuclear matter incompressibility effect on the cross-section of fusion reactions with a weakly bound projectile

Fusion reactions with a weakly bound projectile are studied using the double-folding model along with a repulsive interaction modifying term.Using this modified potential,including nuclear matter incompressibility effects,the fusion reaction cross sections and suppression parameters are calculated for9Be+209Bi,208Pb,29Si and27Al reactions.The results show that applying these effects at energies near the Coulomb barrier improves the agreement between the calculated and experimental cross sections,and modifies the mean values of the suppression parameter.     

Fission fragment anisotropies for 19F +209Bi system

The fission fragment angular distributions have been measured for the system ¹⁹F +²⁰⁹Bi over a range of bombarding energies from 88.0 MeV to 125.6 MeV. The measured fission fragment anisotropies are in agreement with the saddle point statistical model calculations in the above energy range. Combining these data with those available for ¹¹B, ¹²C, ¹⁴N, ¹⁶O and ¹⁸O +²⁰⁹Bi, ²⁰⁸Pb systems, it is concluded that the spherical target plus projectile systems behave “normal” from near- to above – barrier energies. This observation is in contrast to the “anomalous” anisotropies exhibited by the deformed actinide target – projectile systems at near – barrier energies. Received: 5 May 1999 / Revised version: 25 July 1999     

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.     

Above-barrier enhancement of fusion in the 6He + 209Bi nuclear reaction

The fission cross sections for the ⁶He + ²⁰⁹Bi reaction as functions of the ⁶He-beam energy are measured. The experimental excitation functions for the reaction ²⁰⁹Bi(⁶He, 4n)²¹¹ At are also presented. The ⁶He secondary ion beam is obtained on the basis of the extracted-beam transport system of the U400-M accelerator (the Q4DQ spectrometer). A comparison of the experimental data obtained with available results for the ⁶He + ²⁰⁹Bi reaction shows that a pronounced enhancement of the fission cross sections in the above-barrier energy region is observed in the case of the reaction with the ⁶He beam. In order to fit the results of theoretical calculations to the experimental data, it is necessary to reduce the Coulomb barrier by 15% (20%). This corresponds to an increase of 1.5 (1.6) fm in the parameter r ₀ of the nuclear potential.     

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.     

E2 component in subcoulomb breakup of 8B

We calculate the angular distribution and total cross section of the ⁷Be fragment emitted in the break up reaction of ⁸B on ⁵⁸Ni and ²⁰⁸Pb targets at the subcoulomb beam energy of 25.8 MeV, within the non-relativistic theory of Coulomb excitation with proper three-body kinematics. The relative contributions of the E1, E2 and M1 multipolarities to the cross sections are determined. The E2 component makes up about 65% and 40% of the ⁷Be total cross section for the ⁵⁸Ni and ²⁰⁸Pb targets respectively. We find that the extraction of the astrophysical S-factor, S₁₇(0), for the ⁷Be(p,γ)⁸B reaction at solar energies from the measurements of the cross sections of the ⁷Be fragment in the Coulomb dissociation of ⁸B at sub-Coulomb energies is still not free from the uncertainties of the E2 component.     

The proton optical-model potential near the Coulomb barrier

Proton elastic scattering data from ¹⁹⁷Au, ²⁰⁸Pb and ²⁰⁹Bi at energies near the Coulomb barrier are analyzed. The energy dependences of the real volume and imaginary surface-derivative potential depths V_R and W_SF of a local optical-model potential with fixed geometric parameters are found to be much more rapid than at higher energies. The strong energy dependence of V_Rnear the Coulomb barrier is explained in terms of the non-locality of the nucleon-nucleus interaction.     

An empirical fit to estimated neutron emission cross sections from proton induced reactions

Neutron emission cross section for various elements from⁹Be to²⁰⁹Bi have been calculated using the hybrid model code ALICE-91 for proton induced reactions in the energy range 25 MeV to 105 Me V. An empirical expression relating neutron emission cross section to target mass number and incident proton energy has been obtained. The simple expression reduces the computation time significantly. The trend in the variation of neutron emission cross sections with respect to the target mass number and incident proton energy has been discussed within the framework of the model used.     

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].     

Special features of nuclear reactions induced by loosely bound <Superscript>6</Superscript>He and <Superscript>6,7</Superscript>Li nuclei in the vicinity of the Coulomb barrier height

Excitation functions are measured for complete-fusion and transfer reactions induced by the interaction of ⁶He and ⁶Li with ²⁰⁶Pb, ²⁰⁹Bi, and Pt. Data obtained for fusion reactions induced by ⁶He ions deviate from the predictions of the statistical model of compound-nucleus decay at projectile energies in the vicinity of the Coulomb barrier height. A strong enhancement of cross sections for fusion reactions induced by the interaction of ⁶He with target nuclei is observed. The cross sections for reactions of cluster transfer, neutron transfer from ⁶He, and deuteron transfer from ⁶Li at deep-subbarrier energies are also found to be enhanced. These results are discussed from the point of view of the effect of the cluster structure of nuclei on the interaction probability at energies in the vicinity of the Coulomb barrier height.