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.     

Measurement of excitation functions and mean projected recoil ranges of nuclei in12C-induced reactions on vanadium

Excitation function and mean projected recoil ranges of nuclei produced in the¹²C-induced reactions on⁵¹V target were measured by conventional stacked foil and thick-target thick-recoil-catcher technique for bombarding energiesE ≤ 84 MeV for¹²C ion beam. The measured recoil ranges are converted to momentum transfer. Information on momentum transfer was used to get clues about some aspects of the interaction such as complete fusion which corresponds to full momentum transfer and incomplete fusion reaction mechanism. 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 and the geometry dependent hybrid model which describes equilibrium as well as pre-equilibrium decay of the compound nucleus using the Alice/91 code. The measured excitation functions and average ranges of the radioisotope products of the reactions¹²C on⁵¹V indicate that the three separate reaction mechanisms could be attributable to complete fusion of¹²C, incomplete fusion of⁸Be and incomplete fusion of⁴He respectively with the target. The⁸Be and⁴He are the break-up component of¹²C into⁸Be +⁴He. The predictions of the codes, especially the Cascade, generally agree with the measured cross-sections which could be attributed to complete fusion of¹²C with the target⁵¹V.     

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.     

Influence of projectile breakup on complete fusion

Complete fusion excitation functions for ^11,10B+¹⁵⁹Tb and ^6,7Li+¹⁵⁹Tb have been reported at energies around the respective Coulomb barriers. The measurements show significant suppression of complete fusion cross-sections at energies above the barrier for ¹⁰B+¹⁵⁹Tb and ^6,7Li+¹⁵⁹Tb reactions, when compared to those for ¹¹B+¹⁵⁹Tb. The comparison shows that the extent of suppression of complete fusion cross-sections is correlated with the α-separation energies of the projectiles. Also, the measured incomplete fusion cross-sections show that the α-particle emanating channel is the favoured incomplete fusion process. Inclusive measurement of the α-particles produced in ⁶Li+¹⁵⁹Tb reaction has been carried out. Preliminary CDCC calculations carried out to estimate the α-yield following ⁶Li breaking up into α+d fail to explain the measured α-yield. Transfer processes seem to be important contributors.     

7Li quasi-free scattering off the α-cluster in 9Be nucleus

Spectra of coincident charged particles from the reactions induced by a 52 MeV ⁷Li beam incident on a beryllium target were measured. Strong contributions of the ⁷Li quasi-free scattering off the α-cluster in ⁹Be nucleus were observed. This observation supports the conclusions from the study of complete fusion of weakly bound light nuclei at low energies that the “fragility” of the nuclei makes their fusion less probable. Received: 1 June 1998     

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.     

Total cross-section measurements for the production of nuclear gamma rays from light nuclei by low-energy deuterons

The thick target yields of the reactions ⁶Li, ⁹Be, ¹⁰B(d, nγ) for specific final nucleus γ-rays have been measured between deuteron bombarding energies of 48 and 170 keV. The measured thick target yields are used, together with recently published values of the stopping power of low-energy deuterons in matter, to infer the total reaction cross sections for the production of the specific γ-rays between deuteron energies of 65 and 160 keV. The cross sections are compared to appropriate Coulomb barrier penetration probabilities and the astrophysical functions S(E) are deduced.     

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].     

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.     

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.     

X‐ray spectrometry: a powerful tool for the measurement of complete fusion of weakly bound nuclei

We describe how the method of detection of delayed K x‐rays produced by the electron capture decay of the residual nuclei can be a powerful tool in the investigation of the effect of the breakup process on the complete fusion (CF) cross‐section of weakly bound nuclei at energies close to the Coulomb barrier. This is presently one of the most interesting subjects under investigation in the field of low‐energy nuclear reactions, and the difficult experimental task of separating CF from the incomplete fusion (ICF) of one of the breakup fragments can be achieved by the x‐ray spectrometry method. We present results for the fusion of the ⁹Be + ¹⁴⁴Sm system. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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.     

Probing of complete and incomplete fusion dynamics in heavy-ion collision

Three different types of experiments have been performed to explore the complete and incomplete fusion dynamics in heavy-ion collisions. In this respect, first experiment for the measurement of excitation functions of the evaporation residues produced in the ²⁰Ne + ¹⁶⁵Ho system at projectile energy ranges ≈2–8 MeV /nucleon has been done. Measured cumulative and direct cross-sections have been compared with the theoretical model code PACE-2, which takes into account only the complete fusion process. It has been observed that, incomplete fusion fraction is sensitively dependent on projectile energy and mass asymmetry between the projectile and the target systems. Second experiment for measuring the forward recoil range distributions of the evaporation residues produced in the ²⁰Ne + ¹⁶⁵Ho system at projectile energy ≈8 MeV /nucleon has been done. It has been observed that, some evaporation residues have shown additional peaks in the measured forwardrecoil range distributions at cumulative thicknesses relatively smaller than the expected range of the residues produced via complete fusion. The results indicate the occurrence of incomplete fusion involving the breakup of ²⁰Ne into ⁴He + ¹⁶O and /or ⁸Be + ¹²C followed by one of the fragments with target nucleus ¹⁶⁵Ho. Third experiment for the measurement of spin distribution of the evaporation residues produced in the ¹⁶O + ¹²⁴Sn system at projectile energy ≈6 MeV /nucleon, showed that the residues produced as incomplete fusion products associated with fast α and 2 α-emission channels observed in the forward cone, are found to be distinctly different from those of the residues produced as complete fusion products. The spin distribution of the evaporation residues also inferred that in incomplete fusion reaction channels input angular momentum (J ₀) increases with fusion incompleteness when compared to complete fusion reaction channels. Present observation clearly shows that the production of fast forward α-particles arises from relatively larger angular momentum in the entrance channel leading to peripheral collision.     

Near-barrier fusion, breakup and scattering for the Be + Sm system

Fusion, breakup and scattering for the ⁹Be + ¹⁴⁴Sm system at near barrier energies are investigated by different approaches. We show that at energies above the barrier there is a small complete fusion suppression when compared with predictions from a double folding potential and with a similar tightly bound system. At sub-barrier energies there is no significant deviation from the predictions using coupled channel calculations that do not include the breakup channel. The energy dependence of the optical potential does not show the usual threshold anomaly found in tightly bound systems. From a simultaneous analysis of fusion and scattering data we estimate the distance where breakup starts to occur.     

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.     

Elastic scattering of 9Be on light target nuclei

The elastic scattering of ⁹Be on the target nuclei ⁹Be, ¹²C, ¹³C and ¹⁶O was measured at projectile energies of 14, 20 and 26 MeV. All angular distributions show a diffraction-like structure. In addition, excitation curves were measured for the scattering of ⁹Be on ⁹Be at three different angles in the energy range of 9–22 MeV. An optical potential having parameters independent of mass number and energy and reproducing all the measured angular distributions in the forward angular region was found and compared with that for the scattering of ⁹Be on medium and heavy nuclei.     

Residual velocity distributions in complete and incomplete fusion reactions

Theoretical simulation of residual velocity distributions at various mass windows for complete and incomplete fusion reactions have been done for the system⁴⁰Ar+²⁴Mg at the incident energies of 1100, 800 and 600 MeV. The comparison of the residual velocity distributions enables us to have a qualitative understanding about the relative contributions of the complete and incomplete fusion processes in intermediate energy heavy ion reaction.     

Beam-Based Production of 178m2Hf

In this study, the production yield for the reaction ¹⁷⁶Yb(⁹Be, α3n)¹⁷⁸Hf was explored using the FN tandem injected superconducting LINAC at SUNY at Stony Brook at a ⁹Be energy of 65 MeV. By comparing the experimental yield of ¹⁷⁸Hf ground state γ rays with those of ¹⁸⁰W as a function of energy, the cross section for production of the incomplete fusion γ rays in ¹⁷⁸Hf was evaluated. Coincidence measurements were made to get information about the population strength of the high spin states in ¹⁷⁸Hf. From these measurements, the maximum cross section for the reaction ¹⁷⁶Yb(⁹Be, α3n)^178m2Hf is estimated to be no larger than 5 mb. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fusion of halo nuclei

The sub-barrier fusion of halo nuclei such as ¹¹Be and ¹¹Li with heavy target nuclei is discussed. The couplings to the soft dipole mode as well as to the break-up channels are taken into account. At barrier energies, the fusion cross section was found to be more than one order of magnitude smaller than that corresponding to the uncoupled problem. At sub-barrier energies, it was shown to be larger.