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.     

Formation and decay of the compound nucleus studied in the reaction20Ne+27Al

Energy and velocity spectra, angular and mass distributions have been measured for evaporation residue products of the^{20, 22}Ne+²⁷Al system in the energy range ofE _L (²⁰Ne)=51 to 395 MeV and in the angular rangeθ=2° and 30°. Calculations with simple assumptions of the velocity and angular distributions of the evaporation residues are presented and compared to the data. The structure seen in the mass distributions, a competition between α-particle and nucleon evaporation in the deexcitation of the compound nucleus, is described well by calculations with the computer code CASCADE. The evaporation residues exhibit mass distributions varying systematically as a function of the excitation energy. The excitation function of the evaporation residue cross section is compared with theoretical models. At higher incident energies contributions of incomplete momentum transfer (incomplete fusion) are observed. A limitation for complete compound nucleus formation with following light particle evaporation is found.     

Particle emission in central nuclear collisions between48Ti und45Sc at 16 MeV/u

Protons and α-particles were measured in coincidence with fusion residues for the reaction⁴⁸Ti+⁴⁵Sc at 16 MeV/u beam energy. Their velocity distributions show a drastic broadening to higher as well as to lower velocities as compared to the calculated equilibrium emission pattern. This is interpreted as a kinematical effect of variations of the initial velocity of the emitting system, which are attributed to the preequilibrium emission of heavier clusters from the projectile or the target nucleus in incomplete fusion processes. The measured widths of the velocity distributions of the fusion residues are consistent with this mechanism. A peak in the product mass spectrum at masses between 6 and 18 is tentatively identified with the postulated cluster emission.     

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.     

‘Slow’ residues observed in the reaction20Ne+208Pb at E/A=8.6, 11.4 and 15.0 MeV/u

Velocity distributions of heavy residuesA _Res>A _tar,Z _Res>Z _tar identified by means ofα spectroscopy, have been investigated at the velocity filter SHIP in reactions²⁰Ne+²⁰⁸Pb at projectile energies E/A=8.6, 11.4 and 15.0 MeV/u. Besides products from complete or nearly complete fusion, characterized by velocity distributions peaking atν/ν _CN?0.8–1.0, heavy residues with mean velocities of about half of the compound nucleus velocity were observed. The Z-distribution of this component was found to peak atZ=87. It is interpreted as residues from fusion of target nuclei with projectile fragments produced by nearly symmetric break-up. The experimental results were compared with predictions of theoretical models: cross sections for incomplete fusion were calculated using the sum-rule model of Wilcynski et al., while residue cross sections were calculated using the evaporation code HIVAP. A fair agreement between experimental and calculated mass distributions of heavy residues and transferred projectile fragments is achieved if an energy dissipation of ?23% (at E/A=8.6 MeV/u) and ?8% (at E/A=11.4 MeV/u) of the incident projectile energy is introduced. The observed peak of theZ-distribution atZ=87 is predominantly effected due to a higher fission probability of products withZ>87 during the deexcitation process and experimental limitations in the identification of products withZ≦86 by means of a spectroscopy, which cause a decrease of the observed production rates towards lowerZ.     

Incomplete fusion reactions in 16O+165Ho

Excitation functions for evaporation residues of the system ¹⁶O + ¹⁶⁵Ho have been measured up to 100 MeV. Recoil range distribution of long lived reaction products were measured at ¹⁶O beam energy of 100 MeV. Detailed Monte Carlo simulation of recoil range distributions of products were performed with the help of PACE2 code, in order to extract the contributions of incomplete fusion in the individual channels. The results clearly show the incomplete fusion contributions in the tantalum and thulium products. This is confirmed by the predictions of breakup fusion model of the incomplete fusion.     

Gamma-ray spectroscopy with incomplete fusion reactions for the systems 16O +58,64Ni at 100 Me V

Energy spectra and angular distributions of ejectiles with 3 ⩽ Z ⩽ 7 have been measured for the reaction ¹⁶O on ⁶⁴Ni at 100MeV incident energy. Measured optimum Q-values and cross sections are accounted for by an incomplete fusion model. Coincidences between ejectiles detected at grazing angle and discrete γ-rays have been measured for the reactions 100 MeV ¹⁶O+^58,64Ni. The in-plane to out-of-plane anisotropies of discrete γ-rays show a high degree of spin polarization of incomplete fusion residues which can be exploited for spectroscopic studies.     

Fragment angular distributions from fission of238U,209Bi and197Au by 140-MeV4He Ions

The fission fragment angular distributions from reactions of 140-MeV⁴He ions with²³⁸U,²⁰⁹Bi and¹⁹⁷Au have been studied. From the anisotropies in the angular distributions, values for? _eff, the effective moment of inertia at the fission saddle point, have been estimated and compared with results obtained at lower bombarding energies. The derivation of? _eff values has included corrections for the effects of incomplete fusion mechanisms on the orbital angular momentum distribution of the fissioning nuclei and for neutron evaporation prior to fission. The results are also compared with heavy-ion-induced fission data for systems of similar fissility. Also, examination of the forward-backward symmetry of the²³⁸U angular distribution substantiates other results which show that the fraction of fission reactions which follow complete fusion of the target and projectile is less than 0.5 for 140-MeV⁴He-ion bombardment of²³⁸U.     

Disentangling the reaction mechanisms of weakly bound nuclei

Complete and incomplete fusion cross sections for the ⁹Be + ¹⁴⁴Sm reaction have been measured at near-barrier energies, using the delayed X-ray detection technique. At above-barrier energies these show a suppression of complete fusion for this weakly bound projectile on an intermediate mass target. The suppression factor, attributed to ⁹Be break-up, was deduced from a comparison of complete fusion yields with coupled-channels calculations, and appears consistent with measured incomplete fusion product yields. At ∼10%, it is considerably smaller than the value of ∼30% previously found for a ²⁰⁸Pb target. Simultaneous measurements of elastic and inelastic scattering permit a clearer picture of the reaction mechanisms.     

Investigation of the reaction <Superscript>208</Superscript>Pb(<Superscript>18</Superscript>O, <Emphasis Type="Italic">f</Emphasis>): Folding angular distributions of fission fragments and gamma-ray multiplicity

Correlations between folding angular distributions of fission fragments and the gamma-ray multiplicity are studied for ¹⁸O + ²⁰⁸Pb interactions at energies of the beam of ¹⁸O ions in the range E _lab = 78–198.5 MeV. The probabilities are determined for complete-and incomplete-fusion processes inevitably followed by the fission of nuclei formed in these processes. It is found that the probability of incomplete fusion followed by fission increases with increasing energy of bombarding ions. It is shown that, for the incomplete-fusion process, folding angular distributions of fission fragments have a two-component structure. The width of folding angular distributions (FWHM) for complete fusion grows linearly with increasing energy of ¹⁸O ions. The multiplicity of gamma rays from fission fragments as a function of the linear-momentum transfer behaves differently for different energies of projectile ions. This circumstance is explained here by the distinction between the average angular momenta of participant nuclei in the fusion and fission channels, which is due to the difference in the probabilities of fission in the cases where different numbers of nucleons are captured by the target nucleus.     

Complete and incomplete fusion in reactions of 7Li + 56Fe at E(7Li) = 50 and 68 MeV from analysis of recoil range and light-particle measurements

Excitation functions for the production of eight radioactive products of the reactions of ⁷Li on ⁵⁶Fe have been measured up to E(⁷ Li) = 89 MeV. Recoil range distributions for these products, together with inclusive proton, deuteron, triton and alpha spectra, have been measured at energies of 50 and 68 MeV. The α, t and d spectra show characteristic “break-up” components at forward angles, while the recoil distributions show evidence of complete fusion and incomplete-fusion process ⁵⁶Fe( ⁷Li,α) ⁵⁹Co ^* . A parallel study on ⁵⁵Mn shows some evidences of the ( ⁷Li,t) incomplete-fusion process, but the cross-section for this process is significantly less than for the triton fusion process. The recoil distributions can be reproduced on the assumption that essentially all the observed break-up fragments are in fact associated with incomplete fusion, but uncertainties in normalisation leave open the possibility of a significant contribution of pure break-up. A diffraction model of the ( ⁷Li,α) transfer process reproduces the observed break-up α spectra with some success. Received: 29 March 2001 / Accepted: 12 November 2001     

The reactions of 12C with 12C AT 293 MeV

Energy spectra, angular distributions, and elemental yield distributions have been measured for products Z = 1?9 produced in the reactions of ¹²C on ¹²C. A total reaction cross section 1170_?100⁺¹⁷⁰ mb was determined from the measured elemental cross sections and the principle of charge conservation. This total reaction cross section is about 250 mb less than the geometric cross section and agrees with the Glauber-model calculations of DeVries and Peng. The experimental energy spectra, angular distributions, and yield distributions were compared with those from model calculations for the statistical decay of the products of fusion and of incomplete fusion reactions. For both types of calculations, a modified version of the code LILITA was used. By comparing the data to model calculations, an upper limit of 75 mb for the fusion cross section was determined. That limit corresponds to an upper limit of L_crit for fusion of 10? in the sharp-cutoff approximation. The dominant reaction mechanisms appear to be incomplete fusion processes.     

Complete and Incomplete Fusion in the Reaction of 115In with 16O Ions

Angular distributions and differential range distributions have been measured with nuclear chemistry techniques for 20 target residues from the reactions of ¹¹⁵In with 92 and 71MeV ¹⁶O ions.In terms of the increase of impact parameter,the results indicate continuous evolution of the reaction mechanisms from complete fusion,incomplete fusion to direct reaction involving steadily decreasing transfer of mass and momentum.Contribution of incomplete fusion in ¹⁶O+¹¹⁵In reaction is significantly larger than that in ¹⁶O+⁶⁵Cu reaction.     

Complete fusion in a light heavy-ion reaction from 2.5 to 20 MeV/nucleon

Mass distributions of evaporation-residue-like fragments have been measured using a time-of-flight system for the reaction ²⁰Ne + ²⁶Mg in the energy range of 51 to 400 MeV bombarding energy for ²⁰Ne. A good mass resolution allowed for the separation of the evaporation residues and fragments from two-body reactions like e.g. damped processes. The residue distributions were compared with evaporation calculations. The analysis of velocity spectra measured at bombarding energies of 85–395 MeV showed incomplete momentum transfer for evaporation-residue-like fragments at higher energies. Statistical-model calculations and Monte Carlo methods applied to the calculation of the velocity spectra have been used to extract the complete-fusion cross section.     

Angular distributions and forward recoil range distributions of residues created in the interaction of 12C and 16O ions with 103Rh

We have measured the angular distributions and the forward recoil range distributions of residues produced in the interaction of, respectively, 151, 228 and 402 MeV ¹²C ions with ¹⁰³Rh and the forward recoil range distributions of residues produced in the interaction of 303 MeV ¹⁶O ions with ¹⁰³Rh. These data have been successfully reproduced by a theory which assumes that the dominant mechanisms are complete and incomplete fusion of the projectile with the target and single nucleon transfers from the projectile to the target and predicts that, starting from an incident energy of about 250 MeV, a large fraction of the residues has a mass and charge very close to those of the target nucleus. This is because, at incident energies of a few hundred MeV, a large fraction of the kinetic energy of ¹²C and ¹⁶O is carried away by fast ejectiles which then leave behind the intermediate equilibrated nuclei with a rather small excitation energy and small forward linear momentum.     

Fission study for the system84Kr+232Th at 25, 35 and 45 MeV/u

Recoil velocities of heavy residues produced in the bombardment of⁸⁴Kr beams on a²³²Th target at energies about the Fermi velocity were determined using the method of correlations between fission fragments. The masses of both fragments were also measured. The data show events with high recoil velocity which are produced in incomplete fusion processes. Estimates of the energy transfer are given. Comparisons with incomplete fusion data obtained with other projectiles in the same incident velocity range show an increase of the energy transfer with the mass of the projectile.     

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.     

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.     

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.     

Angular momentum transfer in incomplete fusion

Isomeric cross-section ratios of evaporation residues formed in¹²C+⁹³Nb and¹⁶O+⁸⁹Y reactions were measured by recoil catcher technique followed by off-line γ-ray spectrometry in the beam energy range of 55.7–77.5 MeV for¹²C and 68–81 MeV for¹⁶O. The isomeric cross-section ratios were resolved into that for complete and incomplete fusion reactions. The angular momentum of the intermediate nucleus formed in incomplete fusion was deduced from the isomeric cross-section ratio by considering the statistical deexcitation of the incompletely fused composite nucleus. The data show that incomplete fusion is associated with angular momenta slightly smaller than critical angular momentum for complete fusion, indicating the deeper interpenetration of projectile and target nuclei than that in peripheral collisions.