Incomplete Fusion Cross Sections Research Articles

New Approach for Evaluating Incomplete and Complete Fusion Cross Sections with Continuum-Discretized Coupled-Channels Method

We propose a new method for evaluating incomplete and complete fusion cross sections separately using the Continuum-Discretized Coupled-Channels method. This method is applied to analysis of the deuteron induced reaction on a 7Li target up to 50 MeV of the deuteron incident energy. Effects of deuteron breakup on this reaction are explicitly taken into account. Results of the method are compared with those of the Glauber model, and the difference between the two is discussed. It is found that the energy dependence of the incomplete fusion cross sections obtained by the present calculation is almost the same as that obtained by the Glauber model, while for the complete fusion cross section, the two models give markedly different energy dependence. We show also that a prescription for evaluating incomplete fusion cross sections proposed in a previous study gives much smaller result than an experimental value.

Relating Breakup and Incomplete Fusion of Weakly Bound Nuclei through a Classical Trajectory Model with Stochastic Breakup

A classical dynamical model that treats breakup stochastically is presented for low energy reactions of weakly bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete, and complete fusion cross sections. The model is assessed by comparing the breakup observables with continuum discretized coupled-channel quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at energies near the Coulomb barrier.

Near-barrier Fusion and Breakup/Transfer induced by Weakly Bound and Exotic Halo Nuclei

The influence on the fusion process of coupling to collective degrees of freedom has been explored. The significant enhancement of the fusion cross section at sub-barrier energies was compared to predictions of one-dimensional barrier penetration models. This was understood in terms of the dynamical processes arising from strong couplings to collective inelastic excitations of the target and projectile. However, in the case of reactions where at least one of the colliding nuclei has a sufficiently low binding energy, for breakup to become an important process, conflicting model predictions and experimental results have been reported in the literature. Excitation functions for sub- and near-barrier total (complete + incomplete) fusion cross sections have been measured for the 6,7Li+59Co reactions. Elastic scattering as well as breakup/transfer yields have also been measured at several incident energies. Results of Continuum-Discretized Coupled-Channel (Cdcc) calculations describe reasonably well the experimental data for both reactions at and above the barrier. A systematic study of 4,6He induced fusion reactions with a three-body Cdcc method is presented. The relative importance of breakup and bound-state structure effects on total fusion (excitation functions) is particularly investigated. The four-body Cdcc model is being currently developed.

What can one learn about lithium breakup from the fission reaction of 232Th(6Li, f) at energies around the Coulomb barrier?

Abstract Fission fragment mass and energy distributions (MED) and fission fragment folding angle distributions (FFFAD) have been measured in the reaction 6Li + 232Th within the lithium projectile energy range E lab = 28.5 – 62.5 MeV . The values of the ratio between the complete and incomplete fusion cross-sections have been obtained from a combined analysis of MED and FFFAD. The incomplete fusion originates from transfer reactions and/or from the 6Li breakup mainly into α and d clusters. It has been found that the contribution of complete fusion into the total fusion–fission cross-section is only ∼ 27 % at the lithium projectile energy E lab = 28.5 MeV ( ∼ 2 MeV below the Coulomb barrier).

Comprehensive study of reaction mechanisms for theBe9+Sm144system at near- and sub-barrier energies

The delayed x-ray detection technique was used to measure complete and incomplete fusion cross sections for the $^{9}\mathrm{Be}+^{144}\mathrm{Sm}$ reaction at sub- and near-barrier energies. Elastic and inelastic scattering for this system were also measured. Reaction cross sections were derived and the transfer cross sections of one neutron were calculated. The suppression of complete fusion above the barrier, of the order of 10%, is attributed to $^{9}\mathrm{Be}$ breakup and is considerably smaller than the value of 30% found for the $^{9}\mathrm{Be}+^{208}\mathrm{Pb}$ system.

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.

Effect of breakup on the fusion ofLi6,Li7, andBe9with heavy nuclei

Comprehensive high precision complete and incomplete fusion cross sections have been measured for the $^{6}\mathrm{Li}+^{209}\mathrm{Bi}$, $^{7}\mathrm{Li}+^{209}\mathrm{Bi}$, and $^{9}\mathrm{Be}+^{208}\mathrm{Pb}$ reactions, at energies near and below the Coulomb barrier. The experimental details and the analyses procedures for the characteristic $\ensuremath{\alpha}$-decay and fission measurements are described. Three different methods are used to conclusively show the large suppression of complete fusion at energies around and above the average barrier, which is associated with the projectile nuclei having a low energy threshold against breakup. First, theoretical predictions of fusion cross sections above the average barrier are compared with the data, and second the area under the measured barrier distribution is compared with expectations. The sensitivity of the suppression factors to variables which can affect the calculated cross sections is thoroughly investigated. The third method, essentially model independent, compares the complete fusion cross sections for the $^{7}\mathrm{Li}+^{209}\mathrm{Bi}$ and $^{9}\mathrm{Be}+^{208}\mathrm{Pb}$ reactions with those for the fusion of nuclei with a high threshold against breakup, which produce the same compound nucleus. All methods give consistent results, showing that the complete fusion cross sections at energies around and above the barrier are suppressed by $\ensuremath{\sim}30%$ compared with reactions of nuclei having a high energy threshold against breakup. The cross sections for incomplete fusion are found to be similar to the missing complete fusion cross sections. The experimental controversies regarding the effect of breakup on fusion is discussed, and the importance of unambiguously separating complete fusion from incomplete fusion is emphasized. This distinction is also important to achieve theoretically for realistic modelling of fusion of nuclei which break up readily.

Fusion and breakup in the reactions of 6,7Li and 9Be

We develop a three body classical trajectory Monte Carlo (CTMC) method to dicsuss the effect of the breakup process on heavy-ion fusion reactions induced by weakly bound nuclei. This method follows the classical trajectories of breakup fragments after the breakup takes place, and thus provides an unambiguous separation between complete and incomplete fusion cross sections. Applying this method to the fusion reaction $^{6}$Li + $^{209}$Bi, we find that there is a significant contribution to the total complete fusion cross sections from the process where all the breakup fragments are captured by the target nucleus (i.e., the breakup followed by complete fusion).

Study of the Influence of Projectile Breakup on the Fusion Cross Section of6,7Li +12C,59Co

Excitation functions for sub- and near-barrier total (complete + incomplete) fusion cross sections were studied for the 6 , 7 Li+ 5 9 Co reactions using standard γ-ray techniques and the results indicate a small enhancement of total fusion cross section at sub-barrier energies for the more weakly bound 6 Li projectile, with similar cross sections for both reactions at and above the barrier. In order to better understand the breakup contribution to fusion, we perfomed light particle coincidence measurements for the systems 6 , 7 Li+ 1 2 C, 5 9 Co at energies near and above the barrier. A three body kinematics analysis is performed with the objective of separating the contributions of different reaction mechanisms. For small angular differences between the light particles, the sequential and direct breakup seem to dominate. On the other hand, for large detector separations, a sequential decay following transfer is likely to dominate.

Near-barrier fusion of weakly bound6Liand7Linuclei with59Co

Excitation functions for sub- and near-barrier total (complete + incomplete) fusion cross sections are presented for the ${}^{6,7}\mathrm{Li}{+}^{59}\mathrm{Co}$ reactions. Evaporation residues were identified by their characteristic $\ensuremath{\gamma}$ rays and the corresponding yields measured with both the IReS Garel $+$ array at the Vivitron facility and with the S\~ao Paulo Ge array at the 8UD Pelletron tandem facility using standard \ensuremath{\gamma}-ray techniques. The data extend to medium-mass systems previous works exploring the coupling effects (hindrance versus enhancement) in fusion reactions of both lighter and heavier systems. The results indicate a small enhancement of total fusion for the more weakly bound ${}^{6}\mathrm{Li}$ at sub-barrier energies, with similar cross sections for both reactions at and above the barrier.

Effect of projectile structure on evaporation residue yields in incomplete fusion reactions

The excitation functions of heavy residues, representing complete and incomplete fusion products, produced in the reaction of 12C and 13C on 181Ta have been measured over the projectile energy range of 5 to 6.5 MeV/nucleon by the recoil catcher method and off-line γ-ray spectrometry. Comparison of the measured excitation functions with those calculated using the PACE2 code based on the statistical model revealed the occurrence of incomplete fusion reactions in the formation of α emission products. The fraction of incomplete fusion cross sections in the 12C + 181Ta reaction was found to be higher, by a factor of ∼2, than that in the 13C + 181Ta reaction. The results have been discussed in terms of the effect of alpha cluster structure of the projectile on incomplete fusion reactions.

Effect of continuum couplings in fusion of halo11Beon208Pbaround the Coulomb barrier

The effect of continuum couplings in the fusion of the halo nucleus $^{11}$Be on $^{208}$Pb around the Coulomb barrier is studied using a three-body model within a coupled discretised continuum channels (CDCC) formalism. We investigate in particular the role of continuum-continuum couplings. These are found to hinder total, complete and incomplete fusion processes. Couplings to the projectile $1p_{1/2}$ bound excited state redistribute the complete and incomplete fusion cross sections, but the total fusion cross section remains nearly constant. Results show that continuum-continuum couplings enhance the irreversibility of breakup and reduce the flux that penetrates the Coulomb barrier. Converged total fusion cross sections agree with the experimental ones for energies around the Coulomb barrier, but underestimate those for energies well above the Coulomb barrier.

Fusion and competing processes in the32S+12Creaction atE(32S)=19.5MeV/nucleon

Velocity, angular, mass, and charge distributions of isotopically resolved residues coming from the reaction ${}^{32}\mathrm{S}{+}^{12}\mathrm{C}$ were measured at the bombarding energy ${E(}^{32}\mathrm{S})=19.5 \mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{n}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{o}\mathrm{n}.$ Complete and incomplete fusion and direct components have been separated in the velocity spectra using kinematical analysis and deconvolution techniques. For each residue, incomplete and complete fusion cross sections have been extracted and the results are compared with the LILITA code predictions. The complete fusion cross section and the deduced critical angular momentum are also compared with other experimental data and with the predictions of theoretical models.

Complete and incomplete fusion of two-cluster nuclei

We study the influence of the break-up process on the complete and incomplete fusion cross sections. This is done through the introduction of break-up and survival probabilities, which are evaluated with the help of an appropriate polarization potential. For incomplete fusion, we use a spectator model. As examples, we consider several light - heavy-ion collisions, where threshold effects play an interesting role.

Calculations of complete fusion, incomplete fusion, and direct reaction cross sections for deuteron-induced reactions.

Two techniques that enable us to calculate cross sections of complete fusion and various incomplete fusion reactions within the framework of direct reaction theories are combined to calculate cross sections of various reactions initiated by d${+}^{93}$Nb with two incident energies of 15 and 25.5 MeV. It is shown that the predicted cross sections agree well with existing experimental data. This study provides a rather critical test of the two techniques used by examining the consistencies of the predictions of the total incomplete fusion plus direct reaction cross sections and also the regions where these reactions predominantly take place. One of these techniques can be easily used with any optical model code to obtain compound nucleus cross sections (excluding breakup and other direct reaction cross sections) for the Hauser-Feshbach calculations involving deuteron-induced reactions.

Dynamical calculations of linear momentum transfer in α-induced reactions

Linear momentum transfers in α-induced reactions with 20 MeV per nucleon are calculated by considering all important direct and incomplete fusion mechanisms along with complete fusion. The calculated results agree very well with the experimental data. Calculated total inelastic cross section and various incomplete fusion cross sections (including the stripping reactions to bound discrete states) also agree well with the experimental data.

A new approach to heavy-ion fusion.—I

An extension of a previous approach is given in order to reproduce the experimental values of fusion cross-sections for systems with large mass asymmetry. Moreover, an analytical expression to account for incomplete fusion cross-section is suggested.

Inclusive projectile fragmentation in the spectator model

Grazing-angle singles spectra for projectile fragments from nuclear collisions exhibit a broad peak centered near the beam velocity, suggesting that these observed fragments play only a “spectator” role in the reaction. Using only this spectator assumption (but not DWBA), we find that a “prior form” formulation of the reaction leads, via closure, to a 〈 ψ∥ W∥ ψ〉-type estimate of the inclusive spectator spectrum, thus relating it to the reaction cross section for the “participant” with the target. We show explicitly that this expression includes an improved multi-channel version of the Udagawa-Tamura formula for the “breakup-fusion” or incomplete-fusion cross section, and identifies it as the fluctuation part of the participant-target reaction cross section. A Glauber-type estimate of the distorted wave functions which enter clearly shows how the width of the peak in the spectator spectrum arises from the “Fermi motion” within the projectile, as in the simpler Serber model, but is modified by the “overlap geometry” of the collision.