Incomplete Fusion Cross Sections Research Articles

Study of fusion and one-neutron stripping process for 6Li + 94Zr system around the Coulomb Barrier

Abstract The complete and incomplete fusion cross section as well as one-neutron stripping process of 6Li + 94Zr system were measured at the energies around the Coulomb barrier by online γ-ray method. In addition to a 30% suppression factor compared with the measured total fusion process, the complete fusion cross section in 6Li + 94Zr system was observed to be significantly lower than those in the nearby 6Li + 90,96Zr system.The new experimental result implies that the coupling with breakup channel in the 6Li-induced fusion processes would be affected by the inner structure of the target, which is still not clear in any available model calculation.For the one-neutron stripping process, the direct production cross sections for each level in 95Zr were extracted and compared with the coupled reaction channel calculation, offering a unique opportunity to study the single-particle nature of the produced excited states. Due to the fact that an overall overestimation of the production cross section for 954-keV and 1618-keV levels was observed in the comparison, further investigation is highly demanded in order to understand the full reaction mechanism for the one-neutron stripping process induced by 6Li.

Further investigation on the fusion of 6Li with 209Bi target at near-barrier energies

Abstract The complete and incomplete fusion cross sections for 6Li+209Bi were measured via the in-beam γ-ray method around the Coulomb barrier. The cross sections of (deuteron captured) incomplete fusion (ICF) products were re-quantified experimentally for this reaction system. The results reveal that the ICF cross section is equivalent to that of complete fusion (CF) above the Coulomb barrier and dominant near or below the barrier. A theoretical calculation based on the Continuum Discretized Coupled Channel (CDCC) method is performed for the aforementioned CF and ICF cross sections, and the result is consistent with the experimental ones. The universal fusion function (UFF) is also compared with the measured CF cross section with different barrier parameters, demonstrating that the CF suppression factor is quite sensitive to the choice of potential, which can reflect both dynamic and static effects of breakup on the fusion process.

Modelling inclusive breakup: application to incomplete fusion

We propose an extension of the inclusive breakup model of Ichimura, Austern and Vincent [Phys. Rev. C 32, 431 (1985)] for the evaluation of incomplete fusion (ICF) cross sections in nuclear reactions induced by two-body projectiles. The main idea, adopted in other methods, consists in the separation of the participant-target optical potential into its direct reaction and compound reaction components, the latter being responsible for the ICF contribution of the total nonelastic breakup cross section. Preliminary comparison with experimental data shows encouraging results.

Decay aspects of the compound nuclei formed via CF and ICF path in 12C[formula omitted]Cr reaction

The reaction dynamics of 12C+52Cr reaction induced via a cluster-structured projectile (12C) is examined theoretically using the dynamical cluster decay model (DCM) with respect to the recent experimental data available at wide span of center-of-mass energies (Ec.m.=41.84-71.20 MeV). In view of the cluster-structured projectile, a systematic analysis is carried out for both complete fusion (CF) and incomplete fusion (ICF) channel. The calculations are done by including the quadrupole (β2) deformations and optimum (θiopt.) orientation criteria of the decaying fragments. With an aim to have comprehensive analysis of the decay of compound nuclei formed via CF and ICF processes, the role of center-of-mass energy (Ec.m.) and angular momentum (ℓ) is explored in terms of various parameters of DCM such as fragmentation potential, preformation probability, penetrability and barrier modification. Further, the role of diffuseness parameter is also studied for 12C+52Cr reaction. For the given reaction, the contribution of light particles (LPs), and energetically favored intermediate mass fragments (IMFs) constitutes the decay cross sections. Therefore, the contribution of emitted LPs and IMFs is estimated for the decay of both compound nuclei formed via CF and ICF channels. Furthermore, the comparative analysis of different proximity potentials is also worked out for ICF. Finally, the effect of Ec.m. on the contribution of ICF cross sections is studied and compared with the experimental data.

Investigating neutron transfer in the Be9+Au197 system

In this work $\textit{n}$-transfer and incomplete fusion cross sections for $^{9}$Be + $^{197}$Au system are reported over a wide energy range, E$_{c.m.}$ $\approx$ 29-45 MeV. The experiment was carried out using activation technique and off-line gamma counting. The transfer process is found to be the dominant mode as compared to all other reaction channels. Detailed coupled reaction channel (CRC) calculations have been performed for $\textit{n}$-transfer stripping and pickup cross sections. The measured 1$\textit{n}$-stripping cross sections are explained with CRC calculations by including the ground state and the 2$^{+}$ resonance state (E = 3.03 MeV) of $^{8}$Be. The calculations for 1$\textit{n}$-pickup, including only the ground state of $^{10}$Be agree reasonably well with the measured cross sections, while it overpredicts the data at subbarrier energies. For a better insight into the role of projectile structure in the transfer process, a comprehensive analysis of 1$\textit{n}$-stripping reaction has been carried out for various weakly bound projectiles on $^{197}$Au target nucleus. The transfer cross sections scaled with the square of total radius of interacting nuclei show the expected Q-value dependence of 1$\textit{n}$-stripping channel for weakly bound stable projectiles.

One-neutron transfer, complete fusion, and incomplete fusion from the Be9 + Au197 reaction

In this work, one-neutron transfer (pickup and stripping), complete and incomplete fusion cross sections for the $^{9}\mathrm{Be}+^{197}\mathrm{Au}$ system were measured over a wide range of energies around the Coulomb barrier by the offline $\ensuremath{\gamma}$-ray detection method. Coupled-channel calculations were used to determine the elastic, inelastic, and transfer cross sections. Coupled reaction channel calculations were performed to derive the one-neutron stripping and pickup cross sections. Three-body continuum discretized coupled-channel calculations were used to determine the effect of the breakup channel on the other reaction mechanisms. The reduced complete and total fusion were found to be hindered above and enhanced below the Coulomb barrier compared with the universal fusion function due to the breakup plus transfer effects.

Probing the influence of incomplete fusion in the Li6+Y89 reaction up to 7.2 MeV/nucleon energy

The nuclear reaction study with weakly bound heavy nuclei is an enduring open question due to the scarcity of experimental data. In view of this, an experiment has been performed to study the fusion dynamics of weakly bound $^{6}\mathrm{Li}$ projectile in $^{6}\mathrm{Li}+^{89}\mathrm{Y}$ reaction at energies slightly above the Coulomb barrier. The off-beam $\ensuremath{\gamma}$-spectroscopic technique has been used to measure the cross sections of populated residues in $^{6}\mathrm{Li}+^{89}\mathrm{Y}$ reaction, and the data are analyzed using equilibrium and pre-equilibrium models in the framework of the empire3.2.2 code. It has been found that complete fusion (CF) and incomplete fusion (ICF) of $^{6}\mathrm{Li}$ play a substantial role in producing the residues. Subsequently, the ICF cross section, which is a model-dependent quantity, has been extracted. The strength of incomplete fusion has been deduced and compared with the existing data from $^{7}\mathrm{Li}+^{89}\mathrm{Y}$ reaction. The ICF strength is found to be higher for $^{6}\mathrm{Li}+^{89}\mathrm{Y}$ as compared with the $^{7}\mathrm{Li}+^{89}\mathrm{Y}$ system, which possibly indicates the role of the projectile's structure on the ICF occurrence probability. The occurrence of ICF below a critical angular momentum is also anticipated for both $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ interaction with $^{89}\mathrm{Y}$.

Complete and incomplete fusion of Li7 projectiles on heavy targets

We present a detailed discussion of a recently proposed method to evaluate complete and incomplete fusion cross sections for weakly bound systems. The method is applied to collisions of $^{7}$Li projectiles on different heavy targets, and the results are compared with the available data. The overall agreement between experiment and theory is fairly good.

Analysis of Fusion Cross Sections in the 9Be Projectile Breakup on Different Target Nuclei

We present a theoretical study of total fusion (TF), complete fusion (CF), and incomplete fusion (ICF) cross sections in the breakup of 9Be (described as n −8Be) projectile on 124Sn, 144Sm and 208Pb target nuclei. We use the continuum discretized coupled-channel formalism together with a sum-rule model, by extending an approach outlined in Mukeru et al. (Nucl. Phys. A 996:121700, 2020) to another weakly bound projectile in different targets. The applicability of the model to incident energies below and around the Coulomb barrier is verified, being confirmed for all three reactions an empirical energy-dependent cutoff angular momentum expression. We show that the TF and ICF cross sections are strongly dependent on the projectile binding energy eb, whereas the CF is weakly affected by that. Despite this weak dependence, the CF contribution to the TF cross section becomes more suppressed by decreasing eb. The dependence of the ICF probability on the breakup threshold is also highlighted.

Projectile breakup effects in the fusion dynamics of 6,7Li +144,152Sm reactions around Coulomb barrier

This work emphasized the role of the projectile breakup channel by studying the complete fusion (CF) and incomplete fusion (ICF) dynamics of [Formula: see text] reactions. The theoretical calculations for the chosen reactions have been done by opting for the coupled channel approach and the energy dependent Woods–Saxon potential (EDWSP) model. The below barrier fusion enhancements of the studied reactions are reasonably addressed by the outcomes of the adopted models, which in turn can be attributed to the couplings of nuclear structure degrees of freedom of the collision partners to their relative motion. In contrast, at above barrier energies, the CF cross-section data of the chosen reactions are found to be suppressed significantly when compared with the predictions made by using the present models. Interestingly, the fusion suppression factors of the given reactions can be minimized considerably with respect to the reported value when it is analyzed within the framework of the EDWSP model. For instance, in case of [Formula: see text] ([Formula: see text] reaction, the magnitude of fusion suppression factor is minimized up to 7% (13%) relative to the reported value whereas for [Formula: see text] ([Formula: see text] reaction, the fusion suppression factor is found to be less by 7% (8%) with reference to the reported value. Such suppression effects can be correlated with the low breakup threshold of alpha breakup channel associated with the loosely bound projectile. The projectiles being weakly bound systems split into two charged fragments and either of the breakup components is absorbed by the target resulting in the reduction of incoming flux going into fusion channel. The flux lost from the CF channel appears in the form of ICF yields. For [Formula: see text], total fusion (TF) cross-sections that are sum of CF and ICF cross-sections are also analyzed in conjunction with the EDWSP model and thus reasonably explained by the model calculations. In order to identify the ICF contribution, the ratio of ICF/TF cross-section data of [Formula: see text] reaction has been examined and thus properly addressed by using the EDWSP model. The presence of ICF component in TF cross-section clearly pointed out the breakup of projectile due to its loosely bound nature prior to the Coulomb barrier. Although ICF data of other systems are not available in the literature, a similar behavior is expected for ICF and TF data for [Formula: see text] and [Formula: see text] reactions.

Theoretical analysis of 8Li + 208Pb reaction and the critical angular momentum for complete fusion

In a theoretical approach, the complete and incomplete fusions are investigated by considering the Li8+208Pb reaction, within a three-body model where the projectile is described as n−7Li with binding energy εb. By decreasing εb from its known experimental value, the complete fusion is shown to have no meaningful dependence on such variations, whereas the incomplete fusion strongly depends on that. The complete and incomplete fusion cross sections are calculated by using a combination of both continuum-discretized coupled-channel and sum-rule models. To this end, an incident-energy dependent cut-off angular momentum Lc is first obtained by using the available complete fusion experimental data, within an approach which is extended to model results obtained for other incident-energies. An approximated fitted expression linking Lc to the well-known critical value Lcrit derived by Wilczyński (1973) [28] suggests that the sum-rule model could be generalized to energies around and below the Coulomb barrier.

Complete and incomplete fusion cross-sections for 7Li+119Sn reaction using different approaches

In reference to complete fusion (CF) and incomplete fusion (ICF) processes, the analysis of 7 Li+ 119 Sn reaction forming 126 I compound nucleus (CN) is carried out at incident energies spread across the Coulomb barrier. Firstly, the total fusion (TF) cross-sections are calculated using the Wong formula. Since, it overestimates the experimental data, so ℓ-summed Wong approach is employed to address the TF cross-section, which limits the contribution of partial waves up to ℓ max value. Within ℓ-summed Wong model, the energy dependent selection function is used to separate out the contributions of CF and ICF from the TF cross-sections. This phenomenological selection function seems to give adequate distribution of CF and ICF cross-sections at higher energies. Beside this, the CF and ICF contributions are also separated out on the basis of angular momentum window and by using the energy correction formula. In the angular momentum distribution case, CF and ICF cross-sections are estimated in view of ℓ-windows, 0≤ℓ<ℓ critical (for CF) and ℓ critical ≤ ℓ ≤ℓ max (For ICF). Finally, in energy normalization case, the incident energy of 7 Li beam ( 7 Li→ 4 He + 3 H) is distributed among alpha and tritium fragments, and the ICF cross-sections for 3 H+ 119 Sn ICF channel are estimated using the ℓ-summed Wong model.

Measurement of incomplete fusion cross sections in Li6,7+U238 reactions

Background: Incomplete fusion (ICF) in reactions involving weakly bound projectiles is understood to play an important role in enhancing the ratio of asymmetric to symmetric fission at $E\ensuremath{\le}{V}_{b}$, widening the fission fragment folding angle distribution at $E\ensuremath{\le}{V}_{b}$ and suppressing the complete fusion (CF) cross section at $Eg{V}_{b}$. Experimental cross sections for individual ICF channels are necessary to obtain quantitative estimates of the above effects.Purpose: Measurement of the cross sections for individual transfer-induced or ICF-fission channels in $^{6,7}\mathrm{Li}+^{238}\mathrm{U}$ reactions to explain quantitatively the difference in the ratio of asymmetric to symmetric fission for total fission and CF fission.Methods: Triple coincidence measurement of two fission fragments and one light charged projectilelike fragment (PLF) is carried out using two multiwire proportional counter (MWPC) detectors and an array of CSI(Tl) scintillation detectors at energies near the Coulomb barrier. By calculating the efficiency of the detectors by Monte Carlo simulation and fission probability by GEF code, the angle-integrated ICF cross sections corresponding to p, d, t, and $\ensuremath{\alpha}$ emission are obtained. Mass distributions for total fission are calculated by adding the distributions for CF fission and all ICF fissions with weight factors proportional to the measured cross sections.Results: ICF cross sections corresponding to $\ensuremath{\alpha}$ emission are found to be the highest in both the reactions. The relative contribution of ICF to total fusion at the lowest measured energy is found to be $\ensuremath{\approx}70%$ and it decreases with increasing projectile energy, consistent with the systematics of several reactions involving the same weakly bound projectiles. The simulated mass distributions for total fission are found to reproduce the experimental mass distributions.Conclusions: Deuteron (triton) capture is observed to be the major ICF channel in the reaction involving $^{6}\mathrm{Li}\phantom{\rule{0.28em}{0ex}}(^{7}\mathrm{Li})$ projectile. The ratio of the sum of ICF to total fusion cross section for the present systems are consistent with the systematics. The difference in the ratio of asymmetric to symmetric fission between total fission and CF fission is explained quantitatively.

Fusion reaction studies for the Li6+Sn124 system at near-barrier energies

The complete and incomplete fusion along with one neutron stripping and pickup cross sections for the $^{6}\mathrm{Li}+^{124}\mathrm{Sn}$ system are measured using online and offline characteristic $\ensuremath{\gamma}$-ray detection techniques. The complete fusion (CF) cross sections at energies above the Coulomb barrier are found to be suppressed by $\ensuremath{\sim}34%$ compared to the coupled channel calculations. This suppression observed in complete fusion cross sections is found to be commensurate with the measured total incomplete fusion (ICF) cross sections. There is a distinct feature observed in the ICF cross sections, i.e., $d$ capture is found to be dominant than $\ensuremath{\alpha}$ capture at all the measured energies, contrary to the data available for $^{6}\mathrm{Li}+^{209}\mathrm{Bi},^{197}\mathrm{Au}$ systems. The total fusion cross section ratio between $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ induced reactions shows an increasing trend as the energy decreases below the barrier while it remains unity at above-barrier energies. A simultaneous explanation of complete, incomplete, and total fusion (TF) data is also obtained from the calculations based on the continuum discretized coupled channel method with short-range imaginary potentials. The cross section ratios of CF/TF and ICF/TF obtained from the data as well as the calculations shows the dominance of ICF at below-barrier energies and CF at above-barrier energies.

Effects of unconventional breakup modes on incomplete fusion of weakly bound nuclei

The incomplete fusion dynamics of $^6$Li + $^{209}$Bi collisions at energies above the Coulomb barrier is investigated. The classical dynamical model implemented in the {\sc platypus} code is used to understand and quantify the impact of both $^6$Li resonance states and transfer-triggered breakup modes (involving short-lived projectile-like nuclei such as $^8$Be and $^5$Li) on the formation of incomplete fusion products. Model calculations explain the experimental incomplete-fusion excitation function fairly well, indicating that (i) delayed direct breakup of $^6$Li reduces the incomplete fusion cross-sections, and (ii) the neutron-stripping channel practically determines those cross-sections.

Investigation of complete and incomplete fusion in the Li7+Sn124 reaction near Coulomb barrier energies

The complete and incomplete fusion cross sections for $^{7}$Li+$^{124}$Sn reaction were measured using online and offline characteristic $\gamma$-ray detection techniques. The complete fusion (CF) cross sections at energies above the Coulomb barrier were found to be suppressed by $\sim$ 26 \% compared to the coupled channel calculations. This suppression observed in complete fusion cross sections is found to be commensurate with the measured total incomplete fusion (ICF) cross sections. There is a distinct feature observed in the ICF cross sections, i.e., $\textit{t}$-capture is found to be dominant than $\alpha$-capture at all the measured energies. A simultaneous explanation of complete, incomplete and total fusion (TF) data was also obtained from the calculations based on Continuum Discretized Coupled Channel method with short range imaginary potentials. The cross section ratios of CF/TF and ICF/TF obtained from the data as well as the calculations showed the dominance of ICF at below barrier energies and CF at above barrier energies.

CDCC calculations of fusion of 6Li with targets 144Sm and 154Sm: effect of resonance states**A. Gómez Camacho from CONACYT, México, J. Lubian from CNPq, FAPERJ, Pronex, Brazil. S.G.Z was partly supported by the NSF of China (11120101005, 11275248, 11525524, 11621131001, 11647601, 11711540016), 973 Program of China (2013CB834400) and the Key Research Program of Frontier Sciences of CAS. H.Q.Z. from NSF

Continuum Discretized Coupled-Channel (CDCC) model calculations of total, complete and incomplete fusion cross sections for reactions of the weakly bound 6Li with 144,154Sm targets at energies around the Coulomb barrier are presented. In the cluster structure frame of 6Li→α+d, short-range absorption potentials are considered for the interactions between the ground state of the projectile 6Li and α-d fragments with the target. In order to separately calculate complete and incomplete fusion and to reduce double-counting, the corresponding absorption potentials are chosen to be of different range. Couplings to low-lying excited states 2+, 3− of 144Sm and 2+, 4+ of 154Sm are included. So, the effect on total fusion from the excited states of the target is investigated. Similarly, the effect on fusion due to couplings to resonance breakup states of 6Li, namely, l=2, Jπ=3+,2+,1+ is also calculated. The latter effect is determined by using two approaches, (a) by considering only resonance state couplings and (b) by omitting these states from the full discretized energy space. Among other things, it is found that both resonance and non-resonance continuum breakup couplings produce fusion suppression at all the energies considered.

Small suppression of the complete fusion of 6Li + 28Si reaction at near barrier energies

The incomplete fusion cross section of the 6Li + 28Si weakly bound system at above barrier energies was deduced from the measured $ \gamma$ -ray cross sections. The complete fusion cross section was estimated from the measured total fusion and incomplete fusion cross section and is found to be 85-100% of the total fusion cross section. The coupled channel calculation has been performed considering ground and first excited states of 28Si target. The fusion cross section estimated from coupled channel calculation shows good agreement with measured total fusion cross section at higher energies. The suppression of about 15% of the fusion cross section predicted by coupled channel calculation shows good agreement with the complete fusion cross section. The effect of the channel couplings on the elastic scattering angular distribution is also investigated.

Inclusive breakup of three-fragment weakly bound nuclei

The inclusive breakup of three-fragment projectiles is discussed within a four-body spectator model. Both the elastic breakup and the non-elastic breakup are obtained in a unified framework. Originally developed in the 80's for two-fragment projectiles such as the deuteron, in this paper the theory is successfully generalized to three-fragment projectiles. The expression obtained for the inclusive cross section allows the extraction of the incomplete fusion cross section, and accordingly generalizes the surrogate method to cases such as (t,p) and (t,n) reactions. It is found that two-fragment correlations inside the projectile affect in a conspicuous way the elastic breakup cross section. The inclusive non-elastic breakup cross section is calculated and is found to contain the contribution of a three-body absorption term that is also strongly influenced by the two-fragment correlations. This latter cross section contains the so-called incomplete fusion where more than one compound nuclei are formed. Our theory describes both stable weakly bound three-fragment projectiles and unstable ones such as the Borromean nuclei.

No-capture breakup and incomplete fusion reactions induced by stable weakly bound nucleus 9Be

The reactions including the stable weakly bound nucleus 9Be have been studied using the classical trajectory model accompanied with the experimental breakup function and the Aage-Winther interaction potential (AW95). In these calculations, the no-capture breakup and the incomplete fusion cross-sections as well as their competition at around the Coulomb barrier have been investigated. Our calculations showed that at a given far-Coulomb-barrier energy the incomplete fusion reaction in different distributions of angular momentum and energies can dominate the no-capture breakup reaction. This dominating process is reversed at the near-barrier energies.