Complete Fusion Cross Sections Research Articles

Fusion and one-neutron stripping process for 6Li + 94Zr system around the Coulomb Barrier* *This research is supported by the National Nature Science Foundation of China (U2167204, 11975040, 1832130, 12375130), the Director's Foundation of Department of Nuclear Physics, China Institute of Atomic Energy 12SZJJ-202305. The Brazilian authors are grateful to the partial support from financial agencies FAPERJ, CNPq, and INTC-FNA

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 when 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 can 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 examine the single-particle nature of the produced excited states. Given 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.

Investigation of reaction and α production cross sections with 9Be projectile

In order to investigate the contribution of α production in the reaction cross sections, measurements of elastic scattering and inclusive α particle angular distributions have been carried out with the 9Be projectile on 89Y, 124Sn, 159Tb, 198Pt, and 209Bi targets over a wide angular range at energies near the Coulomb barrier. The measured elastic scattering angular distributions were fitted with optical model calculations, and reaction cross sections were extracted. The same data were also analyzed using both global optical model potentials (Global OMP) and microscopic São Paulo potentials (SPP), to obtain the reaction cross sections. The data available in the literature for 9Be projectile includes the elastic scattering angular distributions, α production cross sections, and complete fusion cross sections on these and other targets at several energies are also utilized for comparative studies. The reaction cross section extracted from the three potentials (Best Fit, Global OMP and SPP) are in reasonable agreement for all the targets except for the energies below the barrier where the results from SPP deviate by 30-50%. Inclusive α particle production cross sections were also extracted by integrating the α particle angular distributions. The present data and data available from literature of reaction and α-particle production cross sections were utilized to make systematic studies. Systematics of reaction and α-particle production cross sections revealed their universal behavior. The ratio of complete fusion (CF), inclusive α cross sections, and their sum (CF+α) to reaction cross sections show that at sub-barrier energies inclusive α dominates and above barrier CF dominates, and cumulative of these two processes almost explains the reaction cross section at all energies over a wide range of target mass. A comparative study of α production with other weakly bound projectiles is also performed and a clear distinction between projectile types is observed, which is found to correlate well with α separation energies of the projectiles.

Effect on incomplete fusion of breakup fragments of the weakly bound projectile 8B in reactions with targets 27Al, 28Si, 208Pb and 209Bi

Calculations of total, complete and incomplete fusion cross sections are presented as function of the incident energy of the weakly bound projectile 8B in reactions with light 27Al, 28Si and heavy 208Pb and 209Bi mass targets. In particular, the relative effect of the breakup fragments; proton and 7Be of 8B on incomplete fusion is determined. Also, the effect of an additional proton to the nuclear potential of the targets 28Si, 209Bi respect to 27Al and 208Pb is determined as a function of the incident energy. It is found that the proton absorption becomes more important than for 7Be for light targets for energies around and above the barrier, however, the inverse occurs for heavy targets. The calculations are performed with two different methods. The CDCC to determine the relative projectile-target radial wave functions which subsequently are used in the angular momentum-dependent model of fusion probabilities to calculate complete, incomplete and total fusion.

Understanding heavy-ion fusion cross section data using novel artificial intelligence approaches

We modeled an unprecedentedly large dataset of complete fusion cross section data using a novel artificial intelligence approach. Our analysis aims especially to unveil, in a data-driven way, nuclear structure effects on the fusion between heavy ions and to suggest a universal formula capable to describe all previously available data. The study focused on light-to-mediummass nuclei, where incomplete fusion phenomena are more difficult to occur and less likely to contaminate the data. The method used to derive the models exploits a state-of-the-art hybridization of genetic programming and artificial neural networks and is capable to derive an analytical expression that serves to predict integrated cross section values. For the first time, we analyzed a comprehensive set of nuclear variables, including quantities related to the nuclear structure of projectile and target. In this manuscript, we describe the derivation of two computationally simple models that can satisfactorily describe, with a reduced number of variables and only a few parameters, a large variety of lightto- intermediate-mass collision systems in an energy domain ranging approximately from the Coulomb barrier to the oncet of multi-fragmentation phenomena. The underlying methods are particularly innovative and are of potential use for a broad domain of applications in the nuclear field.

Comprehension of breakup fusion reactions using forward recoil range distribution measurements

To understand the break-up fusion reaction dynamics, the forward recoil range distribution (FRRD) measurements of 12C + 165Ho system at the incident projectile energy of ≈ 88 MeV has been performed. The recoil catcher activation technique followed by the off-line gamma ray spectroscopy was implemented. It is observed that the FRRD measurements of the evaporation residues (ERs) populated via xn and pxn channels have a single Guassian peak at large cumulative thickness. This is attributed to complete momentum transfer from the projectile to the target nucleus. However, in case of the FRRD measurements of the ERs populated via αxn, αpxn and 2αxn emitting channels, in addition to peak corresponding to complete momentum transfer, the Gaussian peaks at lower cumulative thicknesses are also observed. This is accredited to the breakup fusion. Moreover, the effect of projectile breakup on complete fusion cross section is also studied. The suppression in fusion cross section is observed when compared with the universal fusion function, thus indicating the breakup probability of 12C projectile.

Understanding Heavy-ion Fusion Cross Section Data Using Novel Artificial Intelligence Approaches

An unprecedentedly extensive dataset of complete fusion cross section data is modeled via a novel artificial intelligence approach. The analysis was focused on light-to-medium-mass nuclei, where fission-like phenomena are more difficult to occur. The method used to derive the models exploits a state-of-the-art hybridization of genetic programming and artificial neural networks and is capable to derive, in a data-driven way, an analytical expression that serves to predict integrated cross section values. We analyzed a comprehensive set of nuclear variables, including quantities related to the nuclear structure of projectile and target. In this paper, we describe the derivation of two computationally simple models that can satisfactorily describe, with a reduced number of variables and only a few parameters, a large variety of light-to-intermediate-mass collision systems in an energy domain ranging approximately from the Coulomb barrier to the oncet of multi-fragmentation phenomena. The underlying methods are of potential use for a broad domain of applications in the nuclear field.

Continuum-discretized coupled-channels calculations for Li6 fusion reactions with closed channels

Fusion reactions induced by the weakly bound nucleus $^{6}\mathrm{Li}$ with targets $^{28}\mathrm{Si}, ^{64}\mathrm{Ni}, ^{144}\mathrm{Sm}$, and $^{209}\mathrm{Bi}$ at energies around the Coulomb barrier are investigated within a three-body model where $^{6}\mathrm{Li}$ is described with an $\ensuremath{\alpha}+d$ cluster model. The total fusion (TF) cross sections are calculated with the continuum-discretized coupled-channels (CDCC) method and the complete fusion (CF) cross sections are extracted through the sum-rule model. The calculations demonstrate that (i) for the TF cross-section calculations, the continuum states up to 40 MeV are found to be necessary, which corresponds to the inclusion of closed channels for light and medium mass targets, such as $^{28}\mathrm{Si}, ^{59}\mathrm{Co}$, and $^{144}\mathrm{Sm}$; (ii) the converged CDCC results for TF cross section at energies above the Coulomb barrier are almost the same as single-channel results in which the continuum coupling effect is neglected; and (iii) the continuum coupling strongly influences partial-wave fusion cross sections and the closed channels play a significant role in the improvement of the description of the CF cross sections at energies below the Coulomb barrier for the $^{6}\mathrm{Li}+^{28}\mathrm{Si}, ^{59}\mathrm{Co}$, and $^{144}\mathrm{Sm}$ systems.

Study of Fusion Reactions of some Light projectiles on Medium Targets

Background and objectives: The investigation of heavy-ion (HI) induced fusion processes in order to comprehend the many mechanisms involved in these reactions has long been a focus of nuclear physics. The complicated structure and behavior of projectile and target nuclei with various projectile energy allows us to define the reaction process and may aid in the investigation of the potential of creating superheavy elements (SHE) in the laboratory. Methods: The semiclassical and full quantum mechanical complete fusion cross section calculations and the distribution of the fusion barrier for the systems 12C+50Ti,15N+56Fe,16O+63Cu and 40Ar+27Al. The calculations have been carried out by using SCF code for semiclassical and CC code for quantum mechanical calculations. To account for the target and projectile relative motion, we modified these codes. The fusion barrier distribution to be calculated directly from this code by subroutines written in Fortran language and added to the main code. The coupled-channel is considered by taking two channels only due to the difficulty of solving coupled differential equations. Results: The obtained results for and the for the studied systems were compared to the related measured data and discussed. Conclusion: The semiclassical method used to describe the fusion reaction agrees very well with the quantum method and with the measured data and we can conclude that this semiclassical method can be used as alternative to quantum method to study the fusion reaction.

Modeling heavy-ion fusion cross section data via a novel artificial intelligence approach

We perform a comprehensive analysis of complete fusion cross section data with the aim to derive, in a completely data-driven way, a model suitable to predict the integrated cross section of the fusion between light-to-medium mass nuclei at above barrier energies. To this end, we adopted a novel artificial intelligence approach, based on a hybridization of genetic programming and artificial neural networks, capable to derive an analytical model for the description of experimental data. The approach enables to perform a global search for computationally simple models over several variables and a considerable body of nuclear data. The derived phenomenological formula can serve to reproduce the trend of fusion cross section for a large variety of light to intermediate mass collision systems in an energy domain ranging approximately from the Coulomb barrier to the onset of multi-fragmentation phenomena.

Role of neutron transfer in the reaction mechanism of 9Be+169Tm, 181Ta, 187Re and 197Au systems

The contribution of one neutron stripping cross section to the total reaction cross section has been studied for 9Be projectile incident on 169Tm, 181Ta, 187Re and 197Au targets around Coulomb barrier energy. The measured one neutron stripping cross sections for these systems have been compared with the coupled channel calculations. The recently developed global set of optical model potential parameters for 9Be projectile has been used in the present calculations. The cumulative of measured complete fusion (CF), incomplete fusion (ICF), one neutron stripping and calculated non-capture breakup (NCBU) cross sections is found to explain almost the reaction cross sections for all the targets. A very small contribution from target inelastic states and elastic breakup may contribute to the remaining part. The percentage fraction of cross section for CF, ICF, one neutron stripping, and NCBU over reaction cross section show the dominance of neutron transfer and NCBU at below barrier energies while CF and ICF processes have the major contribution at above barrier energies.

Systematic study of fusion suppression for tightly bound projectiles at above-barrier energies

The present work aims to explore the effects of projectile breakup on fusion cross section at energies near the Coulomb barrier to well above it. The complete fusion cross section for the strongly bound non-$\ensuremath{\alpha}$-cluster projectile $^{14}\mathrm{N}$ in interaction with a $^{181}\mathrm{Ta}$ target was obtained by summing the experimentally measured channel-by-channel cross section data of evaporated residues. The obtained total fusion cross section was compared with the theoretical code ccfull and the results were found to be consistent with each other. Further, the experimental fusion function data on $^{181}\mathrm{Ta}$ target with $^{14}\mathrm{N}$ projectile were deduced and compared with those obtained for other strongly bound projectiles, viz., $^{12,13}\mathrm{C}$, $^{16}\mathrm{O}$, and $^{19}\mathrm{F}$, in order to get some systematics in fusion reactions. The analysis of experimental fusion functions was performed within the framework of a benchmark curve called the universal fusion function (UFF). A suppression of about 5--25% with respect to UFF was observed for the presently studied systems at energies above the Coulomb barrier, indicating that the suppression is essentially due to the prompt breakup of the projectiles and is a strong function of breakup threshold of projectiles. The magnitude of such suppression was found to be lower for $^{14}\mathrm{N}$ projectile as compared to other strongly bound projectiles. Moreover, an interesting exponential relation between the experimentally deduced suppression factor and the breakup threshold of the projectile was obtained.

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.

Li6,7+Al27 reactions close to and below the Coulomb barrier

The reactions $^{6,7}\mathrm{Li}+^{27}\mathrm{Al}$ were compared with the reactions $^{17,18}\mathrm{O}+^{16}\mathrm{O}$ which form the same compound nuclei $^{33,34}\mathrm{S}$. Cross-section data for the reactions $^{6,7}\mathrm{Li}+^{27}\mathrm{Al}$ were derived from experimentally determined \ensuremath{\gamma}-ray production cross sections for transitions in several residual nuclei. For the reactions $^{17,18}\mathrm{O}+^{16}\mathrm{O}$ experimental results from the literature were used. It could be shown that the weakly bound projectiles $^{6,7}\mathrm{Li}$ undergo not only fusion processes, but also breakup reactions quite in contrast to the tightly bound projectiles $^{18}\mathrm{O}$ and $^{17}\mathrm{O}$, respectively. Especially below the Coulomb barrier such direct reactions play an important role in competition to complete fusion. Calculations based on the statistical model agree well with the available data for $^{17,18}\mathrm{O}+^{16}\mathrm{O}$, but failed to represent the behavior of the experimentally determined production cross sections for the evaporation residues in the reactions $^{6,7}\mathrm{Li}+^{27}\mathrm{Al}$. But coupled-channel codes and calculations based on a nucleus-nucleus proximity potential are able to reproduce the energy dependence of the complete fusion cross sections.

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.

The total reaction cross section of heavy-ion reactions induced by stable and unstable exotic beams: the low-energy regime

In this review paper we present a detailed account of the extraction and the calculation of the total reaction cross section of strongly bound and weakly bound, stable and unstable, exotic, nuclei. We discuss the optical model and the more general coupled channels model of direct reactions. The effect of long-range absorption due to the coupling to excited states in the target and to the breakup continuum in the projectile is also discussed. The generalized optical theorem for charged particle scattering and the resulting sum-of differences method is then discussed. The so-called "quarter-point recipe" is discussed next, and the quarter-point angle is introduced as a simple and rapid mean to obtain the total reaction cross section. The last topic discussed is the reduction of the total reaction cross section that would allow a large body of data to sit on a single universal function. Such a universal function exists in the case of the fusion data, and the aim of this last topic of the review is to extend the fusion case to the total reaction, by adding the direct reaction contribution. Also discussed is the inclusive breakup cross section and how it can be used to extract the total reaction cross section of the interacting fragment with the target. This method is also known as the Surrogate method and represents a case of hybrid reactions. The sum of the integrated inclusive breakup cross section with the complete fusion cross section supplies the total fusion cross section. The main experimental methods to determine the total reaction cross section are also discussed, with emphasis in recent techniques developed to deal with reactions induced by unstable beams.

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.

Investigation of contribution of complete and incomplete fusion in the total fusion process of 6Li+90,96Zr reactions in vicinity of the Coulomb barrier

The impacts of breakup channel on fusion of L6i with Z90,96r-nuclei are investigated within the context of the coupled channel model and the energy dependent Woods-Saxon potential (EDWSP) model. For studied reactions, the complete fusion (CF) cross-sections data at above barrier energies are found to be suppressed with respect to the calculated results. In case of L6i+90Zr (L6i+96Zr) reaction, the CF data at above barrier energies is found to be less by 34% (25%) with reference to the estimations of the coupled channel approach. However, EDWSP model calculations predict fusion suppression up to 20% (10%) for L6i+90Zr (L6i+96Zr) reaction. The extracted suppression factor for L6i+90Zr(L6i+96Zr) reaction is smaller by 14% (15%) than the reported value. Such effects can be accredited to the low threshold of α-breakup channel associated with the weakly bound system and hence may be responsible for incomplete fusion (ICF) products. Therefore, the total fusion (TF) cross-sections that are the sum of complete fusion (CF) and incomplete fusion (ICF) yields, are not expected to reduce in the above barrier regions when compared with no-breakup case. In this regard, the TF cross-sections data are analyzed within the view of the EDWSP model and so obtained calculations have close agreement with the TF cross-sections data. The EDWSP based results appreciably explained CF, ICF and TF cross-sections data over a wide range of energies around the Coulomb barrier. Although, the cluster-transfer or stripping process from the ground state of weakly bound nucleus L6i may significantly contribute to ICF yields, therefore, the presence of ICF product is an indication of the partial absorption of projectile by target, henceforth, reduces the CF cross-section data in above barrier regimes.

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.