Heavy Fusion Research Articles

Statistical theory of neutron-induced nuclear fission and of heavy-ion fusion

For both reactions I use an approach similar to that of compound-nucleus reaction theory. For neutron-induced fission, the compound system generated by absorption of the neutron and the nuclear system near the scission point are described as two statistically independent systems governed by random-matrix theory. The systems are connected either by a barrier penetration factor or by a set of transition states above the barrier. Each system is coupled to a different set of channels. An analogous model is used for heavy-ion fusion. Under the assumption that (seen from the entrance channel) the system on the other side of the barrier is in the regime of strongly overlapping resonances, closed-form analytical expressions for the total probability for fission and for fusion are obtained for each value of spin and parity. Parts of these expressions can be calculated reliably within existing compound-nucleus reaction theory. The remaining parts are the probabilities for passage through or over the barrier. These may be determined theoretically from the liquid-drop model or experimentally from total fission or fusion cross sections. Published by the American Physical Society 2024

Survival probability of Selenium-induced fusion reactions

In this paper, we investigated every potential scenario for selenium-induced heavy ion fusion reactions using astatine isotopes as the target. In this context, we examined [Formula: see text]Se projectiles and [Formula: see text]At targets having longer half-lives of comprising 21 fusion reactions for the synthesis of superheavy element [Formula: see text]. We assessed fusion cross-sections ([Formula: see text]), compound nucleus formation probability ([Formula: see text]), and survival probability ([Formula: see text]) for [Formula: see text]Se projectiles on [Formula: see text]At targets. The evaporation residue cross-sections ([Formula: see text]) is found to be larger for the fusion reaction of [Formula: see text]At of about 14.1[Formula: see text]fb. Hence, these striking results are useful in the synthesis of superheavy element [Formula: see text].

Effect of nuclear deformation and orientation about the symmetry axis of the target nucleus on heavy-ion fusion dynamics

Effect of nuclear deformation and orientation about the symmetry axis of the target nucleus on heavy-ion fusion dynamics

Compound nucleus formation probability of heavy and superheavy nuclei synthesized using heavy ion fusion reactions

The role of entrance channel parameters such as Z2/A, charge asymmetry αz, mass-asymmetry (ηA), charge product (Z1Z2), mean fissility χm, Coulomb interaction parameter and (N−Z)/(N+Z) on compound nucleus formation of actinide nuclei using heavy ion fusion reactions were investigated. For the formation of compound nuclei, the considered atomic number range of the projectile varies between 5≤Z≤14 and the mass number lies between 10≤A≤34. Similarly, the studied target atomic number varies between 78≤Z≤92 and the mass number range is 197≤A≤238. Among these entrance channel parameters, PCN is more systematic for (N−Z)(N+Z), Z2/A and αz. In addition to entrance channel parameters, the Ecm and EBass also play a significant role in the prediction of PCN. The proposed empirical formulae are applicable to the compound nuclei from Fr to Sg. These findings are significant for the PCN prediction from Fr to Sg.

The slopes of sub-barrier heavy-ion fusion excitation functions shed light on the dynamics of quantum tunnelling

Quantum tunnelling plays a crucial role in heavy-ion fusion reactions at sub-barrier energies, especially in the context of nuclear physics and astrophysics. The nuclear structure of the colliding nuclei and nucleon transfer processes represent intrinsic degrees of freedom. They are coupled to the relative ion motion and, in general, increase the probability of tunnelling. The influence of couplings to nucleon transfer channels relatively to inelastic excitations, on heavy-ion fusion cross sections, is one of the still open problems in this field. We present a new analysis of several systems, based on the combined observation of the energy-weighted excitation functions Eσ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E\\sigma $$\\end{document} in relation to their first energy derivatives d(Eσ)/dE\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d(E\\sigma )/dE$$\\end{document}. The relation between d(Eσ)/dE\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d(E\\sigma )/dE$$\\end{document} and Eσ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E\\sigma $$\\end{document} removes the basic differences due to the varying Coulomb barrier when comparing different systems. We show that, depending on the nuclear structure and/or the presence of strong transfer channels, this representation reveals characteristic features below the barrier. The possible presence of cross section oscillations makes this analysis less clear for light- or medium-light systems.

Quantum mechanical treatment of nuclear friction in coupled-channels heavy-ion fusion

Nuclear friction causes energy dissipation in heavy-ion collisions. Its understanding and inclusion in quantum mechanical reaction models are crucial for advancing the physics of heavy-ion reactions forming heavy elements. The effects of nuclear friction on heavy-ion fusion reactions are investigated using the coupled-channels density-matrix method. In this open-quantum-system description, a phenomenological nuclear friction form factor is introduced along with coherent coupled-channels effects. The key nucleus was the 92Zr target, due to its high density of low-lying non-collective excited states, which was recently theorised to be cause of nuclear friction. The calculations using the 16O + 92Zr collision showed that the inclusion of nuclear friction effects increased the fusion probability significantly, and that the agreement between the theoretical and experimental fusion barrier distributions was improved when nuclear friction effects were included.

Probing deformed nuclei: Experimental insights into excited states of 152,153,154Gd isotopes through fusion-evaporation reactions

The rare-earth region has been the focus of various studies aiming at the understanding of nuclear structure and providing information on the details of the reaction mechanism. The Gd isotopes belong to this group of nuclei and despite the available spectroscopic information, several open questions about their structure still exist, such as the inter-band transitions related to shape evolution or branching-ratios in deformed states. In addition, production cross sections of different reactions to Gd isotopes are largely unknown.In this work, we report on an experimental attempt to populate the excited states in the isotopes 152,153,154Gd by employing the heavy-ion fusion reaction 18O+138Ba → 156-xGd + xn in the 58-64 MeV energy range (center-of-mass). The experiment was conducted at the 9 MV FV Pelletron Tandem at the Horia Hulubei National Institute for Physics and Nuclear Engineering, employing the ROSPHERE array. Several branching-ratios for energy levels in 152,153Gd have been measured, offering new and updated values. Furthermore, relative cross sections regarding the fusion-evaporation reactions 138Ba(18O, 4n)152Gd, 138Ba(18O, 3n)153Gd, and 138Ba(18O, 2n)154Gd have been measured and compared with theoretical calculations with PACE4.

Investigating the impact of the universal function of the nuclear proximity potential in heavy-ion fusion cross sections

The fusion barriers and cross sections of 15 colliding systems with 320 ≤ Z 1 Z 2 ≤ 1512 are investigated in detail to understand the influence of the universal function of proximity potential formalism in the heavy-ion fusion mechanism. To realize this goal, we select three versions of the phenomenological proximity potentials, including Prox. 77, Zhang 2013, and Guo 2013, to calculate the nucleus–nucleus potential. The experimental fusion cross sections for the selected reactions are analyzed using the standard coupled-channel calculations, including couplings to the low-lying 2+ and 3− states in the target and projectile. The calculated results show that the universal functions of the Guo 2013 and Prox. 77 models provide the lowest and highest fusion barriers, respectively. In addition, it is found that the height of the fusion barriers is enhanced by increasing the mass number of the projectile from light to heavy ones. The highest sensitivity to the mass number of the projectile belongs to the results of Prox. 77. A discussion is also presented on the influence of the universal function on the radial behavior of the interaction potential in the allowed region for overlapping configurations. Our results reveal that the best fit to the experimental data of the fusion cross sections for the reactions involving light and medium nuclei is obtained using the universal function of the Zhang 2013 model. For the heavier systems, the results of the Guo 2013 model at sub-barrier energies provide a good description of the available data.

Search for beyond-mean-field signatures in heavy-ion fusion reactions

Search for beyond-mean-field signatures in heavy-ion fusion reactions

Transfer learning and neural networks in predicting quadrupole deformation

Abstract Accurately determining the quadrupole deformation parameters of atomic nuclei is crucial for understanding their structural and dynamical properties. This study introduces an innovative approach that combines transfer learning techniques with neural networks to predict the quadrupole deformation parameters of even-even nuclei. With the application of this innovative technique, the quadrupole deformation parameters of 2331 even-even nuclei are successfully predicted within the nuclear region defined by proton numbers \(8 \leq Z \leq 134\) and neutron numbers \(N \geq 8\). Additionally, the study discusses the impact of nuclear quadrupole deformation parameters on the capture cross-sections in heavy-ion fusion reactions, reconstructing the capture cross-sections for the reactions \(^{48}\text{Ca} + ^{244}\text{Pu}\) and \(^{48}\text{Ca} + ^{248}\text{Cm}\). This research offers new insights into the application of neural networks in nuclear physics and underscores the potential of merging advanced machine learning techniques with both theoretical and experimental data, particularly in fields where experimental data is limited.

Optimal incident energy of heavy ion fusion

Optimal incident energy of heavy ion fusion

Importance of physical information on the prediction of heavy-ion fusion cross sections with machine learning

Importance of physical information on the prediction of heavy-ion fusion cross sections with machine learning

Impact of nuclear structure of correlated pairs of fission fragments in mass distribution spectra of heavy-ion fusion–fission reactions

Impact of nuclear structure of correlated pairs of fission fragments in mass distribution spectra of heavy-ion fusion–fission reactions

Analysis of reaction dynamics considering MAD by Langevin equation

In heavy ion fusion and nucleon transfer reactions, which lead to the synthesis of superheavy elements, it is important to understand the reaction mechanisms. The fusion reaction mechanism is analyzed in the case of deformed target nuclei such as actinide target nuclei. We have analyzed the correlation between fission fragment mass and scattering angle (MAD) using the Langevin equation. Taking into account the effect of the collision direction between the projectile and deformed target nuclei, we present the analysis of the experimental data for the MAD of 32S+232Th.

Low-energy fusion hindrance in medium-light systems

Heavy-ion fusion reactions give fundamental information on the quantum tunnelling of many-body systems where several intrinsic degrees of freedom are contributing. Moreover, the existence of hindrance in the fusion of light systems is critical for a variety of stellar environments. Hindrance is often characterised by a maximum of the astrophysical S factor with decreasing energy, and is an interesting link between heavy-ion fusion and astrophysics. The underlying physical background is still under debate. Recently it has been pointed out that the Pauli exclusion principle influences the ion-ion potential and, as a consequence, low-energy fusion hindrance is produced because of the thicker and higher Coulomb barrier. We recently performed systematic investigations on the fusion of several medium-light systems to establish a reliable basis for the extrapolation to the lighter cases of astrophysical interest. The results obtained for 12C + 24,26Mg and 12C + 30Si are discussed here. Hindrance is observed in all cases, however, with differing features, so extrapolating to lighter systems is not straightforward. Additionally, oscillations are observed in the sub-barrier logarithmic slopes of the 12C + 24,26Mg excitation functions, which complicates identifying the hindrance threshold in those two cases. Coupled-channels calculations for all these systems have been performed. The results show that fusion cross sections are well reproduced by simple tunnelling through the potential barrier, at the lowest energies. An alternative way to represent the data is discussed, which helps identifying the various channel couplings.

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.

Observation of suppression of heavy-ion fusion by slow quasifission

The formation of superheavy elements (SHEs) by nuclear fusion can be conceptually divided into two steps: capture, and compound nucleus formation. Once captured, the two nuclei may reseparate before fusing to form a compact compound nucleus. This outcome is called quasifission. Fusion-fission, in many cases, leads to reactions outcomes inseparable from quasifission. Evaporation residue (ER) measurements are therefore the most reliable, direct experimental signature of fusion. ER cross section measurements forming the same compound nucleus, 220Th, using 16O, 40Ar, 48Ca, 82Se and 124Sn-induced reactions [1–4] revealed [1] that fusion was severely suppressed for the more symmetric reactions relative to the 16O-induced reaction. Here two new reactions forming 220Th using 28Si, 34S projectiles provide conclusive evidence that the ER cross section is exponentially suppressed as a function of ZpZt. The fission characteristics show no mass-angle correlation, demonstrating that here ER cross sections are suppressed by slow quasifission.

Unexpected observations of the heavy-ion fusion excitation function above the Coulomb barrier

Two unexpected behaviors have been observed in heavy-ion fusion excitation functions at energies above the Coulomb barrier. The first behavior is observed in overlapping excitation spectra. Fusion excitation functions σ(E) that have different entrance channels but fuse to the same compound nucleus appear to overlap in the energy domain above the barrier. The overlap emerges after scaling the center of mass energy of each excitation function by a constant scaling factor, SF. The second behaviour stems from the structure of the fusion excitation curve. Contrary to descriptions from coupled-channels or other model calculations, heavy-ion fusion excitation functions are not smooth near and above the Coulomb barrier. There appears to be weak but noticeable oscillations or structures within the excitation functions that can be observed clearly in the representation d(σE)/dE and in comparison with theoretical calculations σ(E) - σth(E). Moreover, the corresponding d(σE)/dE spectra for systems that form the same compound nucleus also overlap well in this energy range, including their fine structures, but the uncertainty is large. It appears the two behaviors are correlated and the reasoning behind these behaviors are yet unknown, but may be due to the compound-channel effect.

Generation of fusion and fusion-evaporation reaction cross-sections by two-step machine learning methods

In order to obtain cross-sections of heavy-ion fusion and fusion-evaporation reactions, artificial neural networks, cubist, random forest, support vector regression, extreme gradient boosting, and multiple linear regression machine learning approaches were used separately in this study. The outcomes from these different methods that are obtained from the training carried out with the existing experimental data in the literature were compared. Furthermore, it has been observed that a two-step process yielded better results for determining the heavy-ion reaction cross-sections, after first estimating which approach would be better for which reaction. In this manner, the method for which the cross-section needs to be calculated is determined by the machine learning classification application, and predictions can be made using the machine learning regression application with the determined method. It has been concluded that the obtained results are in harmony with the experimental data and that the methods can be used safely. The obtained results are published on a web page that allows for online calculation of heavy-ion fusion and fusion-evaporation reaction cross-sections.

Fabrication and characterization of thin [formula omitted]Sn films for heavy-ion nuclear reaction measurements

The fabrication of thin isotopically enriched 120,124Sn targets have been presented. The thin film targets prepared have been used in nuclear physics experiments to apprehend the heavy-ion fusion and multi-nucleon transfer reaction dynamics around the Coulomb barrier. Vacuum evaporation viz. resistive heating technique has been used for the fabrication of the targets with varying areal densities in the range of 50–250 μg/cm2 backed with a carbon layer of ≈20μg/cm2 using a nominal amount of 30 mg isotopically enriched material. The fabricated targets have been characterized using multiple advanced techniques viz. Energy Dispersive X-ray Spectroscopy (EDS), Scanning Electron Microscopy (SEM), and X-ray Diffractometry (XRD). The thickness of the targets has been measured using Rutherford Back-scattering Spectrometry (RBS). The isotopic contamination levels have been ascertained with an in-beam experiment using Heavy Ion Reaction Analyzer at IUAC, New Delhi.