Fusion Cross Sections Research Articles

Recent Results on Direct Measurement of the \(^{12}\)C+\(^{12}\)C Fusion Cross section at Deep Sub-barrier Energies with STELLA

Recent Results on Direct Measurement of the \(^{12}\)C+\(^{12}\)C Fusion Cross section at Deep Sub-barrier Energies with STELLA

Measurement of the 27Al(p, α)24Mg fusion reaction at astrophysical energies via the Trojan Horse Method

In astrophysics, the abundance of 26Al is essential for understanding nucleosynthesis in the Milky Way and Galactic core-collapse supernovae rates. Detection methods involve γ-ray lines and comparing 26Mg overabundance with the common Mg isotope in meteorites. Therefore, stable isotopes 27Al and 24Mg play a crucial role and the MgAl cycle affecting aluminum and magnesium production has to be carefully studied. Recent surveys reveal complexities in stellar populations whose understanding may also benefit from better constraining the closure of the MgAl cycle. The 27Al(p, α)24Mg fusion reaction, a key 27Al destruction channel, is central to these scenarios. Due to uncertainties, the Trojan Horse Method is applied, allowing high-precision spectroscopy on the compound nucleus 28Si. It reveals crucial fusion cross section information in the astrophysically relevant energy range. The indirect measurement by means of the 2H(27Al,α24Mg)n process made it possible to assess the contribution of the 84.3 keV resonance and to set upper limits on nearby resonances. This study evaluates the THM recommended rate’s impact on intermediate-mass asymptotic giant branch stars, showing a notable increase in surface aluminum abundance at lower masses due to fusion cross section modification, while 24Mg remains largely unaffected.

Exploring the role of softness on the fusion dynamics of 58,64Ni+92,100Mo reactions

The structure of target and projectile nuclei can significantly affect the reaction dynamics at low energies. In the present work, the fusion mechanism of 58,64Ni+92,100Mo reactions involving the Mo isotopes exhibiting peculiar soft nature is explored within the relativistic mean-field (RMF) formalism. The cross-section for the considered reactions is obtained using the ℓ-summed Wong model furnished with nuclear interaction potential calculated within the self-consistent RMF formalism. The calculations are done for the two sets of RMF parameters, namely, NL3∗ and NL1, which give different values for various characteristics of nuclear matter at the saturation. A lower fusion barrier and consequently, a higher cross-section is obtained for the parameter set with comparatively softer equation of state (EoS). On comparing the theoretical cross-section with the available experimental data, an underestimation of fusion cross-section with respect to the experimental data at the sub-barrier energies is noted for the NL3∗ parametrizations. The match improves for the NL1 set having soft EoS with slight underestimation of data noted for all the considered reactions. These observations infer that the incomprehensible softness of Mo-isotopes also persists in their fusion dynamics, and the nuclear potential obtained within the RMF formalism is observed to underestimate the fusion probability for the reactions involving Mo-isotopes. The compressible nature of Mo-isotopes is inferred to enhance the fusion cross-section, and nuclear potential obtained for parameter set with soft EoS is observed to be more suitable for the description of their fusion dynamics.

Sub-barrier fusion dynamics in 28,30Si induced reactions with medium mass targets

The state-of-the-art technologies made it possible to reach the realms of fusion between two complex nuclei that offer an opportunity to explore a diverse spectrum of fusion phenomena. In this article, we have reported the influence of positive Q-value neutron transfer (PQNT) channels in fusion dynamics. Significant enhancement in sub-barrier fusion cross section has been observed for the 28Si+158Gd as compared to 30Si+140Ce and other similar systems with nearby mass asymmetry. Current findings include a comparison of the fusion excitation function of multiple systems on a reduced scale. The study sheds light on the influence of PQNT channels and deformation in nuclei on the sub-barrier fusion phenomenon. Further, fusion barrier parameters (barrier height and radius) extracted from the measured data demonstrate a good agreement with the empirical parameterization and proximity potential models.

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.

Alpha heating and avalanche effect simulations for low density proton-boron fusion plasma

The initial interest in p-11B fusion, which produces three (3) alpha particles with total energy of 8.7 MeV, was regained the last few years, due to the important experimental measurements on alpha particle production and theoretical and numerical investigations. The re-evaluation of proton-boron fusion, as an important vector for “aneutronic” energy production, is based on the consideration of the “chain reactions alpha heating effect and the related avalanche effect”, as the important process, for the increase of the fusion species (p, 11B) temperatures, to temperatures corresponding to the optimump-11B fusion cross sections. Investigation of ignition and self-sustained conditions for low density (∼ 1020 m-3) proton-boron fusion plasmas is an interesting study topic for application in magnetic confinement. We use a multi-fluid, global particle and energy balance code, describing the temporal evolution of the physical parameters of the fusion medium, as a function of the initial conditions of density and temperature of the fusion species (p, 11B). For the establishment of the distinct contribution role of the avalanche effect in proton-boron fusion, we explore cases of low (<100 keV) and high (>100 keV) initial p-11B medium temperatures. For these temperature cases, density ratios np /nB > 1between the fusion species (p, 11B) are considered, for the optimization of Bremsstrahlung radiation losses. Simulations using the multi-fluid code in a low density p-11B medium with np /nB > 1, enable the evaluation of the initial temperatures range, which is necessary for the temporal increase of the alpha density, the rapid improvement in the p-11B fusion reaction rate (RR), the temperature rise of the fusion species (p, 11B) and the achievement of higher than 1 Q (Pf /P Brems) values, due to the manifestation of the avalanche effect.In the case of high initial fusion medium temperatures in the range: 150 keV ≤ T in ≤ 350 keV, the chain reactions alpha heating effect and the related avalanche effect contribute to the maintenance and the rise of the fusion species (p, 11B) temperature to high values, for ignition and self-sustained fusion (Q > 1).

Barrier distribution extraction via Gaussian process regression

This work presents a novel method for extracting potential barrier distributions from experimental fusion cross sections. We utilize a simple Gaussian process regression (GPR) framework to model the observed cross sections as a function of energy for three nuclear systems. The GPR approach offers a flexible way to represent the experimental data, accommodating potentially complex behavior without introducing strong prior assumptions. This method is applied directly to experimental data and is compared to the traditional direct extraction technique. We discuss the advantages of GPR-based barrier distribution extraction, including the capability to quantify uncertainties and robustness to noise in the experimental data.

Investigation of deep sub-barrier fusion in asymmetric systems

Enhancement of fusion cross sections below the interaction barrier has been quite successfully explained by coupled-channels methods. However, extending the measurements to deep sub-barrier energies revealed a steeper descent of the excitation function which could not be explained by standard coupled-channels calculations. Though a large number of heavy-ion and light-ion induced reactions have been investigated to understand the dynamics of fusion deep below the barrier, the phenomenon of fusion hindrance has been studied only for a handful of asymmetric systems. We report new measurements of fusion excitation functions for the systems 16O+116Cd and 16O+142Ce. We also present comparisons of the same with the data for existing symmetric systems having nearly similar values of the ζ parameter, characterizing the size of the colliding system. We extracted the logarithmic derivatives of the energy-weighted cross sections and the astrophysical S -factors. Experimental results were reproduced well by coupled-channels calculations. We extrapolated our results, following the systematics, beyond the threshold energy for fusion hindrance for both the systems. From our investigation, we conclude that the present asymmetric systems, as well as the corresponding symmetric systems, show fusion hindrance and this feature is independent of the entrance channel mass asymmetry.

Reaction dynamics of proton drip-line nuclei at energies around the Coulomb barrier

This work briefly introduces our recent studies on reactions induced by proton drip-line nuclei, 8B and 17F, at energies around the Coulomb barrier. Using detector arrays with large solid-angle coverage, the complete kinematics measurements were performed for systems of 8B+120Sn and 17F+58Ni. For the 8B+120Sn, the coincident measurement of the breakup fragments was achieved for the first time for a proton-halo nuclear system. The correlations between the breakup fragments reveal that the prompt breakup occurring on the outgoing trajectory dominates the breakup dynamics of 8B. For 17F+58Ni, the complete reaction channel information, such as quasi-elastic scattering, breakup and total fusion, was derived for the first time. An enhancement of the fusion cross section of 17F+58Ni was observed at the energy below the Coulomb barrier. Theoretical calculations indicate that this phenomenon is mainly due to the couplings to the continuum states. Moreover, different direct reaction dynamics were found in 8B and 17F systems, suggesting the influence of proton-halo structure on the reaction dynamics.

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.

Using indirect methods to explore low-energy fusion cross sections in nuclear astrophysics

Nuclear reactions within stellar environments typically manifest at energies well below 1 MeV. As a consequence, the Coulomb barrier strongly suppresses the cross section, diminishing it to values as minute as a few nanobarns for charged particles. This challenge in obtaining precise input data for astrophysics has prompted the utilization of indirect methodologies. Specifically, approaches such as ANC and THM have been employed to ascertain cross sections for reactions involving photons and charged particles in the exit channel, respectively, obviating the necessity for extrapolation. The discourse explores recent findings arising from the application of these methodologies. For example, the measurement of 6Li(3He,d)7Be is employed to infer the ANC’s of the 3He+4He→ 7Be and p+6Li→ 7Be channels, along with their corresponding radiative-capture cross sections. Furthermore, the THM measurement of the 27Al(p, α)24Mg cross section via the 2H(27Al,α 24Mg)n reaction is emphasized. In both instances, the cross section at astrophysical energies has been ascertained with unparalleled precision.

Analysis of fusion reactions induced by weakly bound nuclei on medium and heavy mass targets

Fusion cross section for reactions induced by weakly bound nuclei 6He, 6,7Li 9,11Be and 10B on targets lying in the mass region 64 ≤ A ≤ 238 have been investigated at around Coulomb barrier energies within the coupled channel formalism. Specifically, the effects of coupling to low-lying excited states of reactants and those arises due to the breakup of projectile have been studied by using Broglia and Winther (BW91), Aage Winther (AW95) and fitted potential (FP) parameterization schemes. Among these the FP scheme is found to be most appropriate in the description of fusion excitation functions of various projectile-target combination. Further, it is observed that in the sub barrier energy region there is an enhancement in the fusion cross section due to coupling to excited states while there occurs fusion suppression at above barrier energies because of the breakup of the projectile.

Analysis of fusion cross-section and S-factor of 13C + 12,13C reactions for different density distributions at astrophysical energies

The effect of the various density distributions on 13C + 12,13C reactions is investigated by using the optical model at energies near and below Coulomb barrier. For this purpose, five different density distributions of the 12C and 13C nuclei are used to produce the real potential over the double folding model. To make a comprehensive analysis, the fusion cross-sections, S-factor and elastic cross-sections are simultaneously analyzed at astrophysical energies. It is seen that the theoretical results are in good agreement with the experimental data. In this study, the hindrance characteristics of the S-factors for the 13C + 12,13C reactions are also examined at low energies, and hindrance behavior is not observed.

Role of multi-neutron transfer channels on fusion enhancement

Fusion reactions 40Ar + 116Sn, 40Ar + 122Sn and 40Ca + 124Sn have been examined by employing coupled channel (CC) approach using code-CCFULL. Here we aim to investigate the influence of multi-neutron transfer channels in addition to coupling of collective excitations on sub-barrier fusion enhancement. Incorporation of inelastic excitations alone reproduced the experimental results for 40Ar + 116Sn system while for 40Ar + 122Sn contribution of 2n transfer channel is required to explain the experimental data. However, CC calculations with 2n transfer could not explain the enhancement at sub-barrier energies for 40Ca + 124Sn system. Therefore, the empirical coupled channel (ECC) calculations have been carried out to include the effect of multi-neutron transfer channels and it is found that the incorporation of sequential 4n transfer channel reproduced the experimental results in entire energy region. Nevertheless, it is observed that multi-neutron transfer coupling significantly contributed in raising the sub-barrier fusion cross sections particularly for the reactions where colliding partners are spherical. Importantly, it is also found that transfer of even number of neutrons play dominating role in sub-barrier fusion enhancement.

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.

Systematic study of fusion suppression and its dependency on projectile breakup threshold energy

Measurements of the excitation function (EF) of the observed evaporation residues (ERs) populated in the 20Ne + 93Nb reaction at E lab ≈ 91−145 MeV are carried out to explore the systematic of fusion suppression and its dependency on projectile breakup threshold energy, by employing the offline γ-ray detection method. The EF of the observed ERs populated through complete and/or incomplete fusion processes are analysed in the framework of statistical mode code PACE4. The fusion function, derived from the experimentally measured fusion cross section data, is compared with the universal fusion function (UFF) to estimate the degree of fusion incompleteness. Based on the observed results, an empirical formula is proposed to interrelate the degree of fusion suppression and breakup threshold energy of the incident projectile.

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.

Evaporation residue cross-section measurements for 30Si+142Ce system

Evaporation residue (ER) cross-sections were measured for 30Si+142Ce reaction at laboratory energies in the range of 105 - 132 MeV using the HYbrid Recoil mass Analyzer (HYRA) at IUAC, New Delhi. The transmission efficiency of the HYRA was estimated using the calibration reaction 28Si+142Ce. Sub-barrier fusion enhancement was observed when compared with the one-dimensional barrier penetration model predictions for the present system. To explore the phenomena responsible for sub-barrier fusion enhancement, coupled-channels calculations were performed using the CCFULL code. The effect of couplings and the role of positive Q-value neutron transfer (PQNT) channels on sub-barrier fusion cross-sections were investigated. Coupled-channels calculations were able to reproduce the data by including the coupling in both projectile and target nucleus along with two neutron-transfer channels having positive Q-value. The measured ER cross-sections were compared with the nearby systems to explore the role of deformation of the colliding nuclei.

Investigations on the Ti-induced fusion cross-sections in the range 44≤Z≤104

As a function of the barrier height, center-of-mass energy, Coulomb interaction parameter and [Formula: see text], a new empirical formula for the astronomical [Formula: see text]-factor has been proposed. Around 14 fusion reactions using [Formula: see text]Ti as projectiles were taken into consideration for various targets, producing compound nuclei with atomic and mass number ranges of [Formula: see text] and [Formula: see text], respectively. The geometric factor, Gamow–Sommerfield factor and empirical [Formula: see text]-factor formulas have been used to determine the fusion cross-sections. Compared to Wong’s formula, this study shows a better agreement with the available experiments except for the [Formula: see text] and [Formula: see text] fusion reactions. When employed to correlate with the experimental data on titanium-induced fusion reactions, this study yields a lower standard deviation value than Wong’s formula except for the fusion reactions leading to the formation of compound nuclei [Formula: see text]Hf and [Formula: see text]Th.

Theoretical modeling of the above-barrier fusion process for nuclei with [formula omitted] based on the experimental nuclear charge densities

Most of theoretical models of nucleus-nucleus collision are based on the nucleus-nucleus potential. Semi-microscopical double-folding model with the M3Y-Paris NN-forces represents one of the advanced methods for evaluating this potential. Nucleon densities (NDs), being crucial ingredient of this model, must reproduce the experimental nuclear charge densities (NCDs). In theoretical approaches for modeling the fusion process, it is not always so. In the present work, we aim to reach satisfactory description of both the charge nucleon density and the above-barrier fusion cross sections of even-even nuclei with Z=N. We construct an approximation for the ND which is abbreviated as FEV-density (Fermi + Exponential tail with Variable diffuseness). The proton and neutron densities are considered to be identical and having a coordinate-dependent diffuseness. Parameters of the nucleon density are varied to obtain the best fit of the experimental NCD. Then the resulting FEV nucleon densities are used to calculate the nucleus-nucleus potential applying the double-folding model with the density-dependent M3Y-Paris NN-forces. This potential is employed for evaluating the above-barrier fusion cross sections for ten reactions: 32S+12C, 24Mg, 40Ca; 28Si+12C, 16O, 24Mg, 28Si; and 24Mg+12C, 16O, 24Mg where the experimental data are available. The cross sections are calculated using either the barrier penetration model or the trajectory model with surface friction. To find the transmission coefficients for the trajectory model, the Langevin-type equations are solved numerically. For all considered reactions, our trajectory model typically reproduces the above-barrier experimental cross sections within 10–15 % with typical χ2<2. The adjustable parameter of the model, the optimal friction strength KRm, was found to be between 20 and 40 zs·GeV−1 which is in reasonable agreement with two systematics found earlier. We also make predictions for the fusion excitation functions for reactions 32S+16O, 32S+28Si, 24Si+40Ca where we did not manage finding experimental data.