Heavy-ion Fusion Reactions Research Articles

Examination of promising reactions with Am241 and Cm244 targets for the synthesis of new superheavy elements within the dinuclear system model with a dynamical potential energy surface

Two actinide isotopes, $^{241}$Am and $^{244}$Cm, produced and chemically purified by the HFIR/REDC complex at ORNL are candidates for target materials of heavy-ion fusion reaction experiments for the synthesis of new superheavy elements (SHEs) with $Z>118$. In the framework of the dinuclear system model with a dynamical potential energy surface (DNS-DyPES model), we systematically study the $^{48}$Ca-induced reactions that have been applied to synthesize SHEs with $Z=112$--118, as well as the hot-fusion reactions with $^{241}$Am and $^{244}$Cm as targets which are promising for synthesizing new SHEs with $Z=119$--122. Detailed results including the maximal evaporation residue cross section and the optimal incident energy for each reaction are presented and discussed.

Systematic study of the effect of individual rotational energy levels on the fusion cross-section of 16 O-based reactions of range 480 ≤ Z P Z T ≤ 592

In heavy-ion fusion reactions, the enhancement in the sub-barrier fusion cross-section has been observed as compared to the 1-Dimensional barrier penetration model due to the coupling of many degrees of freedom to the relative motion. This enhancement can be explained theoretically by including nuclear structure effects like deformation and the coupling of relative motion among two colliding nuclei. The present work aims to investigate the effect of individual rotational energy levels on the fusion cross-sections for 16O-based reaction systems, namely, 16O + 182,184,186W, 16O + 176,180Hf, 16O + 174,176Yb, 16O + 166Er, 16O + 148,152,154Sm, 16O + 150Nd at energies below the fusion barrier. Using the CCFULL code, the effect of low-lying rotational energy levels on the fusion cross-section for 16O induced reactions has been investigated at energies below and around the Coulomb barrier. The calculations are performed by assuming the fixed value of diffuseness parameter a 0 = 0.65 fm in the Woods-Saxon nuclear potential and the other two parameters are optimised by fitting the experimental data at the above barrier. Here we have determined the V 0 and r 0 as a function of Z P Z T , where experimental cross-sections are available. From our calculations, it is observed that the hexadecapole deformation (β 4) with different magnitudes has a significant influence on the fusion cross sections. For the case of the +ve value of β 4, beyond 10+, the rotational levels cease to contribute significantly and also there is a significant difference between the contribution of sequential channels. On the other hand, in the case of -ve β 4, up to 6+ levels contribute significantly. Furthermore, we have established an algebraic systematic of fitting, which one can use to determine the parameters V 0, r 0 of Woods-Saxon nuclear potential within the range of Z P Z T lie in between 480 ≤ Z P Z T ≤ 592.

Survival probability of compound nuclei in heavy-ion fusion reaction

We have developed an empirical formula to calculate the survival probability of superheavy nuclei by analyzing about 95 fusion experiments, which were classified into four categories based on the deformation parameters of a projectile–target system. Every category is analyzed using ten different entrance channel parameters; one of these displays the smoothest variation. That channel is Z 2/A, where Z and A are the atomic number and mass number, respectively. Further, the predicted empirical relation is improved by the inclusion of the fission barrier, separation energy, level density parameter, center of mass energy, and fusion barrier height for the Z 2/A term. Furthermore, the evaporation residue cross-section is maximum at a certain beam energy, called the optimal energy. Thus, finding the survival probability at the optimal energy is important in the synthesis of a superheavy nucleus. We have developed an empirical formula for the survival probability at the optimal energy to facilitate future superheavy nucleus synthesis.

Nuclear structure effects on over-barrier fusion reactions investigated with a new phenomenological model

We investigate the occurrence of nuclear structure effects in the cross section of heavy-ion fusion reactions at energies above the Coulomb barrier. To this end, we initially develop a universal phenomenological model capable to reproduce, with an unprecedented accuracy, all previously published experimental fusion excitation functions with a few parameters. The new model, which foresees exclusively charge, mass, and energy of the colliding systems, shows a clear saturation of the critical angular momentum and avoids analytical non-regularities. The predictions of the newly developed model are then inspected to pin down residual discrepancies with the data, which could be ascribed to the structure of the colliding systems. In this framework, we obtain the following findings: (1) for the first time, we suggest an anomaly in the optimum value of the fusion cross section for systems having nearly-zero fusion Q-values; (2) we point out the occurrence of shell closure effects in the fusion of light systems; (3) we suggest that shell effects are washed-out at relative velocities vrel≳0.07c; (4) in the higher energy part of the fusion excitation function, the cross section for colliding systems involving fluorine or neon isotopes impinging on 2p3/2-1f5/2 nuclei is suppressed, possibly due to the occurrence of α-clustering effects enhancing α-transfer reactions.

Quasifission barriers of heavy ion fusion reaction leading to the synthesis of superheavy nuclei 104 ≤ Z ≤ 126 with actinide targets

Quasifission barriers were studied in the superheavy region [Formula: see text] using different projectile-target combinations. The different entrance channels parameters on quasifission barriers give an insight into the formation of compound nuclei and quasifission process. The quasifission barriers are more systematic for [Formula: see text]. The effect of compound nucleus fissility [Formula: see text] and effective entrance channel fissility [Formula: see text] on quasifission barriers were investigated. The quasifission barriers are strongly influenced by [Formula: see text] and [Formula: see text] entrance channel parameters. The detailed investigations of entrance channel parameters on quasifission barriers provide a thorough understanding of compound nuclei formation in the superheavy element in the region [Formula: see text]. Eventually, this study helps in the selection of projectile-target combinations to synthesis of superheavy nuclei.

Theoretical uncertainty quantification for heavy-ion fusion

Many aspects of physics that spans from the origin of the elements to nuclear technologies rely on a robust description of nuclear reactions. One therefore needs predictive modelling of nuclear quantum many-body dynamics in which the uncertainties are well-understood. The authors use the time-dependent Hartree-Fock approach, and apply uncertainty quantification to the nuclear dynamics, considering a collection of low-energy heavy-ion fusion reactions. They find that the uncertainty in the theoretical results mainly arises from structure properties, such as the skin of neutron-rich nuclei, which are particularly ill-constrained. This work highlights the importance of including reaction data in the construction and constraint of new theoretical models that can treat dynamics and structure on the same footing.

Heavy-ion fusion reactions of astrophysical interest

The hindrance in fusion of heavy-ion reactions crops up in the region of extreme sub-barrier energies. This phenomenon can be effectively analyzed using a simple diffused barrier formula derived assuming a Gaussian distribution of fusion barrier heights. Folding the Gaussian barrier distribution with the classical expression for the fusion cross section for a fixed barrier, the fusion cross section is obtained. The energy dependence of the fusion cross section provides good description to the existing data on sub-barrier heavy-ion fusion for lighter systems of astrophysical interest. Using this simple formula, an analysis has been presented from $^{16}$O + $^{18}$O to $^{12}$C + $^{198}$Pt, all of which were measured down to $<$ 10 $\mu$b. The agreement of the present analysis with the measured values is better than those calculated even from the sophisticated coupled channels calculations. The relatively smooth variation of the three parameters of this formula implies that it may be exploited to estimate the excitation function or to extrapolate cross sections for pairs of interacting nuclei which are yet to be measured. Possible extensions of the present methodology and its limitations have also been discussed.

Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies

Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies

Systematic study of two-proton radioactivity within various versions of proximity formalisms

In this work, we study the two-proton (2p) radioactivity half-lives for nuclei near or beyond the proton drip line within the Coulomb and proximity potential model (CPPM). We investigate the 28 versions of proximity potential formalisms, which were proposed for heavy-ion fusion reactions, heavy-ion elastic scattering, ternary fission and other applications. The results indicate that BW91 and Bass77 are inappropriate for handling 2p radioactivity since the classical turning point r in cannot be obtained for the depth of the total interaction potential between the released two protons and daughter nucleus being greater than the 2p radioactivity released energy. Among the other 26 proximity potential formalisms, the one proposed by Royer et al in 1984 denoted as Prox.77-8 is the best version with the lowest rms deviations between experimental data and relevant theoretical results. It is worth mentioning that the calculations of Coulomb and Proximity Potential Model for Deformed Nuclei (2021 PRC 104, 064 613) has least standard deviation (σ = 0.592) compared with present model and other models/formulae. Furthermore, we use CPPM with Prox.77-8 to predict the 2p radioactivity half-lives of 35 potential candidates whose 2p radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. The predicted results are consistent with previous theoretical models such as the unified fission model (UFM), generalized liquid drop model (GLDM) and effective liquid drop model (ELDM).

Role of optimal beam energies in the heavy ion fusion reaction

Role of optimal beam energies in the heavy ion fusion reaction

Preference of heavy fragments as competing modes for alpha decay of 294Og

Complete binary decay of [Formula: see text]Og formed in the heavy-ion fusion reaction is studied in the frame work of Yukawa-plus-exponential potential with a third-order polynomial potential for the overlapping region. Preformation probability, which is taken as the probability of penetration in the overlapping region, calculated for the use of reduced classical hydrodynamical mass, reveals the preference for near symmetric fission fragments [Formula: see text], [Formula: see text], in competency with alpha decay. Influence of the parameter [Formula: see text] of classical hydrodynamical mass is studied in preformation values. Half-life calculated for alpha decay matches well with experimental value for the use of reduced mass. Half-lives calculated for symmetric, near symmetric fragments [Formula: see text], [Formula: see text] are found to be low for the use of reduced hydrodynamical mass and promises preference of near symmetric fragments emission, as a competing decay mode to alpha decay and confirms the role of shell structure in deciding the most probable fragment.

A modified-Wong formula for heavy-ion fusion reactions

A modified-Wong formula for heavy-ion fusion reactions

Comprehensive analysis of heavy-ion fusion reactions around the Coulomb barrier

We have investigated the fusion dynamics of 12C + 92Zr, 16O + 92Zr, 28Si + 92Zr, 35Cl + 92Zr, 16O + 60Ni, 18O + 58Ni, 12C + 194,198Pt, 16O + 144,148,154Sm and 17O + 144Sm reactions in the close vicinity of the Coulomb barrier. For this purpose, we have opted one-dimensional Wong formula, coupled channel approach, and symmetric-asymmetric Gaussian barrier distribution (SAGBD) model to analyze the fusion data for above mentioned reactions. For all studied systems, the theoretical results obtained from the one-dimensional Wong formula are unable to reproduce the fusion data especially at incident energies lying below the nominal barrier. This appeals for the inclusion of intrinsic degrees of freedom which have been originated from the nuclear structure of fusing nuclei, and thus essentially required to explain the experimental data at energies lying in the sub-barrier realm. For the chosen reactions, the coupled channel analysis suggests that the coupling of relative motion with the inelastic surface excitations and/or nucleon transfer channels associated with the reaction partners have produced a remarkable fusion enhancement at energies lying near and below the nominal barrier. It is particularly intriguing that the SAGBD model can replicate the impacts of dominant intrinsic reaction channels such as multi-phonon quantum states and/or nucleon transfer channels via Gaussian type of weight function. The predictions of the SAGBD approach appropriately reproduce the fusion cross-sections data and related barrier distributions data for the selected reactions due the fact that the multi-dimensional nature induces the barrier lowering effects and subsequently reduces the effective fusion barrier between the participants. In the SAGBD approach, the channel coupling effects are quantitively measured in terms of channel coupling parameter and percentage decrement in height of effective fusion barrier with respect to the Coulomb barrier Furthermore, the recovered -values for selected reactions are found to be smaller and hence clearly demonstrate the applicability of the model outcomes to explore the fusion dynamics of the studied systems.

Investigations on 48Ca and 58Fe-induced heavy ion fusion reactions

In this paper, we have studied all possible [Formula: see text] and [Formula: see text]-induced fusion reactions for the synthesis of superheavy nuclei [Formula: see text]. The semi-empirical formula for fusion barriers of [Formula: see text] and [Formula: see text] is constructed. Fusion and evaporation residue cross-sections are studied using advance statistical model (ASM). The fusion and evaporation residue cross-sections of this work are compared with that of experiments. We have also predicted suitable targets and production cross-sections for the synthesis of superheavy elements using the [Formula: see text] and [Formula: see text]-induced fusion reactions. The [Formula: see text]-induced fusion reactions can be used to synthesize superheavy elements [Formula: see text] and 124 using the targets [Formula: see text]Cm, [Formula: see text]Bk and [Formula: see text]Cf have half-lives greater than one year and produce the cross-sections in terms of pb.

The influence of the nuclear matter incompressibility on heavy-ion fusion reactions at near- and above-barrier energies

Based on simulating the saturation property of cold nuclear matter for complete fusion channel of two approaching nuclei, we systematically investigate the role of nuclear incompressibility in the nucleus-nucleus potential and fusion-evaporation cross section of 69 medium-heavy and heavy mass systems with 208≤Z1Z2≤1520. Our observations based on the uncoupled single-barrier potential model and the M3Y double-folding potential which is corrected with a repulsive core term reveal that the incompressibility of cold nuclear matter can be responsible for the discrepancy between the measured and calculated values of the fusion cross sections at energies around and above the Coulomb barrier. In other words, one can find that the high energy fusion cross sections can not be reproduced using the standard form of the M3Y-DF potential model without considering the repulsive core effects. We show that the strength of the repulsive contact term and also the incompressibility of the compound nuclei exhibit systematic behaviors with respect to the atomic and mass numbers of reacting nuclei. It is shown that the hardness level of nuclear matter reduces when one passes from lighter to heavier systems.

Pauli blocking potential applied to heavy-ion fusion reactions * *Supported by the National Natural Science Foundation of China (12105080, 11822503, 11975091) and the Program for Innovative Research Team (in Science and Technology) in University of Henan Province (21IRTSTHN011), China

In this study, the Pauli blocking potential between two colliding nuclei in the density overlapping region is applied to describe the heavy nuclei fusion process. Inspired by the Pauli blocking effect in the -decay of heavy nuclei, the Pauli blocking potential of single nucleon from the surrounding matter is obtained. In fusion reactions with strong density overlap, the Pauli blocking potential between the projectile and target can be constructed using a single folding model. By considering this potential, the double folding model with a new parameter set is employed to analyze the fusion processes of 95 systems. A wider Coulomb barrier and shallower potential pocket are formed in the inner part of the potential between the two colliding nuclei, compared to that calculated using the Akyüz-Winther potential. The fusion hindrance phenomena at deep sub-barrier energies are described well for fusion systems O + Pb and Ni + Ni.

Heavy-Ion Fusion Reaction Calculations: Establishing the Theoretical Frameworks for 111In Radionuclide over the Coupled Channel Model

In this work, the production of I111n radionuclide has been investigated theoretically via heavy-ion fusion reactions of two stable nuclei: C37l+G74e, M26g+R85b, S30i+B81r, and C46a+C65u reactions. Fusion cross-sections, barrier distributions, and potential energies on mutual orientations in the reactions planes of all reactions have been researched in detail around the barrier region via a coupled channel (CC) model using different codes. First of all, the most suitable codes and calculation parameter sets were determined through the C37l+G74e reaction, whose experimental data were available. The compatibility of the calculations via NRV knowledge base, CCFULL, CCDEF codes, and Wong’s formula with experimental data was analyzed. Barrier distributions and cross-sections for heavy-ion fusion reactions have been investigated with miscellaneous codes and vibrational-rotational nuclei combinations for interacting nuclei. Afterward, calculations were made with the determined parameter values for new reaction suggestions (M26g+R85b, S30i+B81r, and C46a+C65u reactions) and the results were compared. This study aims to suggest the new reaction combinations for the production of 111In radionuclide, to explore the impacts of different calculation codes and nuclear parameter combinations on the heavy-ion fusion cross-sections and barrier distributions, to demonstrate that the results are reliable, and to emphasize the importance of developing these studies in the preparation of new experiments.

Theoretical Inspecting of &lt;sup&gt;211&lt;/sup&gt;At Radionuclide via Coupled-Channel Model for Fusion Reaction of Stable Nuclei

This work has been carried out to obtain and inspect of 211 At radionuclide through fusion reaction. Cross-sections for fusion reaction have been calculated with different interaction combinations and excitations for 19 F + 192 Os and 18 O + 193 Ir reactions. All calculations have been performed on NRV Knowledge Base, CCFULL code, and Wong’s Formula. Firstly, we assigned reaction parameter values taking into account the compatibility with the experimental data 19 F + 192 Os reaction. Afterward, to enrich studies on 211 At radionuclide, we proposed 18 O + 193 Ir reaction which did not have experimental data in the literature with the method and parameter values we determined. We examined the effects of phonon excitations in projectile and target nuclei on fusion cross sections and barrier distributions. With our research, we showed that the coupled channel model and the calculation codes used to explain the fusion cross-section data and barrier distributions well. This research sheds light on the importance of analyzing important medical radionuclides such as 211 At by heavy-ion fusion reactions and encourages new researches.

Systematics of heavy ion fusion with entrance channel and deformation parameters

We have presented the systematics of fusion evaporation with deformation and entrance channel parameters based on 107 experiments in the pre-actinide, actinide, and superheavy region. The experimental evaporation residue cross sections were successfully reproduced by advanced statistical model (ASM) and dinuclear system model (DNS) models. Among the studied entrance channel parameters, the Coulomb interaction parameter $z$ and mean fissility ${\ensuremath{\chi}}_{m}$ influence effectively the fusion reactions. Deformation effects are also included. It can also be concluded that the fusion of two spherical nuclei yields the largest ${\ensuremath{\sigma}}_{\text{ER}}$. The highest ${\ensuremath{\sigma}}_{\text{ER}}$ that can obtained is dictated by the properties of the entrance channel parameters such as Coulomb interaction parameter and mean fissility parameter. By studying these systematics, we have established an entrance channel and deformation parameter dependent empirical formula for maximum evaporation residue cross sections. The presented formula is useful in determining evaporation residue cross sections of the heavy ion fusion reaction to synthesize heavy and superheavy nuclei.

Heavy-ion fusion cross sections in the barrier and high-energy regions: Signature of energy dependence in the repulsive core potential

The effect of incompressibility of cold nuclear matter (CNM) on the high-energy fusion data of the 26Mg+248Cm, 36S+238U, 48Ca+208Pb, 50Ti+209Bi and 40,48Ca+238U colliding systems with 1152≤Z1Z2≤1840 has been analyzed using coupled-channels (CC) calculations. To apply the effect of saturation property of nuclear matter, we use the M3Y double-folding model which is corrected with a repulsive term. The repulsive parameters are adjusted to provide an optimum fit to the available experimental fusion cross sections. For each of the 26Mg+248Cm, 36S+238U, 48Ca+208Pb colliding systems, the best fit to the measured fusion cross sections at high energies is achieved using the CC calculations based on the M3Y+Repulsion potential with a constant value for the strength of the repulsive contact term. While focusing on the heavy-ion fusion reactions existing in the mass range Z1Z2>1800 reveals that it is necessary to consider an energy-dependent behavior for the repulsive parameters. When these conditions are imposed on entrance channel potential, it is possible to obtain an excellent description of the fusion data for 50Ti+209Bi, 40Ca+238U, and 48Ca+238U reactions. Our findings indicate that the extracted values of the strength Vrep of the repulsive contact term increase with increasing incident energy Ec.m.. In addition, we conclude that the repulsive part of the density distribution becomes more diffused with an increase in bombarding energy.