Dinuclear System Model Research Articles

Predictions for the synthesis of new superheavy nuclei with 252Cf target

Abstract The $^{252}$Cf isotope produced at Oak Ridge National Laboratory is a promising target material for the synthesis of new superheavy nuclei through fusion reaction experiments. Within the framework of the dinuclear system model, the reaction systems with the $^{252}$Cf target and the $^{48}$Ca, $^{45}$Sc, $^{50}$Ti, $^{51}$V, $^{54}$Cr, $^{55}$Mn projectiles are investigated for the synthesis of new isotopes $^{295-297}$Og, $^{292-294}$119, $^{297-299}$120, $^{298-300}$121, $^{301-303}$122 and $^{302-304}$123. The decreasing trend of the maximal evaporation residue cross sections with the increasing proton number of the compound nucleus are discussed in the capture, fusion and survival stages. Additionally, the radioactive beam-induced reactions based on the $^{252}$Cf target are investigated to reach the predicted neutron shell closure $N$ = 184, with the maximal evaporation residue cross section predicted to be 21 fb for synthesizing $^{302}$Og. The predicted results fall below the current detection limitation, indicating the necessity for advancement in both accelerator and detection techniques, as well as exploration of alternative reaction mechanisms.

Bayesian uncertainty quantification for synthesizing superheavy elements

To improve the theoretical prediction power for synthesizing superheavy elements beyond Og, a Bayesian uncertainty quantification method is employed to evaluate the uncertainty of the calculated evaporation residue cross sections (ERCS) for the first time. The key parameters of the dinuclear system model (DNS-sysu), such as the diffusion parameter a, the damping factor Ed, and the level-density parameter ratio af/an are systematically constrained by the Bayesian analysis of recent ERCS data. One intriguing behaviour is shown that the optimal incident energies (OIE) corresponding to the largest ERCS weakly depend on the fission process. We also find that these parameters are strongly correlated and the uncertainty propagation considering the parameters independently is not reasonable. The 2σ confidence level of posterior distributions for a=0.586−0.002+0.002 fm, Ed=25.65−3.41+3.43 MeV, and af/an=1.081−0.021+0.021 are obtained. Furthermore, the confidence levels of the ERCS and OIE for synthesizing Z = 119 via the reactions Cr54+243Am, Ti50+249Bk, and V51+248Cm are predicted. This work sets the stage for future analyses to explore the OIE and reaction systems for the synthesis of superheavy elements.

Possibility of synthesizing Z = 119 superheavy nuclei with Z > 20 projectiles* *Supported by the National Natural Science Foundation of China (12175064, U2167203) and the Outstanding Youth Science Foundation of Hunan Province, China (2022JJ10031)

We employ the dinuclear system (DNS) model combined with a statistical model to calculate the evaporation residue cross sections of the reaction systems Ca + Am, Ca + Cm, and Ca + Bk. The theoretical results successfully reproduce the experimental trends in the 3n and 4n evaporation channels of these reaction systems. To synthesize the new element , we predict the evaporation residue cross sections for three reaction systems ( Cr + Am, V + Cm, and Ti + Bk) to select the most promising projectile-target combinations. We also note that the maximum cross sections predicted by our model and other methods appear to be below the detection limits of current experimental facilities, given the projectile-target combinations feasible under current experimental conditions. Therefore, synthesizing superheavy nuclei with will require improvements in beam intensity, detection techniques, and effective separation methods.

Survival probabilities of compound superheavy nuclei towards element 119

To synthesize superheavy element 119 is becoming a highly concerned issue as several experimental projects in major laboratories are being pursued. This work studied the survival probabilities of compound superheavy nuclei after multiple neutron emissions based on microscopic energy dependent fission barriers, demonstrating a significant role of triaxial deformation in decreasing the first fission barriers in the heaviest region. Together with the fusion cross sections by the dinuclear system model, the optimal energy and the residual cross section of 243Am(48Ca, 3n)288Mc are reproduced. Finally the cross sections and optimal beam energies of 54Cr+243Am and 50Ti+249Bk reactions are estimated, providing clues for the synthesis of new elements.

Small cross section of the synthesis of darmstadtium in the Ca48+Th232 reaction

The smallness of the cross section of evaporation residues formed in the hot fusion reaction Ca48+Th232 is analyzed by the dinuclear system model (DNS). The capture probability has been calculated by solving the dynamical equations of motion for the relative distance between the centers of mass of the DNS nuclei. Fusion of nuclei is considered as evolution of the DNS to a stable compound nucleus. The fusion probability has a bell-like shape and quasifission is one of reasons causing smallness of the yield of the evaporation residues products. Another reason is the decrease of the fission barrier for the isotopes Dm275–285 related with the shell effects in the neutron structure. The agreement of the theoretical results obtained for the yield of the evaporation residues with the experimental data measured in the Factory of Superheavy Elements of Joint Institute for Nuclear Research is well. Published by the American Physical Society 2024

Effect of the charge asymmetry and orbital angular momentum in the entrance channel on the hindrance to complete fusion

The hindrance to complete fusion is studied as a function of the charge asymmetry of colliding nuclei and orbital angular momentum of the collision. The formation and evolution of a dinuclear system (DNS) in the heavy-ion collisions at energies near the Coulomb barrier is calculated in the framework of the DNS model. The DNS evolution is considered as nucleon transfer between its fragments. The results prove that a hindrance at formation of a compound nucleus (CN) is related with the quasifission process, which is breakup of the DNS into products instead to reach the equilibrated state of the CN. The role of the angular momentum in the charge (mass) distribution of the reaction products for the given mass asymmetry of the colliding nuclei has been demonstrated. The results of this work have been compared with the measured data for the quasifission yields in the C12+Pb204 and Ca48+Er168 reactions to show the role of the mass asymmetry of the entrance channel. Published by the American Physical Society 2024

Influence of temperature-dependent shell corrections on the prediction of production cross sections for superheavy nuclei

In the framework of the dinuclear system model, we introduce a formula accounting for temperaturedependent shell corrections to assess their influence on the fission barrier calculations and, consequently, the survival probability of excited nuclei. Our approach considers the excitation energy’s effect on the fission barrier, a crucial aspect in determining the likelihood of a nucleus persisting. Leveraging experimental data with associated errors, we constrain the region of the shell correction damping factor. Employing this refined methodology, we predict the production cross sections for the novel superheavy element (SHE) with atomic number Z=119. Specifically, at the 54Cr(243Am,3n)294119 reaction, cross sections are anticipated to range between 3-27 femtobarns (fb), while for the 51V(248Cm,3n)296119 reaction, they are projected to span 21-180 fb. These predictions offer valuable insights into the formation dynamics of this exotic superheavy element.

Evaporation residue cross sections of superheavy nuclei based on optimized nuclear data* *Supported by the National Natural Science Foundation of China (12175170, 11675066)

This study proposes an optimized method for estimating atomic nucleus masses by combining the finite-range droplet model (FRDM) with the support vector machine algorithm. The optimization process significantly improves the accuracy of the FRDM by reducing the root mean square error from 0.606 to 0.253 MeV. The optimized mass data obtained from this method are then used to calculate the evaporation residue cross-sections (ERCSs) for fusion-evaporation reactions, employing the di-nuclear system model. The experimental results for the 48Ca+238U reaction are relatively well reproduced using these optimized mass data. Additionally, the study investigates the impact of mass uncertainties on fusion and survival probabilities. By considering the mass uncertainties, the ERCSs for new elements 119 and 120 are predicted based on the obtained optimized mass data.

Investigation on the Quasifission hindrance to synthesis 298Og

Formation of a compound nucleus and production of its evaporation residue are hindered by quasi-fission process. It reduces the evaporation residue cross section since it takes place before the target and projectile combines to form a composite nucleus. We study the quasifission barriers (Bqf) for 14 fusion reactions in the formation of superheavy element 298Og within the framework of the di-nuclear system model. In particular, the influence of entrance channel parameters on quasifission barriers has been investigated. We notice that the quasifission barriers decreases with an increase in angular momentum and fusion barrier height. We constructed semi-empirical formulae for Bqf as a function of mean fissility. The fusion reaction 48Ca+250Cf poses larger Bqf. The larger evaporation cross section is observed for this fusion reaction for 3n evaporation channel with the cross-section of 0.81pb. Similarly, a smaller evaporation cross-section of about 0.033pb is observed for 51Cr+247Pu fusion reaction for 4n evaporation channel with both projectile and target being deformed, unlike to the previous reaction with spherical projectile and deformed target.

A new dynamical mechanism of incomplete fusion in heavy-ion collisions

The incomplete fusion has been proved as the emission of the α particle from the very mass-asymmetric state the dinuclear system during its evolution to complete fusion which is hindered due to the increase in the intrinsic fusion barrier related with the large rotational energy. The results of the dinuclear system model have confirmed that the incomplete fusion in heavy-ion collisions occurs at a large orbital angular momentum (L>30ħ) when the sufficient part of the initial collision energy removes as centrifugal energy.

Effect of deformation dependence and mirror nucleus corrections energy on multinucleon transfer reaction cross sections

Multinucleon transfer reactions are currently a powerful way to synthesize neutron-rich nuclei. To explore the effect of nucleus deformation and mirror nucleus shell correction energy in the nucleus mass model on the calculation of multinucleon transfer reaction cross sections in the dinuclear system (DNS) model, three macroscopic microscopic mass models are selected and the transfer reaction cross sections are calculated for 136Xe+208Pb and 64Ni+238U by improved DNS model+GEMINI++, respectively. The mirror nucleus shell correction energy does not improve the accuracy of the cross section of the transfer reaction. The introduction of a different dependence of the Coulomb and surface energy on the deformation can improve the calculation of the transfer reaction cross section when the projectile and target nuclei are deformed nuclei.

Production cross sections of new neutron-rich isotopes with Z=92–106 in the multinucleon transfer reaction Au197+Th232

The multinucleon transfer reactions $^{197}\mathrm{Au}+^{232}\mathrm{Th}, ^{186}\mathrm{W}+^{232}\mathrm{Th}$, and $^{238}\mathrm{U}+^{232}\mathrm{Th}$ are investigated within the framework of dinuclear system (DNS) model with a decay model gemini$++$. The calculated isotopic production cross sections in the $^{136}\mathrm{Xe}+^{249}\mathrm{Cf}$ reaction at ${E}_{\mathrm{c}.\mathrm{m}.}=567\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ can reproduce the experimental data well. Due to the subshell closures, the behavior of ``inverse'' quasifission process is found in the collisions of $^{186}\mathrm{W}+^{232}\mathrm{Th}$ and $^{197}\mathrm{Au}+^{232}\mathrm{Th}$. The reaction $^{197}\mathrm{Au}+^{232}\mathrm{Th}$ is more advantageous to produce neutron-rich isotopes with $Z=92--106$ than $^{186}\mathrm{W}+^{232}\mathrm{Th}$ and $^{238}\mathrm{U}+^{232}\mathrm{Th}$, because it has the lowest value of the potential energy that needed to overcome in the nucleon transfer process. Furthermore, the incident energy dependence of isotopic production cross sections in the reaction $^{197}\mathrm{Au}+^{232}\mathrm{Th}$ is studied. It is found that ${E}_{\mathrm{c}.\mathrm{m}.}=756.47$ MeV is more suitable for producing new isotopes with $Z=92--98$, while ${E}_{\mathrm{c}.\mathrm{m}.}=690.69$ MeV is the optimal incident energy for $Z=99--106$. The effect of incident energy on the interaction time is also investigated. The production cross sections of 88 unknown neutron-rich transuranium nuclei are predicted with the cross sections at the order of ${10}^{\ensuremath{-}6}$ to $10\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{b}$.

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.

Dynamics of charge equilibration and effects on producing neutron-rich isotopes around N=126 in multinucleon transfer reactions

The dynamics of the charge equilibration (CE) and the effects on the production of the neutron-rich isotopes around $N = 126$ in multinucleon transfer reactions are still not well understood. In this Letter, we investigate the mechanism of the CE from different viewpoints by using the extended version of the dinuclear system model (DNS-sysu) and the improved quantum molecular dynamics (ImQMD) model. From the macroscopic and microscopic dynamical viewpoints, we find incomplete CE for the mass asymmetry reaction systems even in the very deep collisions, and the behavior of "inverse CE" that the tendency of the fragments is away from the $N/Z$ value of the compound system in the reaction $^{140}$Xe + $^{198}$Pt. Unlike the slow process presented in the ImQMD model, the behavior of fast equilibration with the characteristic time $\sim$ 0.52 zs is obtained based on the DNS-sysu model, which is consistent with the experimental data. By performing the systematic calculation, the correlation between the CE and the mass asymmetry of the reaction systems is clarified, which not only accounts for the observed intriguing phenomena of the CE but also provides essential information for producing the neutron-rich isotopes around $N = 126$.

Influence of entrance channel on production cross sections of exotic actinides in multinucleon transfer reactions

Within the framework of the dinuclear system model, the influence of mass asymmetry and the isospin effect on the production of exotic actinides have been investigated systematically. The isotopic yields populate in multinucleon transfer reactions of Ca(48), Kr(86), Xe(136), and U(238) bombarding on Cm(248) are analyzed and compared to the available experimental data. Systematics on the production of unknown actinides from Ac to Lr via the available stable elements on the earth (from Ar to U) as projectiles-induced reactions with $^{232}$Th, $^{238}$U and $^{248}$Cm are investigated thoroughly. Potential energy surface and total kinetic energy distribution for the reaction system are calculated and can be used to predict the production cross-section trends. It is found that the heavier projectile leads to the wider isotopic chain distribution for the same target. The heavier target-based reactions prefer to produce plenty of exotic actinides through both mechanisms of deep-inelastic and quasi-fission reactions. Isospin relaxation plays a crucial role in the colliding process, resulting in actinide isotopic distribution tends to shift to the drip lines. Massive new actinides have been predicted at the level of nanobarn to millibarn. The optimal projectile-target combinations and beam energies were proposed for the forthcoming experiments.

Properties and synthesis of the superheavy nucleus Fl114298

The one-nucleon separation energy ${S}_{n}$, two-nucleon separation energy ${S}_{2n}$, one-proton separation energy ${S}_{p}$, two-proton separation energy ${S}_{2p}, \ensuremath{\alpha}$-decay energy ${Q}_{\ensuremath{\alpha}}, \ensuremath{\alpha}$-decay half-life and spontaneous fission half-life of $Z=114$ isotopes and $N=184$ isotones are calculated by the finite-range droplet model (FRDM2012). It is found that $N=184$ is a neutron magic number, and $Z=114$ is a proton magic number. The properties of $Z=114$ isotopes and $N=184$ isotones provide a vital signal that $_{114}^{298}\mathrm{Fl}$ may be a spherical double-magic nucleus and also the center of the stability island of superheavy nuclei. Based on this, we began to investigate the optimal conditions for the synthesis of superheavy nucleus $_{114}^{298}\mathrm{Fl}$ within the dinuclear system model. To produce such neutron-rich compound nucleus, we consider using the extremely neutron-rich radioactive beams to bombard actinide targets. The evaporation residue cross section of superheavy nuclei synthesized by radioactive beam is analyzed in detail. Finally, we suggest that for the synthesis of $_{114}^{298}\mathrm{Fl}$, the radioactive beam-induced fusion reaction $^{64}\mathrm{Ti}+^{238}\mathrm{U}$ in the $4n$ evaporation channel with an excitation energy of 43 MeV is optimal.

Predictions for the synthesis of the Z=120 superheavy element

The possible stable and radioactive beam-induced hot fusion reactions for the production of new superheavy element (SHE) $Z=120$ are investigated within the dinuclear system model. Our investigation shows that the reaction $^{45}\mathrm{Sc}+^{252}\mathrm{Es}$ has a relatively large evaporation residue cross-section (ERCS) for the synthesis of SHE $Z=120$ due to its slightly larger mass asymmetry. In addition, we analyzed the effects of fission barrier and neutron separation energy of superheavy nuclei on ERCS. To synthesize the double-magic $Z=120$ and $N=184$ nucleus predicted by the relativistic mean-field model, some radioactive beam-induced fusion reactions, which can be performed in available experimental equipment, for producing superheavy nucleus $^{304}120$ in neutron evaporation channels are investigated systematically. We find that the hot fusion reaction $^{50}\mathrm{Ca}+^{257}\mathrm{Fm}$ in the $3n$ evaporation channel is optimal for synthesizing the superheavy nucleus $^{304}120$. We hope these predictions will shed new light timely for the recent experiments on the synthesis of $Z=120$ superheavy element and the search for superheavy stability islands.

Production of unknown neutron-rich isotopes with Z=99–102 in multinucleon transfer reactions near the Coulomb barrier

Multinucleon transfer reactions provide a possible access to the synthesis of new neutron-rich isotopes. Within the theoretical framework of a hybrid model combining the dinuclear system model and the GRAZING model together, the transfer reaction is investigated in $^{86}\mathrm{Kr}+^{248}\mathrm{Cm}$. In this work, it is found that the hybrid model can reproduce experimental transfer cross sections well. After the verification of the hybrid model, the transfer reactions $^{112,124,132}\mathrm{Sn}+^{249}\mathrm{Cf}$ are investigated by the influence of charge equilibration on the production cross sections of the exotic nuclei. The neutron-deficient projectile $^{112}\mathrm{Sn}$ shows advantages of producing neutron-deficient nuclei, while $^{124,132}\mathrm{Sn}$ are favorable to produce neutron-rich nuclei. In order to obtain available production cross sections of the unknown neutron-rich isotopes with $Z=99\text{\ensuremath{-}}102$, the dependence of cross sections on incident energy in the reaction $^{132}\mathrm{Sn}+^{249}\mathrm{Cf}$ is also investigated. It is found that the reaction $^{132}\mathrm{Sn}+^{249}\mathrm{Cf}$ at 510 MeV is a potential candidate to produce unknown neutron-rich isotopes of trans-target.

Production of neutron-rich heavy nuclei around $$N = 162$$ in multinucleon transfer reactions

Within the framework of the dinuclear system model, the production mechanism of neutron-rich heavy nuclei around \(N = 162\) has been investigated systematically. The isotopic yields in the multinucleon transfer reaction of \(^{238}\)U + \(^{248}\)Cm are analyzed and compared with the available experimental data at GSI. Systematics on the production of superheavy nuclei via the collisions of \(^{238}\)U on actinide nuclides \(^{252,254}\)Cf, \(^{254}\)Es and \(^{257}\)Fm is investigated thoroughly. It is found that the shell effect is of importance in the formation of neutron-rich nuclei around \(N~=~162\) owing to the enhancement of fission barrier and neutron separation energy. The fragments in the multinucleon transfer reactions manifest the broad isotopic distribution and are dependent on the beam energy. The polar angles of the fragments tend to the forward emission with increasing the beam energy. The production cross sections of new isotopes are estimated and the heavier targets are available for the neutron-rich superheavy nucleus formation. The optimal reaction system and beam energy are proposed for the future experimental measurements.

Production mechanism and prediction cross sections of unknown neutron-rich 263–265,267–269Lr isotopes in multinucleon transfer reactions based on the dinuclear system model

Within the framework of the dinuclear system model, the production cross sections for producing the new neutron-rich Lr isotopes in the multinucleon transfer reactions with 249Bk and 254Es targets were predicted. The results show that the 124Sn + 254Es reaction has the highest production cross sections, followed by the 130Te + 249Bk reaction. As far as the existing experimental techniques are concerned, 130Te + 249Bk is the most suitable choice. With experimental techniques developing in the future, 124Sn + 254Es is preferable when the thick 254Es target can be prepared. The optimal energy for producing the new neutron-rich Lr isotopes is 1.1 times the Coulomb barrier for both reaction systems, and both reactions produced 263–265,267–269Lr isotopes. The production mechanism of Lr isotopes has been investigated in the 130Te + 249Bk reaction. It is found that the production of Lr isotopes mainly originates from the contribution of quasifission. And the contribution of quasifission gradually decreases with the increase of the incident angular momentum. The final production cross sections for 263–265,267–269Lr in 130Te + 249Bk reaction at E c.m. = 1.10V C are 0.22 μb, 0.13 μb, 0.15 μb, 4.45 nb, 0.62 nb, and 0.03 nb, respectively