Formation Of Superheavy Nuclei Research Articles

Theoretical study of superheavy elements 294,297Og using different versions of proximity potential

Formation of superheavy nuclei 294,297Og is studied via calculation of evaporation residue cross section. We investigated the influence of nuclear potential on the evaporation residue cross section using nine versions of proximity potential as Prox77, Prox88, BW91, Bass73, Bass77, Denisov, CW76, GP77 and Guo2013. Calculations are performed for 65 projectile-target combinations with convenient half lives. It is found that the combinations 46Ca+248Cf and 48Ca+249Cf are most favorable for the synthesis of the elements 294,297Og with evaporation cross sections 1395 and 279 fb for the 3n channel in proximity potential Guo2013. The lowest value of evaporation cross section is obtained for Bass73 potential. We have also examined the agreement of the results obtained from different potentials with the experimental data for the systems 48Ca+245Cm, 48Ca+248Cm, and 48Ca+249Bk. The results obtained from potentials Guo2013, GP77 and CW76 show better agreement with the experimental results in comparison with other potentials.

The Fusion-by-Diffusion model as a tool to calculate cross sections for the production of superheavy nuclei

This article summarizes recent progress in our understanding of the reaction mechanisms leading to the formation of superheavy nuclei in cold and hot fusion reactions. Calculations are done within the Fusion-by-Diffusion (FBD) model using the new nuclear data tables by Jachimowicz et al. (At Data Nucl Data Tables 138, 101393, 2021). The synthesis reaction is treated in a standard way as a three-step process (i.e., capture, fusion, and survival). Each reaction step is analysed separately. Model calculations are compared with selected experimental data on capture, fissionlike and fusion cross sections, fusion probabilities, and evaporation residue excitation functions. The role of the angular momentum in the fusion step is discussed in detail. A set of fusion excitation functions with corresponding fusion probabilities is provided for cold and hot synthesis reactions.

Potential energy surface and formation of superheavy nuclei with the Skyrme energy-density functional

With the Skyrme energy-density functional theory, the nucleus–nucleus potential is calculated and the potential energy surface is obtained with different effective forces for accurately estimating the formation cross sections of superheavy nuclei in massive fusion reactions. The width and height of the potential pocket are influenced by the Skyrme effective forces SkM, SkM*, SkP, SIII, Ska, and SLy4, which correspond to the different equations of state for the isospin symmetry nuclear matter. It is found that the nucleus–nucleus potential is associated with the collision orientation and Skyrme forces. A more repulsive nuclear potential is pronounced with increasing the incompressible modulus of nuclear matter, which hinders the formation of superheavy nuclei. The available data in the fusion-evaporation reaction of 48Ca+238U are nicely reproduced with the SkM* parameter by implementing the potential into the dinuclear system model.

Systematics on production of superheavy nuclei $$Z = 119-122$$ in fusion-evaporation reactions

The fusion dynamics on the formation of superheavy nuclei is investigated thoroughly within the dinuclear system model. The Monte Carlo approach is implemented into the nucleon transfer process for including all possible orientations, at which the dinuclear system is assumed to be formed at the touching configuration of dinuclear fragments. The production cross sections of superheavy nuclei Cn, Fl, Lv, Ts and Og are calculated and compared with the available data from Dubna. The evaporation residue excitation functions in the channels of pure neutrons and charged particles are analyzed systematically. The combinations with $^{44}$Sc, $^{48,50}$Ti, $^{49,51}$V, $^{52,54}$Cr, $^{58,62}$Fe and $^{62,64}$Ni bombarding the actinide nuclides $^{238}$U, $^{244}$Pu, $^{248}$Cm, $^{247,249}$Bk, $^{249,251}$Cf, $^{252}$Es and $^{243}$Am are calculated for producing the superheavy elements with Z=119-122. It is found that the production cross sections sensitively depend on the neutron richness of reaction system. The structure of evaporation residue excitation function is related to the neutron separation energy and fission barrier of compound nucleus.

Rate of decline of the production cross section of superheavy nuclei with Z=114–117 at high excitation energies

The production cross sections of superheavy nuclei with charge numbers $114-117$ are predicted in the $(5-9)n$-evaporation channels of the $^{48}$Ca-induced complete fusion reactions for future experiments. The estimates of synthesis capabilities are based on a uniform and consistent set of input nuclear data provided by the multidimensional macroscopic-microscopic approach. The contributions of various factors to the final production cross section are discussed. As shown, the specific interplay between survival and fusion probabilities unexpectedly leads to a relatively slow decline of the total cross-sections with increasing excitation energy. This effect is supported by a favorable arrangement of fission barriers protecting the compound nucleus against splitting concerning energetic thresholds for the emission of successive neutrons. In particular, the probabilities of the formation of superheavy nuclei in the $5n$-, $6n$-, and in some cases even in $7n$-evaporation channels are still promising. This may offer a new opportunity for the future synthesis of unknown neutron-deficient superheavy isotopes.

Investigation of fusion probabilities in the reactions with Cr52,54, Ni64 , and Zn68 ions leading to the formation of Z=120 superheavy composite systems

Background: The formation of superheavy nuclei in fusion reactions is suppressed by a competing quasifission process. The competition between the formation of the compound nucleus and the quasifission depends strongly on the reaction entrance channel. Purpose: The investigation of fission and quasifission processes in the formation of Z=120 superheavy composite systems in the Cr52,54+Cm248 and Zn68+Th232 reactions, and their comparison with the Ni64+U238 reaction at energies in the vicinity of the Coulomb barrier. Methods: Mass-energy distributions of fissionlike fragments formed in the reactions Cr52,54+Cm248 and Zn68+Th232 at energies near the Coulomb barrier were measured using the double-arm time-of-flight spectrometer CORSET. Results: Capture cross sections for the reactions under investigation were measured. The most probable fragment masses and total kinetic energies as well as their variances in dependence on the interaction energy were studied for asymmetric and symmetric fragments. The fusion probabilities were estimated from the analysis of mass-energy distributions. Conclusions: The estimated fusion probability drops down by a factor of 103 in the Cr54+Cm248 reaction compared to the reactions of Ca48 ions with actinides. Among the studied reactions, the Cr54+Cm248 is the most favorable one for the production of the superheavy element with Z=120.1 MoreReceived 3 August 2020Accepted 2 September 2020DOI:https://doi.org/10.1103/PhysRevC.102.044605©2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFissionLow & intermediate energy heavy-ion reactionsNuclear fusionPropertiesA ≥ 220Nuclear Physics

Deformed shell effects in Ca48+Bk249 quasifission fragments

Background: Quasifission is the main reaction channel hindering the formation of superheavy nuclei (SHN). Its understanding will help to optimize entrance channels for SHN studies. Quasifission also provides a probe to understand the influence of shell effects in the formation of the fragments.Purpose: Investigate the role of shell effects in quasifission and their interplay with the orientation of the deformed target in the entrance channel.Methods: $^{48}\mathrm{Ca}+^{249}\mathrm{Bk}$ collisions are studied with the time-dependent Hartree-Fock approach for a range of angular momenta and orientations.Results: Unlike similar reactions with a $^{238}\mathrm{U}$ target, no significant shell effects which could be attributed to the $^{208}\mathrm{Pb}$ ``doubly magic'' nucleus are found. However, the octupole deformed shell gap at $N=56$ seems to strongly influence quasifission in the most-central collisions.Conclusions: Shell effects similar to those observed in fission affect the formation of quasifission fragments. Mass-angle correlations could be used to experimentally isolate the fragments influenced by $N=56$ octupole shell gaps.

Quasifission dynamics in TDHF

For light and medium mass systems the capture cross-section may be considered to be the same as that for complete fusion, whereas for heavy systems leading to superheavy formations the evaporation residue cross-section is dramatically reduced due to the quasifission (QF) and fusion-fission processes thus making the capture cross-section to be essentially the sum of these two cross-sections, with QF occurring at a much shorter time-scale. Consequently, quasifission is the primary reaction mechanism that limits the formation of superheavy nuclei. Within the last few years the time-dependent Hartree-Fock (TDHF) approach has been utilized for studying the dynamics of quasifission. The study of quasifission is showing a great promise to provide insight based on very favorable comparisons with experimental data. In this article we will focus on the TDHF calculations of quasifission observables for the $^{48}$Ca+$^{249}$Bk system.

Dinuclear systems in complete fusion reactions

Formation and evolution of dinuclear systems in reactions of complete fusion are considered. Based on the dinuclear system concept, the process of compound nucleus formation is studied. Arguments confirming the validity of this concept are given. The main problems of describing the complete fusion in adiabatic approximation are listed. Calculations of evaporation residue cross sections in complete fusion reactions leading to formation of superheavy nuclei are shown. Isotopic trends of the cross sections of heavy nuclei formation in complete fusion reactions are considered.

Role of the “window” component of the friction tensor in the formation of superheavy nuclei

Formation of superheavy nuclei is greatly hindered by the inner barrier and strong dissipation on the way from the contact point of two colliding nuclei to the compound nucleus configuration. One of the dissipation mechanisms is related to the exchange of particles across the window between two nuclei in relative motion, which is the ``window'' term in the ``wall-plus-window'' formula. By means of the dynamic analysis for the symmetric systems $^{132}\mathrm{Xe}$ + $^{132}\mathrm{Xe}$ and $^{136}\mathrm{Xe}$ + $^{136}\mathrm{Xe}$, we have shown that the window component of friction tensor retards the elongation of the fusing composite nucleus, decreases the height of the inner barrier, and hence increases the fusion probability. Therefore, the friction associated with ``window'' term enhances the formation cross sections of superheavy nuclei. Besides, we have shown the mass difference (in units of the temperature) of the fission and neutron emission saddle points as a function of mass number of the hassium isotopes, which may provide a useful reference for synthesis and study of the nuclei adjacent to the doubly magic nucleus $^{270}\mathrm{Hs}$.

Neutron emission in the fusion process and its effect on the formation of superheavy nuclei

Neutron emission in the fusion process is investigated based on the Langevin equations coupled with the procedures describing the emission of neutron for the reaction systems $^{48}\mathrm{Ca}$ + $^{238}U$ and $^{50}\mathrm{Ti}$ + $^{249}\mathrm{Cf}$. The precompound neutron multiplicity ${n}_{pc}$, defined as the average number of neutron per fusion event, is obtained by means of those dynamic calculations. Influence of precompound neutron emission on the formation of superheavy elements is examined by means of the dynamic calculations using two different approaches, i.e., with and without taking the neutron emission into account in the fusion process. Our results show that the precompound neutron emission enhances the formation cross sections of superheavy nuclei. The origin responsible for the enhancement is that the precompound neutron emission increases the survival probability of the evaporation residue and hence increases the relevant cross sections.

Superheavy elements created at the Joint Institute for Nuclear Research

This study is concerned with the search for the entrance channels suitable to synthesize of superheavy elements. The differences between "cold" and "warm" fusion reactions successfully used for superheavy element productions are discussed. A special attention is made on the quasifission process which competes with fusion process in the reactions with heavy ions and becomes dominant in the reactions leading to the formation of superheavy nuclei.

Cold fusion reaction of58Fe+208Pb analyzed by a generalized model of fusion by diffusion

A generalized version of the fusion by diffusion model is proposed, in which evolution from dinuclear to mononuclear regimes is taken into account in terms of the coupled Langevin equations in the three-dimensional collective space of neck, radial, and asymmetric degrees of freedom. By simulating numerically these dynamic equations, the probability distribution of ${s}_{\mathrm{inj}}$, the separation between the surfaces of two approaching nuclei at the injection point in the asymmetric fission valley, is obtained. From the injection points, the system starts its climb uphill over the saddle point in the presence of thermal fluctuation; thus for very heavy systems the injection-point distance is a very critical constituent in the calculations of fusion probability. The present model is applied for the study of the mass asymmetric system ${}^{58}\mathrm{Fe}\phantom{\rule{0.16em}{0ex}}+{\phantom{\rule{0.16em}{0ex}}}^{208}$Pb. The excitation function for the ${}^{208}$Pb(${}^{58}$Fe,$n$)${}^{265}$Hs reaction is calculated and compared with the experimental data. By comparing the theoretical results with and without taking the asymmetric degree of freedom into account, we have arrived at the conclusion that nucleon flow between the asymmetric reaction partners in the early stage of the fusion process plays an important role in the formation of superheavy nuclei in the cold fusion reactions.

Processes in massive nuclei reactions and the way to complete fusion of reactants. What perspectives for the synthesis of heavier superheavy elements?

By using the dinuclear system (DNS) model we determine the capture of reactants at the first stage of reaction, the competition between the DNS decay by the quasifission (QF) and the complete fusion (CF) process up to formation of the compound nucleus (CN) having compact shape. Further evolution of the CN is considered as its fission into two fragments or formation of evaporation residues (ER) by its cooling after emission of neutrons or/and charged light particles. Disappearance of the CN fission barrier due to its fast rotation leads to the fast fission (FF) by formation of fissionlike fragments. The results of calculations for the mass symmetric 136 Xe+ 136 Xe reaction, almost mass symmetric 108 Mo+ 144 Ba reaction, and mass asymmetric like 24 Mg+ 238 U and 34 S+ 248 Cm reactions are discussed. The fusion probability P CN calculated for many massive nuclei reactions leading to formation of superheavy nuclei have been analyzed. The reactions which can lead in perspective to the synthesis of superheavy elements in the Z = 120 − 126 range and, eventually, also to heaviest nuclei, are discussed.

Dynamical deformation in heavy ion collisions and formation of superheavy nuclei

Dynamical deformation in heavy ion collisions and formation of superheavy nuclei

Influence of entrance channels on the formation of superheavy nuclei in massive fusion reactions

Within the framework of the dinuclear system (DNS) model, the production cross sections of superheavy nuclei Hs ( Z = 108 ) and Z = 112 combined with different reaction systems are analyzed systematically. It is found that the mass asymmetries and the reaction Q values of the projectile–target combinations play a very important role on the formation cross sections of the evaporation residues. Both methods to obtain the fusion probability by nucleon transfer by solving a set of microscopically derived master equations along the mass asymmetry degree of freedom (1D) and distinguishing protons and neutrons of fragments (2D) are compared with each other and also with the available experimental data.

Production mechanism of superheavy nuclei in massive fusion reactions

Within the concept of the dinuclear system (DNS), a dynamical model is proposed for describing the formation of superheavy nuclei in complete fusion reactions by incorporating the coupling of the relative motion to the nucleon transfer process. The capture of two heavy colliding nuclei, the formation of the compound nucleus and the de-excitation process are calculated by using an empirical coupled channel model, solving a set of microscopically derived master equations numerically and applying statistical theory, respectively. Fusion-fission reactions and evaporation residue excitation functions of synthesizing superheavy nuclei (SHN) are investigated systematically and compared them with available experimental data. The possible factors that affecting the production cross sections of SHN are discussed in this workshop.

Formation of superheavy nuclei in cold fusion reactions

Within the concept of the dinuclear system (DNS), a dynamical model is proposed for describing the formation of superheavy nuclei in complete fusion reactions by incorporating the coupling of the relative motion to the nucleon transfer process. The capture of two heavy colliding nuclei, the formation of the compound nucleus, and the de-excitation process are calculated by using an empirical coupled channel model, solving a master equation numerically and applying statistical theory, respectively. Evaporation residue excitation functions in cold fusion reactions are investigated systematically and compared with available experimental data. Maximal production cross sections of superheavy nuclei in cold fusion reactions with stable neutron-rich projectiles are obtained. Isotopic trends in the production of the superheavy elements $Z=110,$ 112, 114, 116, 118, and 120 are analyzed systematically. Optimal combinations and the corresponding excitation energies are proposed.

Isotopic dependence of the evaporation residue cross section in the synthesis of superheavy nuclei

The formation of superheavy nuclei via hot fusion reactions $^{48}\mathrm{Ca}$$+{}^{A}$Ra and $^{48}\mathrm{Ca}$$+{}^{A}$Th is systematically studied within the diffusion model. The effect of the isotopic composition of actinide target on the production cross section is analyzed in detail. The results show that, as a general trend, the evaporation residue cross section exponentially depends on the difference of the effective fission barrier hight and neutron separation energy in units of the temperature. By means of this exponential relationship, the possible optimal isotopic composition of the colliding nuclei can be easily figured out before the experiment.

Superheavy nuclei and giant quasi-atoms

Dynamics of heavy-ion low energy collisions is studied within the realistic model based on multi-dimensional Langevin equations. Symmetric and asymmetric fusion reactions leading to formation of superheavy nuclei are analyzed. Collisions of transactinide nuclei are investigated as an alternative way for production of neutron-rich superheavy elements. In many events lifetime of the composite giant system consisting of two touching nuclei turns out to be rather long ( ⩾ 10 −20 s ); sufficient for observing line structure in spontaneous positron emission from super-strong electric fields, a fundamental QED process.