Formation Of Evaporation Residues Research Articles

Formation of superheavy nuclei in S36+U238 and Ni64+U238 reactions

We describe the capture, fusion, fission, and evaporation residue formation cross sections of superheavy nuclei within the proposed earlier two-stage dynamical model. The approaching of the projectile nucleus to the target nucleus is described in the first stage of the model. In the second stage, the evolution of the system formed after the touching of the projectile and target nuclei is considered. The evolution of the system on both stages is described by the Langevin equations. The transport coefficients of these equations for the shape degrees of freedom are calculated within the microscopic linear-response theory. The mutual orientation of the colliding ions, the tunneling through the Coulomb barrier in the entrance channel and the shell effects in the potential energy on both stages of the calculations are taking into account. The obtained results are compared with the available experimental data and other theoretical predictions.

Fusion barrier distribution and superheavy elements

The barrier distribution, originated from channel coupling effects in heavy-ion fusion reactions, has been extracted experimentally for many systems using either a fusion excitation function or an excitation function of large-angle quasi-elastic scattering. In this article, we discuss an application of the latter method to the 48Ca+248 Cm system, which is relevant to hot fusion reactions to synthesize superheavy elements. To this end, we carry out coupled-channels calculations for this system, taking into account the deformation of the target nucleus, and discuss the role of deformation in a formation of evaporation residues.

Effect of the Structure of Light Loosely Bound Nuclei on the Mechanisms of Nuclear Reactions

The results of experiments devoted to studying fusion and transfer reactions in beams of loosely bound (3He) and cluster (6Li, 7Li) nuclei, as well as nuclei that have a halo structure (6He and 8He), with nuclei of light and heavy elements are generalized. Special features in the behavior of cross sections for the formation of evaporation residues and transfer-reaction products at energies near the barrier are revealed. The behavior of cross sections for nucleon- and cluster-transfer reactions leads to different populations of single-particle and collective states in target-like nuclei. The effect of various channels of nuclear reactions involving light nuclei on the population of the 195mHg and 197mHg(13/2+), 198mTl and 196mTl(7+), and 196mAu and 198mAu(12−) pairs of isomeric states is considered. The values of the isomeric ratios (σm/σg) for reaction products originating from fusion reactions followed by particle evaporation and from nucleon-and cluster-transfer reactions are explained.

Time-dependent Hartree-Fock plus Langevin approach for hot fusion reactions to synthesize the Z=120 superheavy element

We develop a novel approach to fusion reactions for syntheses of superheavy elements, which combines the time-dependent Hartree-Fock (TDHF) method with a dynamical diffusion model based on the Langevin equation. In this approach, the distance of the closest approach for the capture process is estimated within the TDHF approach, which is then plugged into the dynamical diffusion model as an initial condition. We apply this approach to hot fusion reactions leading to formation of the element $Z=120$, that is, the $^{48}$Ca+$^{254,257}$Fm, $^{51}$V+$^{249}$Bk, and $^{54}$Cr+$^{248}$Cm reactions. Our calculations indicate that the distances of the closest approach for these systems are similar to each other and thus the difference in the probabilities of evaporation residue formation among those reaction systems originates mainly from the evaporation process, which is sensitive to the fission barrier height and the excitation energy of a compound nucleus.

Role of charged particle emission on the evaporation residue formation in the 82Se+138Ba reaction leading to the 220Th compound nucleus

We present detailed results of a theoretical investigation on the production of evaporation residue nuclei obtained in a heavy ion reaction when charged particles (proton and α-particle) are also emitted with the neutron evaporation along the deexcitation cascade of the formed compound nucleus. The almost mass symmetric 82Se+138Ba reaction has been studied since there are many experimental results on individual evaporation residue (ER) cross sections after few light particle emissions along the cascade of the 220Th compound nucleus (CN) covering the wide 12–70 MeV excitation energy range. Our specific theoretical results on the ER cross sections for the 82Se+138Ba are in good agreement with the available experimental measurements, but our overall theoretical results concerning all possible relevant contributions of evaporation residues are several times greater than the ERs measured in experiment. The discrepancy could be due to the experimental difficulties in the identification of ER nuclei after the emission of multiple neutral and charged particles, nevertheless the analysis of ER data is very important to test the reliability of the model and to stress the importance on the investigation of ER nuclei also obtained after charged particle emissions.

Formation of Neutron-Enriched Heavy and Superheavy Nuclei in Fusion Reactions

The formation of new isotopes of heavy and superheavy elements in the fusion of neutron-enriched projectiles with actinide targets is discussed. Cross sections for the formation of evaporation residues in fusion reactions is predicted for several combinations of colliding nuclei.

Description of fusion and evaporation residue formation cross sections in reactions leading to the formation of elementZ=122within the Langevin approach

Description of fusion and evaporation residue formation cross sections in reactions leading to the formation of element<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>122</mml:mn></mml:mrow></mml:math>within the Langevin approach

Effects of entrance channels on the evaporation residue yields in reactions leading to theTh220compound nucleus

The evaporation residue yields from the compound nuclei $^{220}\mathrm{Th}$ formed in the $^{16}\mathrm{O}+^{204}\mathrm{Pb}, ^{40}\mathrm{Ar}+^{180}\mathrm{Hf}, ^{82}\mathrm{Se}+^{138}\mathrm{Ba}$, and $^{124}\mathrm{Sn}+^{96}\mathrm{Zr}$ reactions are analyzed to study the entrance channel effects by comparison of the capture, fusion, and evaporation residue cross sections calculated by the combined dinuclear system (DNS) and advanced statistical models. The difference between evaporation residue (ER) cross sections can be related to the stages of compound nucleus formation and/or its survival against fission. The sensitivity of both stages in the evolution of the DNS up to the evaporation residue formation to the angular momentum of DNS is studied. The difference between fusion excitation functions is explained by the hindrance to complete fusion due to the larger intrinsic fusion barrier ${B}_{\mathrm{fus}}^{*}$ for the transformation of the DNS into a compound nucleus and the increase of the quasifission contribution due to the decreasing of the quasifission barrier ${B}_{\mathrm{qf}}$ as a function of the angular momentum. The largest value of the ER residue yields in the very mass asymmetric $^{16}\mathrm{O}+^{204}\mathrm{Pb}$ reaction is related to the large fusion probability and to the relatively low threshold of the excitation energy of the compound nucleus. Due to the large threshold of the excitation energy (35 MeV) of the $^{40}\mathrm{Ar}+^{180}\mathrm{Hf}$ reaction, it produces ER yields less than the almost mass symmetric $^{82}\mathrm{Se}+^{138}\mathrm{Ba}$ reaction having the lowest threshold value (12 MeV).

Experimental study of the quasifission, fusion-fission, and de-excitation of Cf compound nuclei

Background: The fusion-evaporation reaction at energies around the Coulomb barrier is presently the only way to produce the heaviest elements. However, formation of evaporation residues is strongly hindered due to the competing fusion-fission and quasifission processes. Presently, a full understanding of these processes and their relationships has not been reached.Purpose: This work aims to use new fission measurements and existing evaporation residue and fission excitation function data for reactions forming Cf isotopes to investigate the dependence of the quasifission probability and characteristics on the identities of the two colliding nuclei in heavy element formation reactions.Method: Using the Australian National University's 14UD electrostatic accelerator and CUBE detector array, fission fragments from the ${}^{12}\mathrm{C}+{}^{235}\mathrm{U}$, ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$, ${}^{36}\mathrm{S}+{}^{206}\mathrm{Pb}$, ${}^{36}\mathrm{S}+{}^{208}\mathrm{Pb}$, and ${}^{44}\mathrm{Ca}+{}^{198}\mathrm{Pt}$ reactions were measured. Mass and angle distributions of fission fragments were extracted and compared to investigate the presence and characteristics of quasifission.Results: Mass-angle-correlated fission fragments were observed for the ${}^{44}\mathrm{Ca}+{}^{198}\mathrm{Pt}$ reaction; no correlation was observed in the other reactions measured. Flat-topped fission-fragment mass distributions were observed for ${}^{12}\mathrm{C}+{}^{235}\mathrm{U}$ at compound-nucleus excitation energies from 28 to 52 MeV. Less pronounced flat-topped distributions were observed, with very similar shapes, for all three sulfur-induced reactions at excitation energies lower than 45 MeV.Conclusions: A high probability of long-time-scale quasifission seems necessary to explain both the fission and evaporation residue data for the ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$ and ${}^{36}\mathrm{S}+{}^{206}\mathrm{Pb}$ reactions. Flat-topped mass distributions observed for ${}^{12}\mathrm{C}$- and ${}^{34,36}\mathrm{S}$-induced reactions are suggested to originate both from late-chance fusion-fission at low excitation energies and the persistence of shell effects at the higher energies associated with quasifission.

Fusion and transfer reactions in beams of light loosely bound nuclei at energies in the vicinity of the Coulomb barrier

Experiments devoted to studying cross sections for fusion and transfer reactions induced by the interaction of beams of halo-like (6He), cluster (6Li and 7Li), and loosely bound (3He) nuclei with nuclei of light and heavy elements are described. The cross sections obtained experimentally for such reactions are analyzed. Special features in the behavior of the cross sections for the formation of evaporation residues and products of transfer reactions at energies in the vicinity of the Coulomb barrier are revealed. In particular, an increase in the cross sections for fusion and transfer reactions involving halo-like nuclei and proceeding at energies in the subbarrier region is observed. The cross sections for neutron-transfer and light-cluster-transfer reactions reachmaximum values at an energy in the vicinity of the Coulomb barrier for the reaction being considered.

Description of synthesis of super-heavy elements within the multidimensional stochastic model

We describe the fusion-fission processes within the two-stage reaction model. On the first stage (the entrance channel) the time evolution of the system up to the touching point is calculated. All possible orientations of the colliding nuclei are taken into account. The distributions at the touching point obtained on the first step are used for the transition from separated ions to the compact system and as the initial conditions for the description of evolution of compact system (second stage). Both the approach of ions and the evolution of the compact system are described with the help of Langevin equations for the collective coordinates (deformation parameters) which specify the configuration of the system. In both stages the shell structures of the colliding ions and the compound nucleus are taken into account. Within this model we obtain the information on the touching probability and the observable measured in the fusion-fission reactions (mass and energy distributions of the fission fragments, the compound nucleus, and the evaporation residue formation cross sections). In the present work we have carried out the calculations for the reactions $^{64}\mathrm{Ni}+^{238}\mathrm{U}\ensuremath{\rightarrow}{\phantom{\rule{0.16em}{0ex}}}^{302\ensuremath{-}x}120+xn$, $^{58}\mathrm{Fe}+^{244}\mathrm{Pu}\ensuremath{\rightarrow}$ ${}^{302\ensuremath{-}x}120+xn$, $^{54}\mathrm{Cr}+^{248}\mathrm{Cm}\ensuremath{\rightarrow}{\phantom{\rule{0.16em}{0ex}}}^{302\ensuremath{-}x}120+xn$, leading to the synthesis of an element with $Z=120$. The calculated results are compared with the available experimental data and other theoretical predictions.

What perspectives for the synthesis of heavier superheavy nuclei? Results and comparison with models

The possibility to synthesize heavier superheavy elements in massive nuclei reactions is strongly limited by the hindrance to complete fusion of reacting nuclei: due to the onset of the quasifission process in the entrance channel, which competes with complete fusion, and by strong increase of the fission yield along the de-excitation cascade of the compound nucleus in comparison to the evaporation residue formation. We present a wide and detailed procedure allowing us to describe the experimental results (evaporation residue nuclei and fissionlike products) in the mass asymmetric and symmetric reactions. Very reliable estimations and perspectives for the synthesis of superheavy elements in many massive nuclei reactions up to Z = 120 and eventually also for Z > 120 have been obtained.

Allowance for the orientation of colliding ions in describing the synthesis of heavy nuclei

The dynamical model proposed earlier for describing fusion-fission reactions was modified in order to take into account an arbitrary orientation of colliding ions. In this model, the evolution of collective coordinates of the system under study is treated as a two-stage process. The motion of the projectile nucleus toward the target nucleus is considered at the first stage, and the evolution of a continuous dinuclear system formed as soon as the projectile and target nuclei touch each other is calculated at the second stage. At either stage of the calculation, the dynamical evolution of the system is described in terms of Langevin equations. The shell structure of the nuclei involved is taken into account at both stages. The difference between the results obtained for the first stage with allowance for an arbitrary orientation of colliding ions and the respective results for the case where their symmetry axes are aligned are discussed. The cross sections for the touching of primary nuclei and for their fusion are calculated, along with the cross sections for evaporation-residue formation in reactions involving nuclei that are prolate and spherical in the ground state. The results are compared with available theoretical and experimental data.

Emission of heavy clusters in nuclear reactions at low collision energies

A survey of theoretical and experimental investigations of the process involving the emission of heavy clusters from excited nuclear systems produced in heavy-ion reactions at low collision energies is given. The dinuclear system (DNS) model for calculating cross sections for the formation of heavy clusters in complete-fusion and quasifission reactions is described in detail. The results of respective calculations are compared with relevant experimental data and with the results obtained on the basis of different models. The role of the angular momentum, the asymmetry of the entrance channel, the N/Z ratio, and the excitation energy in the formation of final reaction products is studied within the proposed approach. A method is developed for calculating cross sections for evaporation-residue formation. This method takes into account both channels of light-particle emission and channels of heavy-cluster emission. The possibility for the formation of Rn, Fr, and Ra isotopes in channels of heavy-cluster emission from the excited compound nucleus of Pu is demonstrated for the first time. The calculated cross sections and isotopic distributions for residual nuclei arising upon the emission of heavy clusters from an excited compound nucleus of Pu are in good agreement with experimental data. The model developed in the present study permits finding optimum experimental conditions (projectile-target combination and bombarding energy) for studying processes involving the emission of specific complex fragments.

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.

Allowance for the shell structure of the 42 100 Mo and 46 110 Pd nuclei in the synthesis of 84 200 Po, 88 210 Ra, and 92 220 U

The effect of the shell structure of colliding nuclei in calculating the entrance channel on the ensuing evolution of the product system is investigated. The entrance channel is calculated under the assumption of the nose-to-nose orientation of colliding nuclei. The following three reactions involving nuclei that are deformed in the ground state are considered: 42100Mo + 42100Mo → 84100Po, 42100Mo + 46100Pd → 88210Ra, and 46110Pd + 46110Pd → 92220U. The state of the system at the point of touching is determined by the results obtained by calculating the entrance reaction channel. The shape of the system is specified by three collective coordinates (deformation parameters). The evolution of collective coordinates of the system is described in terms of Langevin equations. The potential energy of the system of colliding nuclei is calculated with allowance for their shell structure. It is shown that allowance for individual features of interacting nuclei in the entrance channel of the fusion-fission reactions makes it possible to obtain, for the reactions being considered, cross sections for evaporation-residue formation that are closer to available experimental data than their liquid-drop counterparts.

Effects of the entrance channel and fission barrier in the synthesis of superheavy elementZ=120

The fusion and evaporation residue cross sections for the $^{50}$Ti+$^{249}$Cf and $^{54}$Cr+$^{248}$Cm reactions calculated by the combined dinuclear system and advanced statistical models are compared. These reactions are considered to be used to synthesize the heaviest superheavy element. The $^{50}$Ti+$^{249}$Cf reaction is more mass asymmetric than $^{54}$Cr+$^{248}$Cm and the fusion excitation function for the former reaction is higher than the one for the latter reaction. The evaporation residue excitation functions for the mass asymmetric reaction is higher in comparison with the one of the $^{54}$Cr+$^{248}$Cm reaction. The use of the mass values of superheavy nuclei calculated in the framework of the macroscopic-microscopic model by the Warsaw group leads to smaller evaporation residue cross section for both the reactions in comparison with the case of using the masses calculated by Peter M\"oller {\it et al}. The $^{50}$Ti+$^{249}$Cf reaction is more favorable in comparison with the $^{54}$Cr+$^{248}$Cm reaction: the maximum values of the excitation function of the 3n-channel of the evaporation residue formation for the $^{50}$Ti+$^{249}$Cf and $^{54}$Cr+$^{248}$Cm reactions are about 0.1 and 0.07 pb, respectively, but the yield of the 4n-channel for the former reaction is lower (0.004 pb) in comparison with the one (0.01 pb) for the latter reaction.

Angular momentum distribution for the formation of evaporation residues in fusion of 19F with 184W near the Coulomb barrier

We present γ-ray multiplicity distributions for the formation of evaporation residues in the fusion reaction 19F + 184W → 203 83Bi 120 at beam energies in the range of 90–110 MeV. The measurements were carried out using a 14 element BGO detector array and the Heavy Ion Reaction Analyzer at the Inter University Accelerator Centre. The data have been unfolded to obtain angular momentum distributions with inputs from the statistical model calculation. Comparison with another neighboring system, viz. 19F + 175Lu → 194 80Hg 114 with nearly similar entrance-channel mass asymmetry, hints at the depletion of higher angular momenta after crossing of the Z = 82 shell in the compound nucleus.

Quasifission and difference in formation of evaporation residues in the 16O + 184W and 19F + 181Ta reactions

The role of the entrance channel has been studied to ascertain a cause of the observed difference between the evaporation residue cross sections normalized to the fusion cross sections in the 19F+181Ta and 16O+184W reactions at high excitation energies. The theoretical analysis performed in the framework of the dinuclear system and advanced statistical models showed that the more intense yield of evaporation residues in the 16O+184W reaction in comparison with that in the 19F+181Ta reaction was explained by the large capture and fusion cross sections in the former reaction, which is in agreement with the experimental data. The observed decrease in the evaporation residue cross section normalized to the fusion cross section in the 19F+181Ta reaction, in comparison with one in the 16O+184W reaction at large excitation energies, is caused by the unintentional inclusion of the quasifission and fast fission contributions in the fissionlike fragment yields that were used in reconstructing the experimental fusion cross section in the normalizing procedure. The range of the angular momentum distribution for both systems was similar, but the partial cross sections are different, showing the presence of a difference in the hindrance to complete fusion in both reactions.

Investigation of the role of the projectile-target orientation angles on the evaporation residue production

The measured yield of evaporation residues in reactions with massive nuclei have been well reproduced by using the partial fusion and quasifission cross sections obtained in the dinuclear-system model. The influence of the orientation angles of the projectile- and target-nucleus symmetry axes relative to the beam direction on the production of the evaporation residues is investigated for the 48Ca + 154Sm reaction as a function of the beam energy. At the low beam energies only the orientation angles close to αP = 30° (projectile) and αP = 0°–15° (target) can contribute to the formation of evaporation residues. At large beam energies (about Ec.m. = 140–180 MeV) the collisions at all values of orientation angles αP and αT of reactants can contribute to the evaporation residue cross section which ranges between 10–100 mb, while at Ec.m. > 185 MeV the evaporation residue cross section ranges between 0.1–1 mb because the fission barrier for the compound nucleus decreases by increasing its excitation energy and angular momentum.