为准确预测超重元素的合成截面、确定最佳弹靶组合以及特定碰撞能量下的蒸发道，我们尝试在双核系统（DNS）模型中采用高质量微观核质量（HQMNM），该质量通过Skyrme能量密度泛函理论（DFT）拟合实验数据得到，相关成果发表于《Phys. Lett. B》851卷（2024年）第138578页。原子核质量是DNS模型的关键输入参数，其计算得到的Q值和分离能会直接影响融合概率与存活概率的计算结果。我们的计算重现了热融合的实验数据，并与基于有限程液滴模型（FRDM12）质量计算的结果进行了对比。研究发现，与FRDM12质量计算结果相比，HQMNM对实验结果的拟合效果更优。针对\
英文摘要：
To accurately predict the synthesis cross-sections of superheavy elements, identifying the optimal projectile-target combinations and the evaporation channels at specific collision energies, we have attempted to utilize high-quality microscopic nuclear masses (HQMNM) within the dinuclear system (DNS) model, which are obtained by fitting experimental data with the Skyrme energy density functional theory (DFT), as published in Phys. Lett. B 851 (2024) 138578. The atomic nuclear mass serves as a crucial input for the DNS model, as the Q-values and separation energies it generates directly influence the calculated fusion and survival probabilities. Our calculations have reproduced the experimental data for hot fusion and have been compared with results based on the finite-range droplet model (FRDM12) mass calculations. Compared to the FRDM12 mass results, we have found that the HQMNM provides a better fit to the experimental outcomes. For the specific reaction of \(^{48}\rm{Ca} + ^{243}\rm{Am} \rightarrow ^{291}\rm{Mc}^*\), we have conducted a detailed calculation of capture, fusion, and survival based on the HQMNM model and compared these with calculations based on other mass models. Based on these findings, we have systematically calculated available projectile target combinations for the synthesis of elements 119 and 120, and identified the optimal combinations. We provided the synthesis cross-sections, collision energies, and evaporation channels, offering a reference for conducting experiments on the synthesis of superheavy elements.
Using the dinuclear system concept we present calculations of production cross sections for the heaviest nuclei. The obtained results are in a good agreement with the experimental data. The experimentally observed rapid fall-off of the cross sections of the cold fusion with increasing charge number $Z$ of the compound nucleus is explained. Optimal experimental conditions for the synthesis of the superheavy nuclei are suggested.
Examination of promising reactions with $^{241}$Am and $^{244}$Cm targets for the synthesis of new superheavy elements within the dinuclear system model with a dynamical potential energy surface
The synthesis of superheavy elements is analysed within the dinuclear system concept of compound nucleus formation. The perspectives for using radioactive beams in complete fusion reactions are discussed.
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 systema…
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 combinations play a very important role on the formation cross sections of the evaporation residues. Both methods by solving the master equations along the mass asymmetry degree of freedom (1D) and along the proton and the neutron degrees of freedom (2D) are compared each other and with the available experimental results.
Within the framework of the dinuclear system model, the production of superheavy element Z=117 in possible projectile-target combinations is analyzed systematically. The calculated results show that the production cross sections are strongly dependent on the reaction systems. Optimal combinations, corresponding excitation energies and evaporation channels are proposed in this letter, such as the isotopes ^{248,249}Bk in ^{48}Ca induced reactions in 3n evaporation channels and the reactions ^{45}Sc+^{246,248}Cm in 3n and 4n channels, and the system ^{51}V+^{244}Pu in 3n channel.
Besides right choice of entrance channel, selection of optimal beam energies for synthesis of superheavy elements plays a crucial role. A thorough investigation with the advanced statistical and dinuclear system models on all the experiments performed for the synthesis of the successful superheavy elements Z=104-118 and failed superheavy elements Z=119-120 leads us to infer that improper choice of the beam energies may be responsible for too low production cross sections to measure and thus the cause for the debacle. We have predicted the optimal beam energies to obtain the maximum production …
Within the framework of a dinuclear system (DNS) model, the evaporation-residue excitation functions and the quasi-fission mass yields in the $^{48}$Ca induced fusion reactions are investigated systematically and compared with available experimental data. Maximal production cross sections of superheavy nuclei based on stable actinide targets are obtained. Isotopic trends in the production of the superheavy elements Z=110, 112-118 based on the actinide isotopic targets are analyzed systematically. Optimal evaporation channels and combinations as well as the corresponding excitation energies are…
Within the framework of the dinuclear system (DNS) model, production cross sections of new superheavy nuclei with charged numbers Z=108-114 are analyzed systematically. Possible combinations based on the actinide nuclides $^{238}$U, $^{244}$Pu and $^{248,250}$Cm with the optimal excitation energies and evaporation channels are pointed out to synthesize new isotopes which lie between the nuclides produced in the cold fusion and the $^{48}$Ca induced fusion reactions experimentally, which are feasible to be constructed experimentally. It is found that the production cross sections of superheavy …
Mass parameters for collective variables of a dinuclear system and strongly deformed mononucleus are microscopically formulated with the linear response theory making use of the width of single particle states and the fluctuation-dissipation theorem. For the relative motion of the nuclei and for the degree of freedom describing the neck between the nuclei, we calculate mass parameters with basis states of the adiabatic and diabatic two-center shell model. Microscopical mass parameters are found larger than the ones obtained with the hydrodynamical model and give a strong hindrance for a meltin…
The dependence of fusion cross section on the isotopic composition of colliding nuclei is analysed within the dinuclear system concept for compound nucleus formation. Probabilities of fusion and surviving probabilities, ingredients of the evaporation residue cross sections, depend decisively on the neutron numbers of the dinuclear system. Evaporation residue cross sections for the production of actinides and superheavy nuclei, listed in table form, are discussed and compared with existing experimental data. Neutron-rich radioactive projectiles are shown to lead to similar fusion cross sections…
Within the framework of Skyrme energy-density functional theory, the nucleus-nucleus potential is calculated and 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$^{\ast}$, SkP, SIII, Ska and SLy4, which correspond to the different equation of state for the isospin symmetry nuclear matter. It is found that the nucleus-nucleus potential is associated with the collision orien…
We present a review of the recent progress of theoretical models on the description of the formation of superheavy nuclei in collisions of heavy systems. Two sorts of reactions that are the fusion-evaporation mechanism and the massive damped collisions to produce superheavy nuclei are discussed. Problems and further improvements of the capture of colliding partners, the formation of compound nucleus and the de-excitation process are pointed out. Possible combinations in the synthesis of the gap of the cold fusion and $^{48}$Ca induced reactions are proposed by the calculations based on the din…
The dynamical mechanism of multinucleon transfer (MNT) reactions has been investigated within the dinuclear system (DNS) model, in which the sequential nucleon transfer is described by solving a set of microscopically derived master equations. Production cross sections, total kinetic energy spectra, angular distribution of formed fragments in the reactions of $^{124,132}$Sn+ $^{238}$U/$^{248}$Cm near Coulomb barrier energies are thoroughly analyzed. It is found that the total kinetic energies of primary fragments are dissipated from the relative motion energy and rotational energy of the two c…
Role of the Coulomb interaction, mean fissility, mass asymmetry, and charge asymmetry parameters on the synthesis of heavy and superheavy elements has been examined with respect to the deformation parameters of the projectile and target nuclei explicitly in light of the experimental results. The observed facts are classified into four categories and are then used to study several unsuccessful as well as planned reactions to synthesize the new superheavy elements $Z= 119, 120$. Concrete inference is too difficult to draw from these results because of excessive deviations in evaporation residue …
The microscopic approach of fission rates and neutron emission rates in compound nuclei have been applied to $^{258}$No and $^{286}$Cn. The microscopic framework is based on the finite-temperature Skyrme-Hartree-Fock+BCS calculations, in which the fission barriers and mass parameters are self-consistently temperature dependent. The fission rates from low to high temperatures can be obtained based on the imaginary free energy method. The neutron emission rates are obtained with neutron gases at surfaces. Finally the survival probabilities of superheavy nuclei can be calculated microscopically. …
Half-lives of beta+ decay and electron capture are studied in some selected superheavy nuclei produced in hot fusion reactions, namely, 290Fl, 293Mc, 294Lv, and 295Ts. The nuclear structure is described microscopically from deformed self-consistent Skyrme Hartree-Fock mean-field calculations that include pairing correlations. The sensitivity of the half-lives to deformation and to the QEC energies, which are still not determined experimentally, are studied. The results are compared with phenomenological alpha-decay half-lives, showing that the latter decay mode is dominant in this mass region.
Within the dinuclear system (DNS) conception, instead of solving Fokker-Planck Equation (FPE) analytically, the Master equation is solved numerically to calculate the fusion probability of super-heavy nuclei, so that the harmonic oscillator approximation to the potential energy of the DNS is avoided. The relative motion concerning the energy, the angular momentum, and the fragment deformation relaxations is explicitly treated to couple with the diffusion process, so that the nucleon transition probabilities, which are derived microscopically, are time-dependent. Comparing with the analytical s…
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 o…
The interplay between quadrupole and octupole degrees of freedom is discussed in a series of neutron-rich actinides and superheavy nuclei with $92 \le$ Z $\le 110$ and $186 \le$ N $\le 202$. In addition to the static Hartree-Fock-Bogoliubov approach, dynamical beyond-mean-field correlations are taken into account via both parity restoration and symmetry-conserving Generator Coordinate Method calculations based on the Gogny-D1M energy density functional. Physical properties such as correlation energies, negative-parity excitation energies as well as reduced transition probabilities $B(E1)$ and …
As the result of synthesis of nuclei with large proton numbers a new region of investigations of the structure of nuclei has been discovered. Due to the recent significant increase in the yield of superheavy nuclei their gamma-spectroscopic studies became possible. The purpose of paper is to predict the excitation energies of the $2^+_1$ states of nuclei with Z$\ge 100$ using the microscopic variant of the Grodzins relation derived based on the geometrical collective model. The excitation energies of the $2^+_1$ states of the even-even nuclei from $^{256}$Fm to $^{296}_{120}$X which differ fro…
We have calculated production cross sections of new superheavy elements with atomic number Z=119,120 in the fusion-evaporation reactions of $^{48}$Ca+$^{252}$Es, $^{48}$Ca+$^{257}$Fm, $^{49}$Sc+$^{252}$Es, $^{49}$Sc+$^{251}$Cf, $^{50}$Ti+$^{247}$Bk, $^{50}$Ti+$^{251}$Cf, $^{51}$V+$^{247}$Cm, $^{51}$V+$^{247}$Cf, $^{54}$Cr+$^{243}$Am, $^{54}$Cr+$^{247}$Cm, $^{56}$Mn+$^{244}$Pu, $^{56}$Mn+$^{243}$Am, $^{60}$Fe+$^{237}$Np, $^{60}$Fe+$^{244}$Pu, $^{61}$Co+$^{238}$U, $^{61}$Co+$^{237}$Np, $^{64}$Ni+$^{231}$Pa, $^{64}$Ni+$^{238}$U, $^{65}$Cu+$^{232}$Th, $^{65}$Cu+$^{231}$Pa, and $^{68}$Zn+$^{232}$Th…
The impact of beyond mean field effects on the ground state and fission properties of superheavy nuclei has been investigated in a five-dimensional collective Hamiltonian based on covariant density functional theory. The inclusion of dynamical correlations reduces the impact of the $Z=120$ shell closure and induces substantial collectivity for the majority of the $Z=120$ nuclei which otherwise are spherical at the mean field level (as seen in the calculations with the PC-PK1 functional). Thus, they lead to a substantial convergence of the predictions of the functionals DD-PC1 and PC-PK1 which …
The constrained Hartree-Fock-Bogoliubov approximation, based on the recent parametrization D1M$^{*}$ of the Gogny energy density functional, is used to describe fission in 435 superheavy nuclei. The Gogny-D1M$^{*}$ parametrization is benchmarked against available experimental data on inner and second barrier heights, excitation energies of the fission isomers and half-lives in a selected set of Pu, Cm, Cf, Fm, No, Rf, Sg, Hs and Fl nuclei. Results are also compared with those obtained with the Gogny-D1M energy density functional. A detailed study of the minimal energy fission paths is carried …
We study stability of superdeformed oblate (SDO) superheavy $Z\geq 120$ nuclei predicted by systematic macroscopic-microscopic calculations in 12D deformation space and confirmed by the Hartree-Fock calculations with the realistic SLy6 force. We include into consideration high-$K$ isomers that very likely form at the SDO shape. Although half-lives $T_{1/2}\lesssim10^{-5}$ s are calclulated or estimated for even-even spin zero systems, decay hindrances known for high-$K$ isomers suggest that some SDO superheavy nuclei may be detectable by the present experimental technique.
We introduce a microscopic approach for calculating the excitation energies of systems formed during heavy-ion collisions. The method is based on time-dependent Hartree-Fock (TDHF) theory and allows the study of the excitation energy as a function of time or ion-ion separation distance. We discuss how this excitation energy is related to the estimate of the excitation energy using the reaction $Q$-value, as well as its implications for dinuclear pre-compound systems formed during heavy-ion collisions.
Ground state properties of the superheavy elements (SHE) with Z from 108 to 128 and N from 150 to 192 are investigated using both the Skyrme-Hartree-Fock method with a density-independent contact pairing interaction and the macroscopic-microscopic approach with an average Woods-Saxon potential and a monopole pairing interaction. Detailed analysis of binding energies, separation energies, shell effects, single proton and neutron states, equilibrium deformations, alpha-decay energies, and other observables is given.
The semi-microscopic potential between heavy nuclei is evaluated for various colliding ions in the approach of frozen densities in the framework of the extended Thomas-Fermi approximation with hbar^2 correction terms in the kinetic energy density functional. The proton and neutron densities of each nucleus are obtained in the Hartree-Fock-BCS approximation with SkM* parameter set of the Skyrme force. A simple expression for the nuclear interaction potential between spherical nuclei is presented. It is shown that muon bound with light projectile induces the superheavy elements production in nuc…
This work investigated the first-chance survival probabilities of highly excited compound superheavy nuclei in the prospect of synthesizing new superheavy elements. The main feature of our modelings is the adoption of microscopic temperature dependent fission barriers in calculations of fission rates. A simple derivation is demonstrated to elucidate the connection between Bohr-Wheeler statistical model and imaginary free energy method, obtaining a new formula for fission rates. The best modeling is chosen with respect to reproducing the experimental fission probability of $^{210}$Po. Systemati…
The lifetimes of the consecutive $α$ decay chains of recently synthesized new element 115, $^{287}115$ and $^{288}115$, have been calculated theoretically within the WKB approximation using microscopic $α$-nucleus interaction potentials obtained by folding in the densities of the $α$ and the daughter nuclei with a realistic effective interaction. M3Y effective interaction, supplemented by a zero-range pseudo-potential for exchange along with the density dependence, has been used for calculating the nuclear interaction potentials. Spherical charge distributions have been used for calculating th…
We investigate the entrance channel dynamics for the reactions $\mathrm{^{70}Zn}+\mathrm{^{208}Pb}$ and $\mathrm{^{48}Ca}+\mathrm{^{238}U}$ using the fully microscopic time-dependent Hartree-Fock (TDHF) theory coupled with a density constraint. We calculate excitation energies and capture cross-sections relevant for the study of superheavy formations. We discuss the deformation dependence of the ion-ion potential for the $\mathrm{^{48}Ca}+\mathrm{^{238}U}$ system and perform an alignment angle averaging for the calculation of the capture cross-section. The results show that this parameter-free…
Relativistic energy density functionals (REDF) provide a complete and accurate, global description of nuclear structure phenomena. A modern semi-empirical functional, adjusted to the nuclear matter equation of state and to empirical masses of deformed nuclei, is applied to studies of shapes of superheavy nuclei. The theoretical framework is tested in a comparison of calculated masses, quadrupole deformations, and potential energy barriers to available data on actinide isotopes. Self-consistent mean-field calculations predict a variety of spherical, axial and triaxial shapes of long-lived super…
We systematically calculate the spontaneous fission half-lives for heavy and superheavy nuclei between U and Fl isotopes. The spontaneous fission process is studied within the semi-empirical WKB approximation. The potential barrier is obtained using a generalized liquid drop model, taking into account the nuclear proximity, the mass asymmetry, the phenomenological pairing correction, and the microscopic shell correction. Macroscopic inertial-mass function has been employed for the calculation of the fission half-life. The results reproduce rather well the experimental data. Relatively long hal…
We study the effects of higher-order deformations $β_λ$ ($λ=4,6,8,$ and $10$) on the ground state properties of superheavy nuclei (SHN) near the doubly magic deformed nucleus $^{270}$Hs by using the multidimensionally-constrained (MDC) relativistic mean-field (RMF) model with five effective interactions PC-PK1, PK1, NL3$^{*}$, DD-ME2, and PKDD. The doubly magic properties of $^{270}$Hs are featured by the large energy gaps at $N=162$ and $Z=108$ in the single-particle spectra. By investigating the binding energies and single-particle levels of $^{270}$Hs in multidimensional deformation space, …
The lifetimes of $α$ decays of the recently produced isotopes of the elements 112, 114, 116 and the element $^{294}118$ and of some decay products have been calculated theoretically within the WKB approximation using microscopic $α$-nucleus interaction potentials. These nuclear potentials have been obtained by folding the densities of the $α$ and the daughter nuclei with the M3Y effective interaction, supplemented by a zero-range pseudo-potential for exchange along with the density dependence. Spherical charge distributions have been used for calculating the Coulomb interaction potentials. The…
We study reactions between neutron-rich $^{132}$Sn nucleus and $^{96}$Zr within a dynamic microscopic theory at energies in the vicinity of the ion-ion potential barrier peak, and we compare the properties to those of the stable system $^{124}$Sn+$^{96}$Zr. The calculations are carried out on a three-dimensional lattice using the density-constrained Time-Dependent Hartree-Fock method. In particular, we calculate the dynamic excitation energy $E^*(t)$ and the quadrupole moment of the dinuclear system, $Q_{20}(t)$, during the initial stages of the heavy-ion collision. Capture cross sections for …
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 to…
On the basis of systematic calculations for 1364 heavy and superheavy nuclei, including odd-systems, we have found a few candidates for high-K ground states in superheavy nuclei. The macroscopic-microscopic model based on the deformed Woods-Saxon single particle potential which we use offers a reasonable description of SH systems, including known: nuclear masses, $Q_α$-values, fission barriers, ground state deformations, super- and hyper-deformed minima in the heaviest nuclei. %For odd and odd-odd systems, both ways of including pairing correlations, % blocking and the quasi-particle method, h…
Properties of 8,979 nuclei ranging from oxygen-16 to Z = 136, A = 339 and extending from the proton drip line to the neutron drip line have been calculated by use of the 1992 version of the finite-range droplet model. The calculated quantities include the ground-state mass, deformation, microscopic correction, odd-proton and odd-neutron spins and parities, proton and neutron pairing gaps, binding energy, one- and two-neutron separation energies, quantities related to beta-delayed one- and two-neutron emission probabilities, beta-decay energy release and half-life with respect to Gamow-Teller d…
Energies of the giant Gamow-Teller and analog resonances - $E_{\rm G}$ and $E_{\rm A}$, are presented, calculated using the microscopic theory of finite Fermi system. The calculated differences $ΔE_{\rm G-A}=E_{\rm G}-E_{\rm A}$ go to zero in heavier nuclei indicating the restoration of Wigner SU(4)-symmetry. The calculated $ΔE_{\rm G-A}$ values are in good agreement with the experimental data. The average deviation is 0.30 MeV for the 33 considered nuclei for which experimental data is available. The $ΔE_{\rm G-A}$ values were calculated for heavy and superheavy nuclei up to the mass number $…
Entrance-channel potentials in nucleus-nucleus collisions, relevant for the synthesis of superheavy elements, are systematically studied within a semi-microscopic approach, where microscopic nuclear densities of the colliding spherical or deformed nuclei are used in semi-classical expressions of the energy-density functional. From experimental data on fusion windows evidence is found that the existence of pockets in the entrance-channel potentials is crucial for fusion. Criteria for the choice of best collision systems for the synthesis of superheavy elements are discussed.
The probability of $α$ particle emission for some recently observed superheavy nuclei (SHN) are investigated. The $α$-decay half lives of SHN are calculated in a quantum tunneling model with density dependent M3Y (DDM3Y) effective nuclear interaction using theoretical and measured $Q_α$ values. We determine the density distribution of $α$ and daughter nuclei from the relativistic mean field theory (RMF) using FSUGold force, NL3 and TM1 parameter sets. The double folded nuclear potential is numerically calculated in a more microscopic manner using these density distributions. The estimated valu…
A recent high-resolution $α$, $X$-ray, and $γ$-ray coincidence-spectroscopy experiment offered first glimpse of excitation schemes of isotopes along $α$-decay chains of $Z=115$. To understand these observations and to make predictions about shell structure of superheavy nuclei below $^{288}115$, we employ two complementary mean-field models: self-consistent Skyrme Energy Density Functional approach and the macroscopic-microscopic Nilsson model. We discuss the spectroscopic information carried by the new data. In particular, candidates for the experimentally observed $E1$ transitions in $^{276}…
We study pre-equilibrium giant dipole resonance excitation and fusion in the neutron-rich system $^{132}$Sn+$^{48}$Ca at energies near the Coulomb barrier, and we compare photon yields and total fusion cross sections to those of the stable system $^{124}$Sn+$^{40}$Ca. The dynamic microscopic calculations are carried out on a three-dimensional lattice using both the Time-Dependent Hartree-Fock method and the Density Constrained TDHF method. We demonstrate that the peak of the GDR excitation spectrum occurs at a substantially lower energy than expected for an equilibrated system, thus reflecting…
The production cross sections of heaviest isotopes of superheavy nuclei with charge numbers 112--118 are predicted in the $xn$--, $pxn$--, and $αxn$--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. Nuclear masses, deformations, shell corrections, fission barriers, and decay energies are calculated within the macroscopic-microscopic approach for even-even, odd-Z, and odd-N nuclei. For odd systems, the blocking procedure is used. To find, the gr…
The evolution of structure property along the fission path in the superheavy nucleus $^{256}$Sg is predicted through the multi-dimensional potential-energy(or Routhian)-surface calculations,in which the phenomenological deformed Woods-Saxon potential is adopted. Calculated nuclear deformations and fission barriers for $^{256}_{106}$Sg$_{150}$ and its neighbors, e.g., $^{258,260}$Sg, $^{254}$Rf and $^{252}$No are presented and compared with other theoretical results. A series of energy maps and curves are provided and used to evaluate the corresponding shape-instability properties, especially i…
