Recent experimental advances have made it possible to study excited structure in superheavy nuclei. The observed states have often been interpreted as quasi-particle excitations. We show that in superheavy nuclei collective vibrations systematically appear as low-energy excitation modes. By using the microscopic Triaxial Projected Shell Model, we make a detailed prediction on gamma-vibrational states and their E2 transition probabilities to the ground state band in Fermium and Nobelium isotopes where active structure research is going on, and in 270Ds, the heaviest isotope where decay data have been obtained for the ground-state and for an isomeric state.
Three different ways for description of binding energy of superheavy nuclei are discussed. First, one can consider superheavy nuclei as a part of a whole system of nuclei for which a global mass formula is found. Another way is the detailed local description of energy of superheavy nuclei taking into account the effects of shells and subshells. The third way of description, applied for nuclei in the region limited by principal magic numbers, is attached to the beta-stability line.
A formula for the relationship between the $α$-decay energies ($Q$ values) of superheavy nuclei (SHN) is presented, which is composed of the effects of Coulomb energy and symmetry energy. It can be employed not only to validate the experimental observations and measurements to a large extent, but also to predict the $Q$ values of heaviest SHN with a high accuracy generally which will be very useful for future experiments. Furthermore, the shell closures in superheavy region and the effect of the symmetry energy on the stability of SHN against $α$-decay are discussed with the help of this formu…
Potential energy surfaces and fission barriers of superheavy nuclei are analyzed in the macroscopic-microscopic model. The Lublin-Strasbourg Drop (LSD) is used to obtain the macroscopic part of the energy, whereas the shell and pairing energy corrections are evaluated using the Yukawa-folded potential. A standard flooding technique has been used to determine the barrier heights. It was shown the Fourier shape parametrization containing only three deformation parameters reproduces well the nuclear shapes of nuclei on their way to fission. In addition, the non-axial degree of freedom is taken in…
The alpha decay half-lives of the recently produced isotopes of the 112, 114, 116 and 118 nuclei and decay products have been calculated in the quasi-molecular shape path using the experimental Qalpha value and a Generalized Liquid Drop Model including the proximity effects between nucleons in the neck or the gap between the nascent fragments. Reasonable estimates are obtained for the observed alpha decay half-lives. The results are compared with calculations using the Density-Dependent M3Y effective interaction and the Viola-Seaborg-Sobiczewski formulae. Generalized Liquid Drop Model predicti…
We have constructed new proximity function particularly for interaction between two superheavy nuclei based on the experimental alpha decay half-lives. The new proximity function is used to produce the alpha decay half-lives of superheavy nuclei whose experimental values are known. The new proximity function produces the alpha decay half-lives close to the experiments. Hence we can conclude that the new proximity function can be used to study the interaction between two superheavy nuclei.
Recent microscopic calculation based on the density functional theory predicts long-lived superheavy elements in a variety of shapes, including spherical, axial and triaxial configurations. Only when N=184 is approached one expects superheavy nuclei that are spherical in their ground states. Magic islands of extra-stability have been predicted to be around Z=114, 124 or, 126 with N=184, and Z=120, with N=172. However, the question of whether the fission-survived superheavy nuclei with high Z and N would live long enough for detection or, undergo alpha-decay in a very short time remains open. I…
Potential energy surfaces of even-even superheavy nuclei are evaluated within the macroscopic-microscopic approximation. A very rapidly converging analytical Fourier-type shape parametrization is used to describe nuclear shapes throughout the periodic table, including those of fissioning nuclei. The Lublin Strasbourg Drop and another effective liquid-drop type mass formula are used to determine the macroscopic part of nuclear energy. The Yukawa-folded single-particle potential, the Strutinsky shell-correction method, and the BCS approximation for including pairing correlations are used to obta…
The conditions of optimum orientations (lowest barrier and largest interaction radius) for deformed colliding nuclei are introduced in "cold" fusion of superheavy nuclei. Also, the role of (octupole and) hexadecupole deformations is studied. We have used the proximity potential and applied our method to Ca-induced reactions.
The fusion-by-diffusion model proposed by Swiatecki {\it et al.} [Phys. Rev. C71, 014602 (2005)] has provided a simple and convenient tool to estimate evaporation residue cross sections for superheavy nuclei. I extend this model by taking into account deformation of the target nucleus, and discuss the role of orientation of deformed target in hot fusion reactions at energies around the Coulomb barrier. To this end, I introduce an injection point for the diffusion process over an inner barrier which depends on the orientation angle. I apply this model to the $^{48}$Ca+$^{248}$Cm reaction and sh…
Superheavy nuclei are investigated in a nonlinear chiral SU(3)-model. The proton number Z=120 and neutron numbers of N=172, 184 and 198 are predicted to be magic. The charge distributions and alpha-decay chains hint towards a hollow structure.
A model based on chiral SU(3)-symmetry in nonlinear realisation is used for the investigation of nuclei, superheavy nuclei, hypernuclei and multistrange nuclear objects (so called MEMOs). The model works very well in the case of nuclei and hypernuclei with one Lambda-particle and rules out MEMOs. Basic observables which are known for nuclei and hypernuclei are reproduced satisfactorily. The model predicts Z=120 and N=172, 184 and 198 as the next shell closures in the region of superheavy nuclei. The calculations have been performed in self-consistent relativistic mean field approximation assum…
Cold reaction valleys in the radioactive decay of superheavy nuclei {286}^112, {292}^114 and {296}^116 are studied taking Coulomb and Proximity Potential as the interacting barrier. It is found that in addition to alpha particle, 8^Be, 14^C, 28^Mg, 34^Si, 50^Ca, etc. are optimal cases of cluster radioactivity since they lie in the cold valleys. Two other regions of deep minima centered on 208^Pb and 132^Sn are also found. Within our Coulomb and Proximity Potential Model half-life times and other characteristics such as barrier penetrability, decay constant for clusters ranging from alpha parti…
The alpha decay half-lives of recently synthesized superheavy nuclei (SHN) are calculated by applying a new approach which estimates them with the help of their neighbors based on some simple formulas. The estimated half-life values are in very good agreement with the experimental ones, indicating the reliability of the experimental observations and measurements to a large extent as well as the predictive power of our approach. The second part of this work is to test the applicability of the Wentzel-Kramers-Brillouin (WKB) approximation for the quantum mechanical tunneling probability. We calc…
The alpha-decay half-lives of recently synthesized superheavy nuclei (SHN) are investigated based on a unified fission model (UFM) where a new method to calculate the assault frequency of alpha-emission is used. The excellent agreement with the experimental data indicates the UFM is a useful tool to investigate these alpha-decays. It is found that the half-lives become more and more insensitive to the Q_alpha values as the atomic number increases on the whole, which is favorable for us to predict the half-lives of SHN. In addition, a formula is suggested to compute the Q_alpha values for the n…
The current status of the application of covariant density functional theory to the description of fission barriers in actinides and superheavy nuclei is reviewed. The achievements and open problems are discussed.
Effects of the density dependence of the nuclear symmetry energy on ground-state properties of superheavy nuclei are studied in the relativistic mean-field theory. It is found that the softening of the symmetry energy plays an important role in the empirical shift [Phys. Rev. C 67, 024309 (2003)] of spherical orbitals in superheavy nuclei. The calculation based on the relativistic mean-field models NL3 and FSUGold supports the double shell closure in $^{292}120$ with the softening of the symmetry energy. In addition, the significant effect of the density dependence of the symmetry energy on th…
We calculate the ground state properties of recently synthesized superheavy nuclei starting from $Z$=105-120. The nonrelativistic and relativistic mean field formalisms is used to evaluate the binding energy, charge radius, quadrupole deformation parameter and the density distribution of nucleons. We analyzed the stability of the nuclei based on the binding energy and neutron to proton ratio. We also studied the bubble structure of the nucleus which reveals about the special features of the superheavy nucleus.
Properties of transactinide nuclei needed for the interpretation of spectroscopic data and for the extrapolation to the expected "island of stability" of superheavy nuclei are reviewed from a theorist's point of view in the framework of self-consistent mean-field models.
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.
The extrapolation of self-consistent nuclear mean-field models to the region of superheavy elements is discussed with emphasis on the extrapolating power of the models. The predictions of modern mean-field models are confronted with recent experimental data. It is shown that a final conclusion about the location of the expected island of spherical doubly-magic superheavy nuclei cannot be drawn on the basis of the available data.
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, …
By using a newly developed di-nuclear system model with a dynamical potential energy surface---the DNS-DyPES model, hot fusion reactions for synthesizing superheavy nuclei (SHN) with the charge number Z = 112-120 are studied. The calculated evaporation residue cross sections are in good agreement with available data. In the reaction 50Ti+249Bk -> (299-x)119 + xn, the maximal evaporation residue (ER) cross section is found to be about 0.11 pb for the 4n-emission channel. For projectile-target combinations producing SHN with Z=120, the ER cross section increases with the mass asymmetry in the in…
Atomic nuclei are composite systems, and they may be dynamically excited during nuclear reactions. Such excitations are not only relevant to inelastic scattering but they also affect other reaction processes such as elastic scattering and fusion. The coupled-channels approach is a framework which can describe these reaction processes in a unified manner. It expands the total wave function of the system in terms of the ground and excited states of the colliding nuclei, and solves the coupled Shrödinger equations to obtain the $S$-matrix, from which several cross sections can be constructed. Thi…
A systematic study on the alpha decay half lives of various isotopes of superheavy element \textit{Z} = 121 within the range 290 $\leq$ A $\leq$ 339 is presented for the first time using Coulomb and proximity potential model for deformed nuclei (CPPMDN). The calculated $α$ decay half lives of the isotopes within our formalism match well with the values computed using Viola-Seaborg systematic, Universal curve of Poenaru et al., and the analytical formula of Royer. In our study by comparing the $α$ decay half lives with the spontaneous fission half lives, we have predicted $2α$ chain from $^{309…
Spontaneous fission and alpha decay are the main decay modes for superheavy nuclei. The superheavy nuclei which have small alpha decay half-life compared to spontaneous fission half-life will survive fission and can be detected in the laboratory through alpha decay. We have studied the alpha decay half-life and spontaneous half-life of some superheavy elements in the atomic range Z = 100-130. Spontaneous fission half-lives of superheavy nuclei have been calculated using the phenomenological formula and the alpha decay half-lives using Viola-Seaborg-Sobiczewski formula (Sobiczewski et al. 1989)…
We have studied properties and shell structure of the superheavy elements from Z=102 to Z=120 within the framework of the RMF theory. The region of study spans nuclides with neutron numbers N=150-190. The Lagrangian model NL-SV1 with the inclusion of the vector self-coupling of the omega-meson has been employed in this work. We have performed RMF + BCS calculations for an axially deformed configuration of nuclei. The ground-state binding energies, single-particle properties and quadrupole deformation of nuclei have been obtained from the mean-field minimizations. Two-neutron separation energie…
The analysis of quasiparticle spectra in heaviest $A\sim 250$ nuclei with spectroscopic data provides an additional constraint for the choice of effective interaction for the description of superheavy nuclei. It strongly suggest that only the parametrizations of the relativistic mean field Lagrangian which predict Z=120 and N=172 as shell closures are reliable for superheavy nuclei. The influence of the central depression in the density distribution of spherical superheavy nuclei on the shell structure is studied. Large central depression produces large shell gaps at Z=120 and N=172. The shell…
We have investigated most stable superheavy nuclei by studying the decay properties such as alpha decay, cluster decay and spontaneous fission. We have investigated nine stable nuclei in the island of stability which can be detected through fission are 318123(10.5ms), 319123(4.68μs), 317124(1.74x104 y), 318124(2.70x101 y), 319124(2.83x10-2 y), 320124(1.91x10-5 y), 319125(2.46x109 y), 320125(3.81x106 y) and 321125(3.99x103 y). Present work also investigates three stable superheavy nuclei which can be detected through alpha decay which are 318125(1.03x1012 y), 319126(5.77x1011 y) and 320126(3.99…
The stability of excited superheavy nuclei (SHN) with $100 \leq Z \leq 134$ against neutron emission and fission is investigated by using a statistical model. In particular, a systematic study of the survival probability against fission in the 1n-channel of these SHN is made. In present calculations the neutron separation energies and shell correction energies are consistently taken from the calculated results of the finite range droplet model which predicts an island of stability of SHN around Z=115 and N=179. It turns out that this island of stability persists for excited SHN in the sense th…
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.
Bound, strange, neutral superheavy nuclei, stable against strong decay, may exist. A model effective field theory calculation of the surface energy and density of such systems is carried out assuming vector meson couplings to conserved currents and scalar couplings fit to data where it exists. The non-linear relativistic mean field equations are solved assuming local baryon sources. The approach is calibrated through a successful calculation of the known nuclear surface tension.
The HFB self-consistent method has been applied to study the properties of several neutron deficient superheavy nuclei with Z=120-124, N=160-168. Their distinctive feature is the existence of minima of the total HFB energy for strongly deformed, oblate shapes. The self-consistent results agree quite remarkably with those currently obtained by using microscopic-macroscopic method.
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…
We employ Relativistic Mean Field (RMF) model with NL3 parametrization to investigate the ground state properties of superheavy nucleus, Z = 124. The nuclei selected (from among complete isotopic series) for detailed investigation show that the nucleon density at the center is very low and therefore, these nuclei can be treated as semi-bubble nuclei. The considerable shell gap appears at neutron numbers N = 172, 184 and 198 showing the magicity corresponding to these numbers. The results are compared with the macro-microscopic Finite Range Droplet Model (FRDM) wherever possible.
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…
We found that a true ternary fission with formation of a heavy third fragment (a new type of radioactivity) is quite possible for superheavy nuclei due to the strong shell effects leading to a three-body clusterization with the two doubly magic tin-like cores. The simplest way to discover this phenomenon in the decay of excited superheavy nuclei is a detection of two tin-like clusters with appropriate kinematics in low-energy collisions of medium mass nuclei with actinide targets. The three-body quasi-fission process could be even more pronounced for giant nuclear systems formed in collisions …
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 a…
Octupole deformed shapes in neutron-rich actinides and superheavy nuclei as well as extremely deformed shapes of the N~Z light nuclei have been investigated within the framework of covariant density functional theory. We confirmed the presence of new region of octupole deformation in neutron-rich actinides with the center around Z~96, N~196 but our calculations do not predict octupole deformation in the ground states of superheavy Z~108 nuclei. As exemplified by the study of 36Ar, the nodal structure of the wavefunction of occupied single-particle orbitals in extremely deformed structures allo…
The experimentally available data on the alpha decay half lives and Q? values for 96 superheavy nuclei are used to fix the parameters for a modified version of the Brown empirical formula through two fitting procedures which enables its comparison with similar fits using Viola-Seaborg and Royer formulas. The new expressions provide very good agreement with experimental data having fewer or the same number of parameters. All formulas with the obtained parameters are then extrapolated to generate half lives predictions for 125 unknown superheavy alpha emitters. The nuclei where the employed empi…
A recently published highly extrapolatable semiempirical shell model mass equation is shown to describe rather well the energies of several seemingly well identified alpha-decay chains with known end product nuclei observed in superheavy elements research. The equation is also applied to the interpretation problem of some recent hot fusion-evaporation experiments with unknown end products and several conceivable reaction channels. Some plausible interpretations are indicated.
Recently synthesis of superheavy nuclei has been achieved in hot fusion reactions. A systematic theoretical calculation of alpha decay half-lives in this region of the periodic system, may be useful in the identification of new nuclei in these type of reactions. Alpha decay half-lives are obtained in the framework of the barrier penetration theory, built with the use of proximity and Coulomb forces. It is estimated from a classical viewpoint, a possible angular momentum maximum value for odd and odd-odd nuclei alpha particles. The masses of the nuclei are obtained from a macro-microscopic mode…
We present a selection of the first results obtained in a comprehensive calculation of ground state properties of even-even superheavy nuclei in the region of 96 < Z < 136 and 118 < N < 320 from the Quark-Meson-Coupling model (QMC). Ground state binding energies, the neutron and proton number dependence of quadrupole deformations and Q$_α$ values are reported for even-even nuclei with 100 < Z < 136 and compared with available experimental data and predictions of macro-microscopic models. Predictions of properties of nuclei, including Q$_α$ values, relevant for planning future experiments are p…
Systematic calculations of fission barriers allowing for triaxial deformation are performed for even-even superheavy nuclei with charge number $Z=112-120$ using three classes of covariant density functional models. The softness of nuclei in the triaxial plane leads to an emergence of several competing fission pathes in the region of the inner fission barrier in some of these nuclei. The outer fission barriers are considerably affected by triaxiality and octupole deformation. General trends of the evolution of the inner and the outer fission barrier heights are discussed as a function of the pa…
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 …
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…
Configuration-constrained calculations of potential-energy surfaces in even-even superheavy nuclei reveal systematically the existence at low excitation energies of multi-quasiparticle states with deformed axially symmetric shapes and large angular momenta. These results indicate the prevalence of long-lived, multi-quasiparticle isomers. In a quantal system, the ground state is usually more stable than the excited states. In contrast, in superheavy nuclei the multi-qausiparticle excitations decrease the probability for both fission and $α$ decay, implying enhanced stability. Hence, the systema…
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 $…
Half-lives of beta+ decay and electron capture are studied in some selected superheavy nuclei produced in hot fusion reactions, namely, 290Fl, 293Mc, 294Lv, and 295Ts. The nuclear structure is described microscopically from deformed self-consistent Skyrme Hartree-Fock mean-field calculations that include pairing correlations. The sensitivity of the half-lives to deformation and to the QEC energies, which are still not determined experimentally, are studied. The results are compared with phenomenological alpha-decay half-lives, showing that the latter decay mode is dominant in this mass region.
The competition between alpha- and beta+/EC-decay modes is studied systematically in nuclei along the alpha-decay chains following the synthesis of superheavy nuclei with Z = 119 and Z = 120. A microscopic approach based on deformed self-consistent Hartree-Fock mean-field calculations with Skyrme forces and pairing correlations is used to describe the beta+ and electron capture weak decays, whereas the alpha-decay is estimated from existing phenomenological expressions. It is shown that alpha-decay is in most cases the dominant decay mode, but interesting instances are identified where the hal…
The triaxial-octupole Y$_{32}$ correlation in atomic nuclei has long been expected to exist but experimental evidence has not been clear. We find, in order to explain the very low-lying 2$^-$ bands in the transfermium mass region, that this exotic effect may manifest itself in superheavy elements. Favorable conditions for producing triaxial-octupole correlations are shown to be present in the deformed single-particle spectrum, which is further supported by quantitative Reflection Asymmetric Shell Model calculations. It is predicted that the strong nonaxial-octupole effect may persist up to the…
We investigate the structure of the potential energy surfaces of the superheavy nuclei 258Fm, 264Hs, (Z=112,N=166), (Z=114,N=184), and (Z=120,N=172) within the framework of self-consistent nuclear models, i.e. the Skyrme-Hartree-Fock approach and the relativistic mean-field model. We compare results obtained with one representative parametrisation of each model which is successful in describing superheavy nuclei. We find systematic changes as compared to the potential energy surfaces of heavy nuclei in the uranium region: there is no sufficiently stable fission isomer any more, the importance …
We have investigated properties of $α$-decay chains of recently produced superheavy elements Z=115 and Z=113 using the new Lagrangian model NL-SV1 with inclusion of the vector self-coupling of $ω$ meson in the framework of the relativistic mean-field theory. It is shown that the experimentally observed alpha-decay energies and half-lives are reproduced well by this Lagrangian model. Further calculations for the heavier elements with Z=117-125 show that these nuclei are superdeformed with a prolate shape in the ground state. A superdeformed shell-closure at Z=118 lends an additional binding and…
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…
