An extensive theoretical search for the proton magic number in the superheavy valley beyond $Z=$82 and corresponding neutron magic number after $N=$126 is carried out. For this we scanned a wide range of elements $Z=112-130$ and their isotopes. The well established non-relativistic Skryme-Hartree-Fock and Relativistic Mean Field formalisms with various force parameters are used. Based on the calculated systematics of pairing gap, two neutron separation energy and the shell correction energy for these nuclei, we find $Z=$120 as the next proton magic and N=172, 182/184, 208 and 258 the subsequent neutron magic numbers.
A semiempirical shell model mass equation applicable to superheavy elements up to Z = 126 is presented and shown to have a high predictive power. The equation is applied to the recently discovered superheavy nuclei Z = 118, A = 293 and Z = 114, A = 289 and their decay products.
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.
We have explored the occurrence of the spherical shell closures for superheavy nuclei in the framework of the relativistic Hartree-Fock-Bogoliubov (RHFB) theory. Shell effects are characterized in terms of two-nucleon gaps $δ_{2n(p)}$. Although the results depend slightly on the effective Lagrangians used, the general set of magic numbers beyond $^{208}$Pb are predicted to be $Z = 120$, $138$ for protons and $N = 172$, 184, 228 and 258 for neutrons, respectively. Specifically the RHFB calculations favor the nuclide $^{304}$120 as the next spherical doubly magic one beyond $^{208}$Pb. Shell eff…
Systematic alpha-nucleus folding potentials are used to analyze alpha-decay half-lives of superheavy nuclei. Preformation factors of about several per cent are found for all nuclei under study. The systematic behavior of the preformation factors and the volume integrals of the potentials allows to predict alpha-decay energies and half-lives for unknown nuclei. Shell closures can be determined from measured alpha-decay energies using the discontinuity of the volume integral at shell closures. For the first time a double shell closure is predicted for Z_magic = 132, N_magic = 194, and A_magic = …
The magic proton and neutron numbers are searched in the superheavy region with proton number $Z$=100 - 140 and neutron number $N$= ($Z$+30) - (2$Z$+32) by the relativistic continuum Hartree-Bogoliubov (RCHB) theory with interactions NL1, NL3, NLSH, TM1, TW99, DD-ME1, PK1, and PK1R. Based on the two-nucleon separation energies $S_{2p}$ and $S_{2n}$, the two-nucleon gaps $δ_{2p}$ and $δ_{2n}$, the shell correction energies $E_{shell}^{p}$ and $E_{shell}^{n}$, the pairing energies $E_{pair}^{p}$ and $E_{pair}^{n}$, and the pairing gaps $Δ_{p}$ and $Δ_{n}$, $Z$=120, 132, and 138 and $N$=172, 184,…
Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond Z=82 and N=126 within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as spherical doubly magic superheavy nuclei, whereas N=1…
The ground state bulk properties such as binding energy, root-mean-square radius, pairing energy, nuclear density distributions, and single-particle energies are calculated for the isotopic chain of Ca, Sn, Pb, and Z = 120 nuclei. The relativistic mean-field with recently developed G3, IOPB-1, and Relativistic-Hartree-Bogoliubov with density-dependent DD-ME1 and DD-ME2 parameter sets are used in the present analysis. The respective shifts over the isotopic chain for the structural observables and surface property like symmetry energy are also estimated using a three-point method, which is cruc…
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.
In this paper, we have calculated the $α$-decay half-lives of superheavy nuclei with $106 \leq Z \leq 126$ and a neutron number of $150 \leq N \leq 200$ within proximity potentials and deformed-spherical Coulomb potentials by using $WS4$ $α$-decay energy and the semi-classical Wentzel-Kramers-Brillouin approximation for penetration probability. Besides, we have included the preformation factor within the cluster-formation model. We have investigated magic numbers and submagic numbers in the mentioned region; with high probability 162, 178, and 184 are predicted as neutron magic numbers. We als…
The $α$-decay chain of $^{293}$118, first proposed in the Berkeley cold fusion experiment $^{208}$Pb($^{86}$Kr,1n) and now retracted, is calculated by using the preformed cluster model (PCM) of one of us (RKG). Also, the possible branchings of $α$-particles to heavier cluster decays of all the parents in this chain are calculated for the first time. The calculated Q-values, penetrabilities and preformation factors for $α$-decays suggest that the $^{285}$114 nucleus with Z=114, N=171 is a magic nucleus, either due to the magicity of Z=114, or of N=172 or of both. The N=172 is proposed to be a m…
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…
This paper refers to an another attempt to search for spherical double shell closure nu- clei beyond Z=82, N=126. All calculations and results are based on a newly developed approach entitled as simple effective interaction. Our results predict the combination of magic nucleus occurs at N=182 (Z=114,120,126). All possible evidences for the oc- currence of magic nuclei are discussed systematically. And, the obtained results for all observables compared with the relativistic mean field theory for NL3 parameter.
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 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.
Beyond uranium heavy elements rapidly become increasingly unstable with respect to spontaneous fission as the proton number Z increases, because of the disruptive effect of the long-range Coulomb force. However, in the region just beyond Z = 100 magic proton and neutron numbers and the associated shell structure enhances nuclear stability sufficiently to allow observation of additional nuclei. Some thirty years ago it was speculated that an island of spherical, relatively stable superheavy nuclei would exist near the next doubly magic proton-neutron combination beyond 208:Pb, that is, at proto…
Quantum stabilization of superheavy elements is quantified in terms of the shell-correction energy. We compute the shell correction using self-consistent nuclear models: the non-relativistic Skyrme-Hartree-Fock approach and the relativistic mean-field model, for a number of parametrizations. All the forces applied predict a broad valley of shell stabilization around Z=120 and N=172-184. We also predict two broad regions of shell stabilization in hyperheavy elements with N approx 258 and N approx 308. Due to the large single-particle level density, shell corrections in the superheavy elements d…
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.
The influence of the central depression in the density distribution of spherical superheavy nuclei on the shell structure is studied within the relativistic mean field theory. Large depression leads to the shell gaps at the proton Z=120 and neutron N=172 numbers, while flatter density distribution favors N=184 for neutrons and leads to the appearance of a Z=126 shell gap and to the decrease of the size of the Z=120 shell gap. The correlations between the magic shell gaps and the magnitude of central depression are discussed for relativistic and non-relativistic mean field theories.
A highly extrapolatable semiempirical shell model mass equation applicable to translead elements up to Z=126 is presented. The equation is applied to the recently discovered superheavy nuclei with Z=118 and A=293 and with Z=114 and A=289 and their decay products.
We present the first attempt of systematically investigating the effects of shell correction energy for a dynamical process, which includes fusion, fusion-fission and quasi-fission processes. In the superheavy mass region, for the fusion process, shell correction energy plays a very important role and enhances the fusion probability when the colliding partner has a strong shell structure. By analyzing the trajectory in three-dimensional coordinate space with the Langevin equation, we reveal the mechanism of the enhancement of the fusion probability caused by `cold fusion valleys'. The temperat…
We study the extrapolation of nuclear shell structure to the region of superheavy nuclei in self-consistent mean-field models -- the Skyrme-Hartree-Fock approach and the relativistic mean-field model -- using a large number of parameterizations. Results obtained with the Folded-Yukawa potential are shown for comparison. We focus on differences in the isospin dependence of the spin-orbit interaction and the effective mass between the models and their influence on single-particle spectra. While all relativistic models give a reasonable description of spin-orbit splittings, all non-relativistic m…
A recent paper [M. Rashdan, Phys. Rev. C 63, 044303 (2001)] introduces the new parameterization NL-RA1 of the relativistic mean-field model which is claimed to give a better description of nuclear properties than earlier ones. Using this model ^{298}114 is predicted to be a doubly-magic nucleus. As will be shown in this comment these findings are to be doubted as they are obtained with an unrealistic parameterization of the pairing interaction and neglecting ground-state deformation.
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 …
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.
The possibility of synthesizing a doubly magic superheavy nucleus, $^{298}114_{184}$, is investigated on the basis of fluctuation-dissipation dynamics. In order to synthesize this nucleus, we must generate more neutron-rich compound nuclei because of the neutron emissions from excited compound nuclei. The compound nucleus $^{304}114$ has two advantages to achieving a high survival probability. First, because of small neutron separation energy and rapid cooling, the shell correction energy recovers quickly. Secondly, owing to neutron emissions, the neutron number of the nucleus approaches that …
The shell structure of superheavy nuclei is investigated within various parametrizations of relativistic and nonrelativistic nuclear mean field models. The heaviest known even-even nucleus 264Hs is used as a benchmark to estimate the predictive value of the models. From that starting point, doubly magic spherical nuclei are searched in the region Z=110-140 and N=134-298. They are found at (Z=114, N=184), (Z=120, N=172), or at (Z=126, N=184), depending on the parametrization.
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 feasibility for the alpha decay and the heavy particle decay from the even-even superheavy (SH) nuclei with Z = 116-124 have been studied within the Coulomb and proximity potential model (CPPM). The Universal formula for cluster decay (UNIV) of Poenaru et al., the Universal Decay Law (UDL) and the Scaling Law of Horoi et al., has also been used for the evaluation of the decay half lives. A comparison of our predicted half lives with the values evaluated using these empirical formulas are in agreement with each other and hence CPPM could be considered as a unified model for alpha and cluste…
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, …
A fully systematic study of even and odd isotopes (281 $\leq$ A $\leq$ 380) of Z = 121 superheavy nuclei is presented in theoretical frameworks of Relativistic mean-field plus state dependent BCS approach and Macroscopic-Microscopic approach with triaxially deformed Nilson Strutinsky prescription. The ground state properties namely shell correction, binding energy, two- and one- proton and neutron separation energy, shape, deformation, density profile and the radius are estimated that show strong evidence for magicity in N = 164, 228. Central depletion in the charge density due to large repuls…
We present two tables of calculated masses of translead nuclei, for 351 nuclei with N from 94 to 126 and Z from 82 to 100, and for 1969 nuclei with N from 126 to 184 and Z from 82 to 126. The tables are calculated from a semiempirical shell-model mass equation based on Z = 126 as a proton magic number which seems to be highly extrapolatable inside shell regions. Useful separation and decay energies are given as well. Some properties of the calculated masses and applications to superheavy elements are indicated in the introduction.
We have carried out a study of superheavy nuclei in the framework of the Relativistic Mean-Field theory. Relativistic Hartree-Bogoliubov (RHB) calculations have been performed for nuclei with large proton and neutron numbers. A finite-range pairing force of Gogny type has been used in the RHB calculations. The ground-state properties of very heavy nuclei with atomic numbers Z=100-114 and neutron numbers N=154-190 have been obtained. The results show that in addition to N=184 the neutron numbers N=160 and N=166 exhibit an extra stability as compared to their neighbors. For the case of protons t…
Magic islands for extra-stable nuclei in the midst of the sea of fission-instability were predicted to be around Z=114, 124 or, 126 with N=184, and Z=120, with N=172. Whether these 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 an open question. Alpha-decay half lives of nuclei with 130 < Z < 100 have been calculated in a WKB framework using density-dependent M3Y interaction with Q-values from different mass formulae. The results are in excellent agreement with the experimental data. Fission survive…
The existence of bubble nuclei identified by the central depletion in nucleonic density is studied for the conventional magic N (Z) $=$ 8, 20, 28, 40, 50, 82, 126 isotones (isotopes) and recently speculated magic N $=$ 164, 184, 228 superheavy isotones. Many new bubble nuclei are predicted in all regions. Study of density profiles, form factor, single particle levels and depletion fraction (DF) across the periodic chart reveals that the central depletion is correlated to shell structure and occurs due to unoccupancy in s-orbit (2s, 3s, 4s) and inversion of (2s, 1d) and (3s, 1h) states in nucle…
This research article is a follow up of earlier work by M. Ikram et al., reported in International Journal of Modern Physics E {\bf{25}}, 1650103 (2016) wherein we searched for $Λ$ magic numbers in experimentally confirmed doubly magic nucleonic cores in light to heavy mass region (ie.$^{16}O - ^{208}Pb$) by injecting $Λ$'s into them. In present manuscript, working within the state-of-art relativistic mean field theory with inclusion of $ΛN$ and $ΛΛ$ interaction in hypernuclei using the predicted doubly magic nucleonic cores ie. $^{292}$120, $^{304}$120, $^{360}$132, $^{370}$132, $^{336}$138, …
Probable projectile-target combinations for the synthesis of superheavy element $^{302}$120 have been studied taking Coulomb and proximity potential as the interaction barrier. The probabilities of compound nucleus formation, PCN for the projectile-target combinations found in the cold reaction valley of $^{302}$120 are estimated. At energies near and above the Coulomb barrier, we have calculated the capture, fusion and evaporation residue cross sections for the reactions of all the probable projectile-target combinations so as to predict the most promising projectile-target combinations for t…
The impact of particle-vibration coupling and polarization effects due to deformation and time-odd mean fields on single-particle spectra is studied systematically in doubly magic nuclei from low mass $^{56}$Ni up to superheavy ones. Particle-vibration coupling is treated fully self-consistently within the framework of relativistic particle-vibration coupling model. Polarization effects due to deformation and time-odd mean field induced by odd particle are computed within covariant density functional theory. It has been found that among these contributions the coupling to vibrations makes a ma…
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 recently observed $α$-decay chains $^{293-294}117$ were produced by the fusion reactions with target $^{249}Bk$ and projectile $^{48}Ca$ at Dubna in Russia. The reported cross-sections for the mentioned reaction are $σ=0.5(+1.1,-0.4)$pb and $σ$=1.3(+1.5,-0.6)$pb$ at $E^{*}=35MeV$ and $E^{*}=39MeV$, respectively. The Q-values of $α$-decay and the half-lives $Log_{10}T^α_{1/2}$(s) are calculated for the $α$-decay chains of $^{293-294}117$ nuclei, within the framework of Isospin Cluster Model (ICM). In the ICM model the proximity energy is improved by using the isospin dependent radius of par…
We investigate outer crust compositions for a wide range of magnetic field strengths, up to $B\simeq 4\times10^{18}$ G, employing the latest experimental nuclear masses supplemented with various mass models. The essential effects of the magnetic field are twoholds: 1) Enhancement of electron fraction, which is connected to that of protons via the charge neutrality condition, due to the Landau-Rabi quantization of electron motion perpendicular to the field, namely, neutron-richness is suppressed for a given pressure. As a result, 2) nuclei can exist at higher pressures without dripping out neut…
A comparison of calculated and experimental Q_alpha values of superheavy even-even nuclei and a few selected odd-N nuclei is presented in the framework of the relativistic mean-field model with the parameterization NL-Z2. Blocking effects are found to be important for a proper description of Q_alpha of odd mass nuclei. The model gives a good overall description of the available experimental data. The mass and charge assignment of the recently measured decay chains from Dubna and Berkeley is in agreement with the predictions of the model. The analysis of the new data does not allow a final conc…
The Skyrme energy-density functional approach has been extended to study the massive heavy-ion fusion reactions. Based on the potential barrier obtained and the parameterized barrier distribution the fusion (capture) excitation functions of a lot of heavy-ion fusion reactions are studied systematically. The average deviations of fusion cross sections at energies near and above the barriers from experimental data are less than 0.05 for 92% of 76 fusion reactions with $Z_1Z_2<1200$. For the massive fusion reactions, for example, the $^{238}$U-induced reactions and $^{48}$Ca+$^{208}$Pb the captur…
In present work, we systematically study the $α$ decay half-lives of 170 even-even nuclei with $60 \leqslant Z \leqslant 118$ within the two-potential approach while the $α$ decay preformation factor $P_α$ is obtained by the cluster-formation model. The calculated results can well reproduce the experimental data. In addition, we extend this model to predict the $α$ decay half-lives of 64 even-even nuclei with $104 \leqslant Z \leqslant 128$ whose $α$ decay is energetically allowed or observed but not yet quantified. For comparing, the two famous models i.e. SemFIS proposed by D. Poenaru ${et\ …
We investigate the cold fission of 252Cf within the two center shell model to compute the potential energy surface. The fission yields are estimated by using the semiclassical penetration approach. It turns out that the inner cold valley of the total potential energy is strongly connected with Z=50 magic number. The agreement with experimental values is very much improved only by considering mass and charge asymmetry degrees of freedom. Thus, indeed cold fission of 252Cf is a Sn-like radioactivity, related the other two "magic radioactivities", namely alpha-decay and heavy-cluster decay, calle…
Using two theoretical models (the post form finite range distorted wave Born approximation and the adiabatic model) we calculate the parallel momentum distribution of the charged core in the Coulomb breakup of Be isotopes on a heavy target at 100 MeV/u. We show that the full width at half maxima of the parallel momentum distribution can be used to study the breakdown of N = 8 magic number away from the valley of stability.
In the present work, we study α decay and proton emission half-lives within the modified Gamow-like model, which introduces the effects of the nucleus's deformation. The calculations show that it is necessary to consider the deformation in the calculation for nuclei far from the shell. Moreover, we use the improved model to predict the proton emission half-lives of the nuclei far from the shell. The calculation results indicate that our model is in good agreement with most models. Furthermore, the deformed Gamow-like model is used to find the following neutron magic number. This work is meanin…
Parameter-free deformation variables of the proxy-SU(3) symmetry in even-even actinide, superheavy and hyperheavy nuclei with Z=82-126, N=82-258
National Centre for Scientific Research “Demokritos”（德谟克利特国家科学研究中心）；Physical Research Laboratory（物理研究实验室）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）；Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering（霍里亚·胡卢贝伊核物理与核工程研发国家研究所）；National and Kapodistrian University of Athens（雅典国立卡波季斯特里安大学）；Bulgarian Academy of Sciences（保加利亚科学院）
