Effects of Various Deformation on the First Fission Barrier in Even-A N = 152 Isotones

The first(namely, inner) fission barriers for even-A N = 152 nuclei have been studied systematically in the framework of macroscopic-microscopic model by means of potential energy surface(PES) calculations in the threedimensional(β_(2, γ), β_4) deformation space. Their collective properties, such as ground-state deformations, are compared with previous calculations and available observations, showing a consistent trend. In addition, it has been found that the microscopic shell correction energy plays an important role on surviving fission in these N = 152 deformed shell nuclei. The inclusion of non-axial symmetric degree of freedom γ will pull the fission barrier down more significantly with respect to the calculation involving in hexadecapole deformation β_4. Furthermore, the calculated Woods-Saxon(WS) single particle levels indicate that the large microscopic shell correction energies due to low level densities may be responsible for such a reduction on the inner fission barrier.     

Calculations of the β-decay half-lives of neutron-deficient nuclei

In this work,β~+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation(QRPA),where neutron-neutron,proton-proton and neutron-proton(np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov(HFB) transformation.In addition to the pairing interaction,the Br¨uckner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions.Calculations are performed for even-even proton-rich isotopes ranging from Z =24 to Z =34.It is found that the np pairing interaction plays a significant role inβ-decay for some nuclei far from stability.Compared with other theoretical calculations,our calculations show good agreement with the available experimental data.Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference.     

Properties of nuclei at the third-minimum deformation

Potential-energy surfaces of heavy nuclei in the Ra-Th region are calculated by the macroscopic-microscopic method using the modified oscillator potential. A rather large region of nuclei with a third minimum along the fission trajectory is found. This minimum appears at a very large quadrupole deformation, ε₂ ∼ 0.9, and has a stable octupole deformation with ε₃ ∼ 0.2. It is found that in addition to the deformation parameters ε₂, ε₃, ε₄ and ε₅ it is important to include also ε₆. Particular attention is paid to the Th-isotopes, for which experimental evidence for the existence of a third minimum in the fission barrier has been found. Properties like the moment of inertia, the decoupling parameter and the energy splitting between positive- and negative-parity rotational bands are studied.     

Potential energy surfaces and fission fragment mass yields of even-even superheavy nuclei

Potential energy surfaces and fission barriers of superheavy nuclei are analyzed in a macroscopic-microscopic model. The Lublin-Strasbourg Drop (LSD) model 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 is utilized to determine barrier heights. A Fourier shape parametrization containing only three deformation parameters is shown to effectively reproduce the nuclear shapes of nuclei approaching fission. In addition, a non-axial degree of freedom is taken into account to better describe the structure of nuclei around the ground state and in the saddle region. In addition to the symmetric fission valley, a new highly asymmetric fission mode is predicted in most superheavy nuclei. The fission fragment mass distributions of the considered nuclei are obtained by solving 3D Langevin equations.     

Semiempirical atomic mass formula

An atomic mass formula based on the liquid-drop model with shell and deformation energies determined from the Nilsson model and BCS pairing energy has been adjusted simultaneously to ground-state binding energies and to fission barrier heights. A short table of calculated values is included, and additional calculations are available.     

Study of Fission Barrier Heights of Uranium Isotopes by the Macroscopic-Microscopic Method

Potential energy surfaces of uranium nuclei in the range of mass numbers 229 through 244 are investigated in the framework of the macroscopic-microscopic model and the heights of static fission barriers are obtained in terms of a double-humped structure. The macroscopic part of the nuclear energy is calculated according to Lublin-Strasbourg-drop (LSD) model. Shell and pairing corrections as the microscopic part are calculated with a folded-Yukawa single-particle potential. The calculation is carried out in a five-dimensional parameter space of the generalized Lawrence shapes. In order to extract saddle points on the potential energy surface, a new algorithm which can effectively find an optimal fission path leading from the ground state to the scission point is developed. The comparison of our results with available experimental data and others' theoretical results confirms the reliability of our calculations.     

On the stability of superheavy nuclei against fission

We use the methods, which we developed in a previous paper, for the calculation of potential energy surfaces and lifetimes for superheavy nuclei. Two regions of relative stability against spontaneous fission, which are connected with the magic proton numbersZ=114 andZ=164 and which will both become accessible for experiments in the near future, are discussed. Especially the nuclei aroundZ=164 are investigated here at the first time. The lifetimes for α-decay are also estimated and appear to be long enough for experimental work. Furthermore, we have investigated the dependence of the fission barrier on the level-distributions at the fermi-surface. At the end we discuss the difficulties in the usual microscopic calculations for the fission process and show a way to overcome the limitations and inconsistencies of the usually used Strutinsky-type calculations.

     

Possible α decay chains from isotopes of superheavy element 120

We investigate the α decay half-lives of even-Z superheavy nuclei up to Z = 120 by the modified two-potential approach. Based on the density-dependent cluster model, the α daughter potential is obtained from the double folding integral, taking into account the effect of nuclear deformation. A reasonable formula related with the fissility parameter and the fission barrier height, is applied to evaluate the spontaneous fission half-lives of the studied nuclei. After the performance of the competition between α decay and spontaneous fission, possible α decay chains are proposed in pursuit of being useful for the future experiment.     

Microscopic description of fission in neutron-rich plutonium isotopes with the Gogny-D1M energy density functional

The most recent parametrization D1M of the Gogny energy density functional is used to describe fission in the isotopes ^232-280Pu . We resort to the methodology introduced in our previous studies (Phys. Rev. C 88, 054325 (2013) and Phys. Rev. C 89, 054310 (2014)) to compute the fission paths, collective masses and zero point quantum corrections within the Hartree-Fock-Bogoliubov framework. The systematics of the spontaneous fission half-lives t _SF , masses and charges of the fragments in plutonium isotopes is analyzed and compared with available experimental data. We also pay attention to isomeric states, the deformation properties of the fragments as well as to the competition between the spontaneous fission and α-decay modes. The impact of pairing correlations on the predicted t _SF values is demonstrated with the help of calculations for ^232–280Pu, in which the pairing strengths of the Gogny-D1M energy density functional are modified by 5% and 10%, respectively. We further validate the use of the D1M parametrization through the discussion of the half-lives in ^242–262Fm. Our calculations corroborate that, though the uncertainties in the absolute values of physical observables are large, the Gogny-D1M Hartree-Fock-Bogoliubov framework still reproduces the trends with mass and/or neutron numbers and therefore represents a reasonable starting point to describe fission in heavy nuclear systems from a microscopic point of view.     

Formation of heavy compound nuclei,their survival,and correlation with longtime-scale fission

Fusion of two massive nuclei with formation of a superheavy compound nucleus is driven by the potential energy gradient, as follows from the analysis of nuclear reaction cross sections. The conservative energy of the system is deduced in a simple approximation using regularized nuclear mass and interaction barrier values. Different reactions for the synthesis of Z = 110−118 nuclei are compared and favorable conditions are found for fusion of the stable W-Pt isotopes with radioactive fission fragment projectiles, like ⁹⁴Kr or ¹⁰⁰Sr. Thus, the cold-fusion method can be extended for a synthesis of elements with Z > 113. Survival of the evaporation residue is defined by the neutron-to-fission probability ratio and by the successful emission of gammas at the final step of the reaction. Numerical estimates are presented. Fixation of evaporation residue products must correlate with longtime-scale fission, and available experimental results are discussed. The text was submitted by the authors in English.     

基于相对论平均场理论对超重核冷熔合反应截面的研究

在形变约束的相对论平均场理论框架下计算了合成Z=102—118元素的(可能)冷熔合反应中复合核及蒸发一或两个中子剩余核的位能曲面,得到了复合核和剩余核平衡点和鞍点的性质、静态裂变垒高度和冷熔合反应的最佳入射能;利用壳修正和对修正方法计算了平衡点和鞍点的壳修正能、对修正能和微观能.利用由此得到的壳结构信息,用简单的熔合蒸发唯象模型计算了相应反应的冷熔合截面.结果发现,TM1参数提供的结构性质给出了与实验接近的反应截面.     

On the Possibility of Delayed Fission of Nuclei in the Region of Superheavy Transuranium Elements

Delayed fission of atomic nuclei was discovered in 1966. It is observed primarily in odd–odd nuclei for which the energy released in beta decay (K capture) is commensurate with the fission barrier in the nucleus formed after this process. Delayed fission was found in four nuclide regions: neutrondeficient isotopes in the Pb region, neutron-deficient isotopes in the Ac and Pa regions, and neutrondeficient and neutron-rich isotopes of transuranium elements. In the wake of investigations into the properties of isotopes of superheavy transuranium elements, numerous calculations were performed in order to determine the masses of new nuclei and to predict their decay properties. Explored and predicted properties of superheavy-element nuclides, where, for some odd–odd nuclei of transuranium elements, the K-capture energy is commensurate with the fission barriers in the corresponding daughter nuclei formed after K capture, are analyzed. Estimates of the delayed-fission probability are presented for some isotopes of elements whose charge number Z ranges from 103 to 107.     

Microscopic calculations of fission barriers and critical angular momenta for excited heavy nuclear systems

An extended version of Strutinsky's macro-microscopic method is used to calculate effective potential energies for rotating, excited heavy compound nuclei undergoing fission. Nuclear deformation is parameterized in terms of Lawrence's family of shapes. A two-center single-particle potential corresponding to these shapes is employed, with BCS pairing added. Statistical excitation is introduced by temperature-dependent occupation of (quasi-) particle energy levels. We calculate shell corrections to the energy, the free energy and the entropy as functions of deformation and temperature. The associated average quantities are derived from a temperature-dependent liquid drop model. The resulting static deformation energy is augmented by the rotational energy to yield the isothermal effective potential energy as a function of deformation, temperature and angular momentum. Moments of inertia are obtained from the adiabatic cranking model with temperature-dependent pairing included.We have also calculated the effective potential for constant entropy rather than constant temperature. Although this isentropic process physically is more appropriate than the isothermal process, it has not been treated before. For the same amount of excitation energy in the spherical state of the compound nucleus, the isentropic barriers turn out higher than the isothermal ones. For both processes we have extracted the critical angular momentum (defined as the one for which the barrier approximately vanishes) as a function of excitation. Our model is applied to the super-heavy nuclei ²⁷⁰110, ²⁷⁸110, ²⁹⁸114, ²⁹²118 and ³²²128, which have been tried to form in krypton and argon induced heavy ion reactions.     

Macroscopic-microscopic calculations of fission potential surface of uranium isotopes in the three quadratic surfaces parametrization

Five-dimensional (5D) fission potential energy surfaces (PES) for uranium nuclei are investigated based on the macroscopic-microscopic Lublin-Strasbourg drop model in the three-quadratic-surface parametrization, and the heights of static fission barriers are obtained. Asymmetric and symmetric fission paths are presented on the 5D PES of ²³⁶U for different nuclear shapes. The calculated barrier heights, E_A and E_B, are quite consistent with the experimental data for all even-even nuclei of uranium isotopes, from ²³⁰U to ²⁴⁴U.     

Fission of medium mass elements induced by 126 MeV 14N ions

Ni, Se, Mo, Ag, Ho and Au targets were bombarded by 126 MeV ¹⁴N ions in order to study compound nucleus fission. The large angular momentum brought in by the projectile implies much greater fission probabilities than those obtained when the same compound nuclei are created with light projectiles. We employed two surface-barrier detectors. The results obtained are fission cross sections, angular correlations and kinetic energy and mass distributions. Fissilities are found to decrease exponentially with the ratio Z²/A of the fissioning nucleus until Z²/A = 19 (molybdenum) and then to increase again for lower Z²/A. The calculations of fissilities performed with the fission barrier of Myers and Swiatecki, and including angular momentum effects in evaporation-fission competition, gives the same variation of fissilities as the experimental one, but the results obtained are lower than the experimental values. The total kinetic energies measured are higher than the predictions of the liquid drop model by around 10 MeV (Nix). The shapes of the mass distributions indicate that the value of x_BG (Businaro-Gallone point) is lower than 0.4 (silver).     

Half lives of heaviest nuclei with Woods-Saxon potential

Adapting the realistic single-particle Woods-Saxon potential the half-lives of elements withZ≧104 are estimated. Spontaneous fission, alpha decay and electron capture processes are treated. Alleven-even, odd-even andodd-odd nuclei are considered. In calculations of spontaneous fission half lives phenomenological mass parameters are applied. The results allow to estimate hindrance factors for odd systems. As compared to calculations with Nilsson model and microscopic mass parameters, present results for spontaneous fission half lives are 3–5 orders of magnitude higher in the case of heaviest nuclei (Z≧107).     

Basic distinctions between cold- and hot-fusion reactions in the synthesis of superheavy elements

Superheavy elements (SHE) of charge number in the range of Z = 106–112 were synthesized in so-called cold-fusion reactions. The smallness of the excitation energy of compound nuclei is the main advantage of cold-fusion reactions. However, the synthesis of SHEs of charge number in the region of Z ≥ 112 is strongly complicated in cold-fusion reactions by a sharp decrease in the cross section of a compound nucleus formation in the entrance channel because of superiority of quasifission in the competition with complete fusion. Two favorable circumstances contributed to the success of the experiments aimed at the synthesis of the Z = 113–118 elements and performed at the Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research: large cross sections for the production of a compound nucleus, which are characteristic of hot-fusion reactions, and an increase in the fission barrier for nuclei toward the stability island. The factor that complicates the formation of a compound nucleus in cold-fusion reactions is discussed.     

Systematic study of the heavy-ion fusion barrier in the frozen approximation

The height and position of the fusion barrier for the real part of the interaction potential between two colliding nuclei are studied as a function of the Coulomb strength. The calculations are performed in the framework of the spherical constrained HF + BCS formalism using the frozen approximation. The effective Skyrme type force SKa is used. The model contains no free parameters. For the height of the fusion barrier good agreement is found with the values obtained using the empirical Bass potential that is known to reproduce well the data for many nuclear systems. In contrast, the recently observed apparent rise of the fusion barrier (‘extra-extra-push’) for very massive nuclear systems with a product of nuclear chargesZ ₁ xZ ₂ above 1600 cannot be reproduced. We also give estimations for the overlap of the mass densities of both colliding nuclei at the fusion barrier distance.     

A dynamic analysis of spontaneous-fission half-lives

Spontaneous-fission half-lives of even-even heavy nuclei (Z = 92–110) are calculated without any adjustable parameters. The fission-barrier penetration is treated as a one-dimensional problem in multidimensional deformation space. Deformations of multipolarities 2, 3, 4, 5 and 6 (describing elongated, necked and reflection asymmetric shapes of a nucle'us) are considered. The potential energy is calculated by the macroscopic-microscopic method and the inertia tensor by the cranking method. The action integral is minimized by variational procedures.The barrier heights are reproduced with an accuracy better than 1.5 MeV and the half-lives to within a factor of about 50, on the average.     

Decay time characteristics of the U-like excited nuclei

The unified energy dependence of the induced fission times obtained by the crystal blocking technique for heavy nuclei with Z=91–94 in the range of initial excitation energy from 5 to 250 MeV was analyzed. It was demonstrated that, for excitation energies of the investigated heavy fissionable nuclei up to 60–70 MeV, the fission times can be described in the framework of the statistical theory of nuclear reactions taking into account the double-humped structure of the fission barrier and the lifetimes of both classes of excited nuclear states realized in the first and second potential wells. However, for excitation energies above 70 MeV, there is a need to consider the dynamical effects in the fission channel.