Multidimensional Deformation Space Research Articles

Revisiting the island of hexadecapole-deformation nuclei in the A ≈ 150 mass region: focusing on the model application to nuclear shapes and masses

Based on the potential-energy-surface calculation, the impact of different deformation degrees of freedom on a single-particle structure and binding energies in nuclei around 152Nd, located on one of the hexadecapole-deformation islands, is analyzed in a multi-dimensional deformation space. Various energy maps, curves and tables are presented to indicate nuclear properties. The calculated equilibrium deformations and binding energies with different potential parameters are compared with experimental data and other theories. It is found that the inclusion of the hexadecapole deformations, especially the axial one, can improve the theoretical description of both nuclear shapes and masses. In addition, our calculated potential-energy curve shows that a critical deformation-point, β 2 ≈ 0.4, exists—the triaxial (hexadecapole) deformation effect can be neglectable but the hexadecapole (triaxial) one plays an important role before (after) such a critical point.

Fission hindrances in transfermium nuclei

Very heavy nuclei owe their stability against spontaneous fission to quantum shell effects, which depend on the local density of single-particle states. The height but also the width and the structure of the barrier in multi-dimensional deformation space determine the fission half-lives. Other effects come into play, such as the conservation of quantum numbers and superfluidity or stiffness of the system in the fission process. This is why odd nuclei have longer fission partial half-lives with respect to their even neighbours and also why multi-quasi-particle states, such as high-K states, are thought to be more stable against fission than the ground state. We will report here on two different fission studies carried out with the GABRIELA detector array at the focal plane of the recoil separator SHELS. The first study concerns the fission properties of 253Rf, the most neutron deficient Rf isotope known to date. The second study focusses on a new measurement of the fission hindrance of the known 8- isomer in 254No.

Macroscopic–microscopic calculations of the ground state properties of Z = 120 isotopes and their α-decay chains

One of the substantial successes achieved in nuclear physics in the last two decades was the synthesis of dozens of isotopes of new elements up to [Formula: see text]Og, which closed the seventh row of the periodic table and inspired the ambition of adding more elements. This work aims to study extensively the ground state structure and decay properties of proposed [Formula: see text] isotopes. We employed Macroscopic–microscopic scheme based on the Skyrme energy density functional, the Woods–Saxon single-particle potential and Strutinsky’s method to find the structure properties, in a multidimensional deformation space. The same nucleon–nucleon potential is used to find the [Formula: see text]-decay half-life, within the Preformed Cluster Model. For 45 [Formula: see text]120 isotopes, the total energy surfaces, ground state masses, binding energy, deformations and fissionability are determined. The [Formula: see text]-values of the different competing decays and [Formula: see text]-decay half-lives are investigated based on the obtained structure. The results indicate the [Formula: see text]120 isotopes to be the most bound among the studied isotopes. The smallest fission barriers are indicated for the [Formula: see text]120 isotopes. The [Formula: see text]120 isotopes showed the longer half-lives against [Formula: see text]-decay, with an order of [Formula: see text]. The longest half-lives are estimated for the [Formula: see text]120 ([Formula: see text] and [Formula: see text]120 ([Formula: see text] isotopes. The longest full decay chain ending with the stable [Formula: see text]Pb nucleus is anticipated for the [Formula: see text]120 isotope. The shortest decay chain of [Formula: see text]120 terminates after three [Formula: see text]-decays by the spontaneous fission of [Formula: see text]Fl.

Microscopic study of higher-order deformation effects on the ground states of superheavy nuclei around 270Hs * *Supporteds by the National Key R&D Program of China (2018YFA0404402), the National Natural Science Foundation of China (11525524, 12070131001, 12047503, 11975237, 11961141004), the Key Research Program of Frontier Sciences of Chinese Academy of Sciences (QYZDB-SSWSYS013), the Strategic Priority Research Program of Chinese Academy of

We investigate the effects of higher-order deformations ( and 10) on the ground state properties of superheavy nuclei (SHN) near the doubly magic deformed nucleus using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model with five effective interactions: PC-PK1, PK1, NL3*, DD-ME2, and PKDD. The doubly magic properties of include large energy gaps at and in the single-particle spectra. By investigating the binding energies and single-particle levels of in the multidimensional deformation space, we find that, among these higher-order deformations, the deformation has the greatest impact on the binding energy and influences the shell gaps considerably. Similar conclusions hold for other SHN near . Our calculations demonstrate that the deformation must be considered when studying SHN using MDC-RMF.

Energy sharing based on microscopic level densities

The transformation of a moderately excited heavy nucleus into two excited fission fragments is modeled as a strongly damped evolution of the nuclear shape. The resulting Brownian motion in the multi-dimensional deformation space is guided by the shape-dependent level density which has been calculated microscopically for each of nearly ten million shapes (given in the three-quadratic-surfaces parametrization) by using a previously developed combinatorial method that employs the same single-particle levels as those used for the calculation of the pairing and shell contributions to the five-dimensional macroscopic-microscopic potential-energy surface. The stochastic shape evolution is followed until a small critical neck radius is reached, at which point the mass, charge, and shape of the two proto-fragments are extracted. The available excitation energy is divided statistically on the basis of the microscopic level densities associated with the two distorted fragments. Specific fragment structure features may cause the distribution of the energy disvision to deviate significantly from expectations based on a Fermi-gas level density. After their formation at scission, the initially distorted fragments are being accelerated by their mutual Coulomb repulsion as their shapes relax to their equilibrium forms. The associated distortion energy is converted to additional excitation energy in the fully accelerated fragments. These subsequently undergo sequential neutron evaporation which is calculated using again the appropriate microscopic level densities. The resulting dependence of the mean neutron multiplicity on the fragment mass, as well as the dependence of on the initial excitation energy of the fissioning compound nucleus, exhibit features that are similar to the experimentally observed behavior, suggesting that the microscopic energy sharing mechanism plays an important role in low-energy fission.

Ground-state and stability properties of [formula omitted] isotopes based on semi-microscopic calculations

In this study, we present theoretical predictions on the stability properties of the yet unknown Og118276−293,295−308 isotopes using the Skyrme-SLy4 nucleon–nucleon interaction and the deformed Woods–Saxon single-particle potential in a semi-microscopic approach. The ground-state masses, binding energy, deformations and fission barriers are calculated from the total energy surfaces produced in a multidimensional deformation space using the dynamical differential evolution optimization method. Besides, the Q-values of the different decay modes and the nucleon separation energies for each isotope, and its α-decay (Tα) and spontaneous fission half-lives are also calculated. Our study revealed the Og290−296 elements to be the most bound Oganesson isotopes, among which 302,304,306Og elements are predicted to be spherical nuclei, and 299,300,301,303,305Og elements are shown to be almost spherical. The predicted ground-state and decay properties successfully reproduced the available data of the solely known Oganesson isotope 294Og. In addition to the principle α-decay modes, we studied the rival decay modes that challenge the stability of nuclei in the superheavy regions, namely the electron capture β+ decays and the spontaneous fission. An overall oscillating increasing behavior of Tα with the mass number is obtained, which obviously reverses the hesitating decreasing behavior of Qα and follows increasing trend of the corresponding change in the neutron-skin thickness after α-decays. The Og291,294−296,299−302 isotopes are expected to have relatively long half-lives, Tα≈ 1–45 ms, while 295Og is found to have the longest half-life between the considered nuclei. The Og291−300 isotopes exhibited relatively high fission barriers and small branching ratios for their spontaneous fission modes.

Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei: systematic investigation of the triaxiality effect on the fission barrier**Supported by National Natural Science Foundation of China (11675148, 11505157), the Project of Youth Backbone Teachers of Colleges and Universities of Henan Province (2017GGJS008), the Foundation and Advanced Technology Research Program of Henan Province (162300410222), the Outstanding Young Talent Research Fund

Static fission barriers for 95 even-even transuranium nuclei with charge number Z = 94–118 have been systematically investigated by means of pairing self-consistent Woods-Saxon-Strutinsky calculations using the potential energy surface approach in multidimensional (β2, γ, β4) deformation space. Taking the heavier 252Cf nucleus (with the available fission barrier from experiment) as an example, the formation of the fission barrier and the influence of macroscopic, shell and pairing correction energies on it are analyzed. The results of the present calculated β2 values and barrier heights are compared with previous calculations and available experiments. The role of triaxiality in the region of the first saddle is discussed. It is found that the second fission barrier is also considerably affected by the triaxial deformation degree of freedom in some nuclei (e.g., the Z=112–118 isotopes). Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths as a function of the nucleon numbers are investigated. In addition, the effects of Woods-Saxon potential parameter modifications (e.g., the strength of the spin-orbit coupling and the nuclear surface diffuseness) on the fission barrier are briefly discussed.

Sensitivity of the nuclear deformability and fission barriers to the equation of state

The model-dependent analysis of the fission data impacts the extracted fission-related quantities, which are not directly observables, such as the super- and hyperdeformed isomeric states and their energies. We investigated the model dependence of the deformability of a nucleus and its fission barriers on the nuclear equation of state. Within the microscopic–macroscopic model based on a large number of Skyrme nucleon–nucleon interactions, the total energy surfaces and the double-humped fission barrier of 230Th are calculated in a multidimensional deformation space. In addition to the ground-state (GS) and the superdeformed (SD) minima, all the investigated forces yielded a hyperdeformed (HD) minimum. The contour map of the shell-plus-pairing energy clearly displayed the three minima. We found that the GS binding energy and the deformation energy of the different deformation modes along the fission path increase with the incompressibility coefficient K0, while the fission barrier heights and the excitation energies of the SD and HD modes decrease with it. Conversely, the surface-energy coefficient asurf, the symmetry-energy, and its density-slope parameter decrease the GS energy and the deformation energies, but increase the fission barrier heights and the excitation energies. The obtained deformation parameters of the different deformation modes exhibit almost independence on K0, and on the symmetry-energy and its density-slope. The principle deformation parameters of the SD and HD isomeric states tend to decrease with asurf.

Nonaxial hexadecapole deformation effects on the fission barrier

Fission barrier of the heavy nucleus [Formula: see text]Cf is analyzed in a multi-dimensional deformation space. This space includes two quadrupole ([Formula: see text]) and three hexadecapole deformation ([Formula: see text]) parameters. The analysis is performed within an unpaired macroscopic–microscopic approach. Special attention is given to the effects of the axial and non-axial hexadecapole deformation shapes. It is found that the inclusion of the nonaxial hexadecapole shapes does not change the fission barrier heights, so it should be sufficient to minimize the energy in only one degree of freedom in the hexadecapole space [Formula: see text]. The role of hexadecapole deformation parameters is also discussed on the Lublin–Strasbourg drop (LSD) macroscopic and the Strutinsky shell energies.

Structural properties of heavy and superheavy nuclei in a semi-microscopic approach

The structure of some heavy and superheavy nuclei with [Formula: see text] and [Formula: see text] is studied using a semi-microscopic model. In this approach, the macroscopic energy part of the total energy of a nucleus is obtained from the Skyrme nucleon–nucleon interaction in the semi-classical extended Thomas–Fermi approach. The microscopic shell-plus pairing correction energies are calculated in Strutinsky’s approach. Within this semi-microscopic approach, the total energy surfaces are investigated in multidimensional deformation space. For each nucleus, the model predictions for the binding energy, deformation energy, the deformation parameters and comparison with other theoretical models are presented. The proposed model shows a significant consistency with other models, and it is found to be successful in reproducing the structural properties of nuclei in heavy and superheavy region.

Isotopic fission fragment distributions as a deep probe to fusion-fission dynamics

During the fission process, the atomic nucleus deforms and elongates up to the two fragments inception and their final separation at the scission deformation. The evolution of the nucleus energy with deformation defines a potential energy landscape in the multidimensional deformation space. It is determined by the macroscopic properties of the nucleus, and is also strongly influenced by the single-particle structure of the nucleus, which modifies the macroscopic energy minima. The fission fragment distribution is a direct consequence of the deformation path the nucleus has encountered, and therefore is the most genuine experimental observation of the potential energy landscape of the deforming nucleus. Very asymmetric fusion-fission reactions at energy close to the Coulomb barrier, produce well-defined conditions of the compound nucleus formation, where processes such as quasi-fission, pre-equilibrium emission and incomplete fusion are negligible. In the same time, the excitation energy is sufficient to reduce significantly structural effects, and mostly the macroscopic part of the potential is responsible for the formation of the fission fragments. We use inverse kinematics combined with a spectrometer to select and identify the fission fragments produced in 238U+12C at a bombarding energy close to and well-above the Coulomb barrier. For the first time, the isotopic yields are measured over the complete atomic-number distribution, between Z=30 and Z=63. In the experimental set-up, it is also possible to identify transfer-induced reactions, which lead to low-energy fission

Estimating the reliability of revealing the fine structure in mass-kinetic energy distributions of nuclear reaction products

Theoretical descriptions of nuclear reactions such as fission and quasi-fission make it possible to represent the evolution of a nuclear system as a trajectory in a multidimensional deformation space. We propose a strategy for revealing images of such trajectories in the space of experimentally observed variables at a specified reliability level. The approach proposed is based on mathematical methods of morphological analysis of images and makes possible a detailed analysis of successive stages of nuclear reactions with a duration of about 10?20 s.

PROPERTIES OF HEAVIEST NUCLEI AT THE SADDLE-POINT CONFIGURATION

Properties of heaviest nuclei at their saddle point are studied in a multidimensional deformation space. The main attention is given to deformation and the shell correction to energy of the nuclei at this point. The analysis is performed within a macroscopic-microscopic approach. A 10-dimensional deformation space is used. A large number of about 300 even-even heavy and superheavy nuclei with proton number 98 ≤ Z ≤ 126 and neutron number 134 ≤ N ≤ 192 are considered. Detailed results are illustrated for nuclei of the element 120. A large shell correction (up to about 7 MeV) is found for these nuclei. For most of them, the correction is larger than the height of the barrier, itself, as the macroscopic contribution to this height is negative.

COLLINEAR CLUSTER TRIPARTITION IN FISSION OF ACTINIDE NUCLEI

A new ternary decay channel connected with magic constituents from Cf and U has been observed in recent experiments. It was called Collinear Cluster Tripartition (CCT) because the decay products fly apart almost collinearly. It is a decay of the fissioning system into the three fragments of comparable masses from the strongly elongated configuration. A total yield of the CCT events was found at the order of 10-3 per binary fission. The first theoretical description of the high lying energy minima on the potential energy landscape are presented for U and Cf . They have been obtained by the Strutinsky shell correction calculations in the multidimensional deformation space.

EFFECT OF NON-AXIAL DEFORMATIONS OF HIGHER MULTIPOLARITY ON THE FISSION-BARRIER HEIGHT OF HEAVIEST NUCLEI

The static fission-barrier height [Formula: see text] of heaviest nuclei is studied in a multidimensional deformation space. The main attention is given to the effect of the hexadecapole non-axial shapes on [Formula: see text]. The analysis is performed within a macroscopic-microscopic approach. A 10-dimensional deformation space is used. A large number of about 300 even-even heavy and superheavy nuclei with proton number 98 ≤ Z ≤ 126 and neutron number 134 ≤ N ≤ 192 are considered. It is found that the inclusion of the non-axial hexadecapole shapes lowers the barrier by up to about 1.5 MeV.

SIMPLE TOOL TO SEARCH QUASI-MAGIC STRUCTURES IN DEFORMED NUCLEI

Evaluation of shell effects in nuclei plays an important role in studying the nuclear structure. In the Strutinsky method the smooth energy of the nucleus is obtained by a folding procedure of the single-particle (s.p.) energy density in the s.p. energy space e. An alternative way of energy smoothing is obtained by folding the s.p. energy sum in the particle-number space [Formula: see text]. For non degenerated s.p. spectra both types of folding yield smooth energies which are close to each other. In the case of strongly degenerated spectra which appear at sphericity or in regions of shape isomers, the smooth energy obtained by the [Formula: see text]-folding is a couple of MeV larger than the traditional average Strutinsky energy. It is shown that this smooth energy difference can serve as a simple tool to search for magic or quasi-magic structures in the s.p. spectra, e.g. to find shape isomers in the multidimensional deformation space.

SADDLE-POINT SHELL EFFECTS OF HEAVIEST NUCLEI

The shell correction to the potential energy of heaviest nuclei is studied in a multidimensional deformation space. The correction is calculated at the saddle point of the nuclei and compared with that obtained at the equilibrium (ground state) point. Although generally much smaller than at the equilibrium point, the correction at the saddle point is still found to be large and significant. The analysis is performed within a macroscopic-microscopic approach.

MACROSCOPIC DYNAMICAL DESCRIPTION OF ROTATING Au + Au SYSTEM

Events with more than two heavy fragments have been abundantly observed in heavy-ion semi-peripheral (fission-like) reaction 197 Au +197 Au at 15 MeV/nucleon. This raised interesting questions about their origin and about the time-scale at which they occur. As a possible explanation of this process, the surface instability of the cylindrical neck that is formed along the path from contact to reseparation of the rotating Au + Au system is investigated in the present paper. For this purpose the Los Alamos finite-range macroscopic dynamical model was used. The calculations were performed at relatively high angular momenta, L = 100 to 300 ħ, for two types of dissipation mechanisms: two-body viscosity and one-body dissipation. Various initial nuclear deformations and initial kinetic energies in the fission direction were considered. The resulting dynamical evolution in the multidimensional deformation space always led to multifragment scission configurations suggesting that ternary and quaternary break-up can occur during the heavy-ion reaction studied.

DEFORMATIONS OF MULTIPOLARITY SIX AT THE SADDLE POINT OF HEAVIEST NUCLEI

Saddle-point configuration of heaviest nuclei is studied in a multidimensional deformation space. Main attention is given to the role of the deformation of multipolarity six of a general type, described by four independent parameters. The dependence of the potential energy of a superheavy nucleus on these parameters at the saddle-point configuration is illustrated. The analysis is performed within a macroscopic-microscopic approach.

ROLE OF THE ZERO-POINT CORRECTIONS IN FISSION DYNAMICS

The way of evaluating spontaneous fission half-lives of nuclei in a multidimensional deformation space is discussed. The cranking as well as the generator coordinate method were used to obtain the collective inertia tensor and the 'zero-point' corrections to the fission barriers. The fission probability was evaluated within the WKB approximation along the least-action trajectory to fission. The influence on the fission life-times of the dynamics in the pairing degrees of freedom as well as the effect of the higher even-multipolarity shape parameters and the role of the reflection asymmetry is examined.