Calculation Of Fission Barriers Research Articles

Influence of temperature-dependent shell corrections on the prediction of production cross sections for superheavy nuclei

In the framework of the dinuclear system model, we introduce a formula accounting for temperaturedependent shell corrections to assess their influence on the fission barrier calculations and, consequently, the survival probability of excited nuclei. Our approach considers the excitation energy’s effect on the fission barrier, a crucial aspect in determining the likelihood of a nucleus persisting. Leveraging experimental data with associated errors, we constrain the region of the shell correction damping factor. Employing this refined methodology, we predict the production cross sections for the novel superheavy element (SHE) with atomic number Z=119. Specifically, at the 54Cr(243Am,3n)294119 reaction, cross sections are anticipated to range between 3-27 femtobarns (fb), while for the 51V(248Cm,3n)296119 reaction, they are projected to span 21-180 fb. These predictions offer valuable insights into the formation dynamics of this exotic superheavy element.

New calculations of five-dimensional fission barriers for actinide nuclei

New calculations of fission barrier heights in a five-dimensional (5D) deformation space for actinide nuclei have been performed based on a macro-microscopic (MM) model. To calculate potential energy surface (PES), we use the 5D generalized Lawrence shape (GLS) realistic parameterization as the shape description, the Lublin-Strasbourg Drop (LSD) model for the macroscopic energy and the folded-Yukawa model as the single-particle potential. A method to use two-center oscillator basis in calculating Hamiltonian matrix on any kind of shape description was presented. For the pairing energy, we use the SBCS model. Finally, Strutinsky method is used to calculate the microscopic correction energy. To find the fission barriers and fission paths, some concepts, such as basins, edges and neighbors from geography, are extended to identify the topographical structures on the 5D PES and we assume that the fission path follows the line of steepest descent. The fission barriers and double-humped paths of U and Pu isotopes are calculated.

Fission barrier of actinides and superheavy nuclei: effect of pairing interaction

Systematic calculations of fission barriers for axial deformation are performed for even-even nuclei in actinides region of the nuclear chart and superheavy nuclei. These calculations were performed using relativistic Hartree-Bogoliubov (RHB) formalism with separable pairing.

Spontaneous fission properties of superheavy elements

Spontaneous fission properties of transuranium isotopes are reviewed. Specific emphasis was laid on brief historical overviews of theoretical descriptions and experimental determination of basic properties as spontaneous fission half-lives, fission barriers, or total kinetic energy release in fission. Experimental spontaneous fission half-lives are compared with the results of recent theoretical predictions. Hindrance factors for spontaneous fission of odd-mass nuclei are discussed in context with the configuration (spin, parity) of the fissioning states and the change in energy of single particle levels at deformation. Kinetic energy release and mass distributions are discussed in the context of different fission modes, as symmetric and asymmetric or fission from elongated or compact shapes of the nascent fission fragments. An overview of recent fission barrier calculations of superheavy elements on the basis of macroscopic-microscopic models or self-consistent calculations is given, and the results are compared for selected examples.

Fission barriers in covariant density functional theory: Extrapolation to superheavy nuclei

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 particle numbers.

SPONTANEOUS FISSION HALF-LIVES IN VARIOUS MACROSCOPIC-MICROSCOPIC MODELS

The problem of describing spontaneous fission for the entire region of superheavy nuclei is continually present in theoretical investigations. This study outlines the results of the calculations of fission barriers and spontaneous fission half-lives for superheavy nuclei in the region of Z =100-122 using a mean field model. We examine four distinct macroscopic models and two types of pairing interactions. Our approach is based on the deformed Woods-Saxon potential. Spontaneous fission half-lives are calculated using a multi-dimensional dynamical-programming method, where the action integral is minimized within a three dimensional deformation space (β2, β4, β6).

Charge radii in macroscopic-microscopic mass models

We show that the FRLDM model currently being used in macroscopic-microscopic fission-barrier calculations gives a rather poor agreement with measured charge radii. Considerable improvement in this respect can be made by adjusting the diffuseness parameter b.

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. V. Extension to fission barriers

Large-scale fission barrier calculations have been performed in the framework of the Skyrme-Hartree-Fock model. Our Hartree-Fock-Bogoliubov calculations restore broken symmetries such as translational invariance, particle-number conservation, parity, and, in a more approximate way, rotational invariance. Axial symmetry is imposed, but reflection asymmetry is allowed. The energy surface properties are analyzed with the flooding method. A large set of Skyrme interactions, which were fitted to all known masses under different specific constraints, is used to study the main effects influencing the energy surface and the barrier heights. The principal interaction used in the comparison with experimental barriers is BSk8, the force on which the HFB-8 mass table is based. We found that for nuclei with $92\ensuremath{\le}Z\ensuremath{\le}98$ the agreement of our calculations with experimental data is excellent; the rms deviation on the primary barriers is 0.722 MeV. For lighter nuclei, however, the calculated primary barriers are always too high because of the existence of a third barrier at very high deformations. However, our calculated superheavy barriers appear to be too low, although they are consistent with previous calculations.

Microscopic HFB Fission Barriers for r-Process Nucleosynthesis Calculations

New systematic calculations of fission barriers are performed in the 3-dimensional deformation space using the constrained Skyrme-Hartree-Fock-Bogoliubov (SHFB) plus Particle-Number Projection method. The BSk8 Skyrme force, fitted to the full set of more than 2000 experimentally known masses, is used. The energy surfaces are analysed using the flooding method, a necessary tool if more than two dimensions are spanned. The SHFB outer fission barriers are compared with experimental data. The reflection asymmetry is shown to play a significant role in the Z ≈ 94 open-shell region. Extrapolations in the neutron-rich region can differ with the previous compilations of fission barriers.

Self-consistent calculations of fission barriers in the Fm region

The fission barriers of the nuclei 254Fm, 256Fm, 258Fm, 258No and 260Rf are investigated in a fully microscopic way up to the scission point. The analysis is based on the constrained Hartree-Fock-Bogoliubov theory and Gogny's D1S force. The quadrupole, octupole and hexadecapole moments as well as the number of nucleons in the neck region are used as constraints. Two fission paths, corresponding to the bimodal fission, are found. The decrease with isotope mass of the half-life times of heavy Fm isotopes is also explained.

Large-scale fission-barrier calculations with the ETFSI method

Within the context of a project to treat all the nuclear aspects of the astrophysical r-process on a unified microscopic basis, we have extended the ETFSI (extended Thomas-Fermi plus Strutinsky Integral) method to the calculation of fission barriers, and compared our results to a large number of measured barrier heights. With the force SkSC4, on which the ETFSI-1 mass formula was based, we find that if the primary (highest) barrier is lower than 10 MeV, the error never exceeds 1.4 MeV, with either sign being possible. For primary barrier heights lying between 10 and 15 MeV we probably overestimate the height by around 1.5 MeV. It should thus be possible to use the ETFSI method to make reliable calculations of the experimentally inaccessible fission barriers relevant to the r-process.

Relativistic extended Thomas-Fermi calculations of finite nuclei with realistic nucleon-nucleon interactions

A relativistic energy density functional is constructed to investigate the Dirac effects on different properties of the structure and scattering of finite nuclei. The kinetic energy density has been derived within a relativistic extended Thomas-Fermi model and includes gradient corrections to second order in \ensuremath{\Elzxh}. The effective mass and the volume term of the potential energy density have been obtained from a local density approximation to Dirac-Brueckner calculations of nuclear matter carried out with a realistic nucleon-nucleon interaction. This volume term is supplemented by the Coulomb energy and by conventional phenomenological surface and symmetry terms, and the few free parameters of the functional are suitably adjusted. Attention is then focused on the calculation of fission barriers of rotating nuclei and of the complex optical potential for heavy ion collisions at intermediate energies. It turns out that the effects of the density-dependent Dirac spinor which have been incorporated in this approach allow for a reasonable description of the investigated properties.

On the quantization of linear maps: A. Lakshminarayan and N. L. Balazs. Department of Physics, State University of New York Stony Brook, Stony Brook, New York 11794

The Thomas-Fermi model of average nuclear properties described in Part I (Myers and Swiatecki, Ann. Phys. (N.Y.)204, 1990, 401–431) is simplified further and then applied to the calculation of fission barriers and charge distributions. An extensive comparison with experimental data reveals a small but clear-cut barriers vs size discrepancy: if the radius constant r0 is chosen to be 1.13 fm so as to reproduce measured nuclear sizes, the calculated fission barriers are too high. The suggestion is made that an extension of the Thomas-Fermi method is called for in order to describe the presence in nuclei of the “quantal halo”, i.e., of the classically forbidden region around the nuclear surface where matter exists at negative kinetic energy.

A self consistent Thomas Fermi calculation of fission barriers at finite temperature and angular momentum as applied to the205At

A two dimensional, self consistent Thomas Fermi calculation of fission barriers, adapted to rotating nuclei at finite temperatures, is described. The Thomas-Fermi equations, applied to the205At nucleus, are solved by a procedure analogous to that adopted in solving constrained Hartree-Fock equations. It is shown that the computed fission barrier decreases with increasing temperature and angular momentum.

Angular-momentum-dependent fission barriers in the rare-earth region

Fission and evaporation residue excitation functions of $^{153}\mathrm{Tb}$ and $^{181}\mathrm{Re}$ compound systems are investigated in the context of angular-momentum-dependent fission barrier calculations in which effects of the finite range of the nuclear force and of the diffuseness of the nuclear surface are included. Carbon- and neon-induced reactions are studied in both the $^{153}\mathrm{Tb}$ and $^{181}\mathrm{Re}$ cases. Reasonable agreement is found between experimental and calculated excitation functions without adjustments of the theoretical fission barriers.

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

Abstract 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 270 110, 278 110, 298 114, 292 118 and 322 128, which have been tried to form in krypton and argon induced heavy ion reactions.

Semiclassical calculation of fission barriers with Skyrme forces

We present semiclassically calculated fission barriers for 240Pu starting from effective nuclear interactions of the Skyrme type. We show that at least one of the existing Skyrme parametrisations leads to a reasonably low fission barrier.

Determination of fission barrier heights from ?-delayed fission

Beta delayed fission (βDF) gives a possibility to investigate the fission barrier for nuclei far off beta stability. However, before any information on the fission barrier can be extracted, the effect of low-lying structures in the beta-strength function (Sβ) on theβDF branching ratio has to be considered. This is in general not done. In this paper the lowlying structures that occur inSβ are discussed and microscopic calculations for the Gamow-Teller strength function are presented for232Th (β−-decay) and232Pu,240Cm,244,248Cf and248Fm (β+-decay). Using the calculated strength functionsβ+DF branching ratios are calculated and compared with the experimental ones. The sensitivity of the results to different shapes ofSβ is investigated. It is concluded that, when the expected structures inSβ are considered, there are at present no indications fromβ+ DF measurements that the errors in the fission barrier calculations are larger than the uncertainty given for those calculations. The difference in magnitude between theβ− DF and theβ+DF branching ratios is also explained by the occurrence of low-lying structures inSβ.

Discussion of fission barrier calculations by the shell correction method

The potential energy surface of actinides calculated by the shell correction method is discussed. Equality of the size and deformation of the liquid droplet and of the microscopic density distribution generated by the average nuclear potential is required. A smaller stiffness of the potential energy surface toward hexadecapole deformation is obtained. A new strongly deformed hexadecapole shape isomeric state of 240Pu is predicted. It is found to be of great importance that the average pairing term in the potential energy with surface area proportional pairing strength should be treated more precisely.

What Do We Know About Nuclear Fission?

AbstractNuclear fission, although a physical phenomenon, is also of interest to the chemist. It was discovered by chemists, and chemists have made a material contribution to our present knowledge in this field. A comprehensive theory of nuclear fission has not, as yet, been developed, despite the volume of experimental data that has amassed in the 35 years since its discovery. In the past few years discoveries have been made which cannot be explained with conventional theoretical models of nuclear fission. The most important discovery was that of shape isomerism, a novel type of nuclear isomerism. It would appear that an accurate calculation of fission barriers is a prerequsite for precise explanation of many experimental findings. Recent results in this connection and an outline of the present state of our knowledge of nuclear fission constitute the main theme of this paper.