A. Baran

Microscopic description of complex nuclear decay: Multimodal fission

Our understanding of nuclear fission, a fundamental nuclear decay, is still incomplete due to the complexity of the process. In this paper, we describe a study of spontaneous fission using the symmetry-unrestricted nuclear density functional theory. Our results show that the observed bimodal fission can be explained in terms of pathways in multidimensional collective space corresponding to different geometries of fission products. We also predict a new phenomenon of trimodal spontaneous fission for some rutherfordium, seaborgium, and hassium isotopes.

Fission barriers and probabilities of spontaneous fission for elements with Z ≥ 100

Abstract This paper briefly reviews recent progress in theoretical studies on fission barriers and fission half-lives of even–even superheavy nuclei. We compare and discuss results obtained in the semi-classical macroscopic–microscopic approach, the self-consistent mean-field models with the Skyrme and Gogny energy density functionals and in the relativistic mean-field theory. A short part of the paper is devoted to the calculation of the mass parameters and nuclear fission dynamics. We also discuss the predictive power of Skyrme energy density functionals applied to key properties of the fission path of 266Hs. Standard techniques of error estimates in the framework of a χ 2 analysis are applied.

Broyden's Method in Nuclear Structure Calculations

Broydens method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the unitary gas problem, the nuclear density functional theory with Skyrme functionals, and the nuclear coupled-cluster theory. The stability of the method, its ease of use, and its rapid convergence rates make Broydens method a tool of choice for large-scale nuclear structure calculations.

Spontaneous fission half-life-times of double-odd nuclei (Z≧97)

Spontaneous fission half life times of odd-odd and even-even nuclei in the region 97≦Z≦109 and 140≦N≦ 160 are calculated. New Nilsson potential parameters (κ, μ) generating the proper single particle spectrum are estimated. Angular momentum projections of odd-odd particles are properly taken into account. Hindrance factors 5–7 orders of magnitude are found forZ≦101 nuclei and 1–3 orders of magnitude for nucleiZ≧ 103.

Augmented Lagrangian method for constrained nuclear density functional theory

Abstract.The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of multi-dimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves the accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia; and is well adapted to supercomputer applications.

Ground state properties of the β stable nuclei in various mean field theories

Abstract The separation energies of neutrons and protons, binding energies, mean square charge radii, electric quadrupole moments and deformation parameters of the proton and neutron distributions are evaluated for β stable even-even nuclei with 16 ⩽ A ⩽ 256. We compare the theoretical estimates obtained within the Hartree-Fock plus BCS model with a few sets of Skyrme forces, relativistic mean-field theory and frequently used Saxon-Woods and Nilsson potentials with experimental data.

Some dynamical aspects of the fission process

Abstract The properties of the nuclear mass parameter and its influence on the fission process are discussed. In particular, correlations between dynamical and statical paths to fission are considered. The least action trajectories idea is used for finding the dynamical path to fission. Ritz method for the action integral minimalization is applied. An example of the nucleus 252 Fm is considered.

Spontaneous fission lifetimes from the minimization of self-consistent collective action

The spontaneous fission lifetime of 264Fm has been studied within nuclear density functional theory by minimizing the collective action integral for fission in a two-dimensional quadrupole collective space representing elongation and triaxiality. The collective potential and inertia tensor are obtained self-consistently using the Skyrme energy density functional and density-dependent pairing interaction. The resulting spontaneous fission lifetimes are compared with the static result obtained with the minimum-energy pathway. We show that fission pathways strongly depend on assumptions underlying collective inertia. With the non-perturbative mass parameters, the dynamic fission pathway becomes strongly triaxial and it approaches the static fission valley. On the other hand, when the standard perturbative cranking inertia tensor is used, axial symmetry is restored along the path to fission; an effect that is an artifact of the approximation used.

Quadrupole collective inertia in nuclear fission: Cranking approximation

Collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian Overlap Approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in ^{256}Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and perturbative cranking approximations to ATDHFB, and within GOA, are discussed.

\(\delta\)-pairing forces and collective pairing vibrations

Abstract.The collective pairing Hamiltonian is obtained in the framework of the generator coordinate method in the Gaussian overlap approximation with a slightly modified BCS function used as a generator function. The collective variable