Microscopic study of induced fission dynamics of Th226 with covariant energy density functionals

Abstract

Static and dynamic aspects of the fission process of 226 Th are analyzed in a self-consistent framework based on relativistic energy density functionals. Constrained relativistic mean-field (RMF) calculations in the collective space of axially symmetric quadrupole and octupole deformations, based on the energy density functional PC-PK1 and a δ-force pairing, are performed to determine the potential energy surface of the fissioning nucleus, the scission line, the single-nucleon wave functions, energies and occupation probabilities, as functions of deformation parameters. Induced fission dynamics is described using the time-dependent generator coordinate method in the Gaussian overlap approximation. A collective Schrödinger equation, determined entirely by the microscopic single-nucleon degrees of freedom, propagates adiabatically in time the initial wave packet built by boosting the ground-state solution of the collective Hamiltonian for 226 Th. The position of the scission line and the microscopic input for the collective Hamiltonian are analyzed as functions of the strength of the pairing interaction. The effect of static pairing correlations on the pre-neutron emission charge yields and total kinetic energy of fission fragments is examined in comparison with available data, and the distribution of fission fragments is analyzed for different values of the initial excitation energy. * Electronic address: zpliphy@swu.edu.cn A microscopic description of fission presents one of the most complex problems in lowenergy theoretical nuclear physics [1, 2]. For a comprehensive recent review and an exhaustive list of references, we refer the reader to Ref. [1]. The spontaneous or induced fission process in which a heavy nucleus splits into fragments is out of reach for ab initio methods and, therefore, modern microscopic approaches are based on the framework of nuclear energy density functionals (NEDFs). Nuclear density functional theory (DFT) and its timedependent (TD) generalization have enabled a self-consistent treatment of both static and dynamic aspects of fission [3-11]. The slow large-amplitude collective motion of the compound system that eventually leads to the formation of the final fragments can be described, in a first approximation, as an adiabatic process in which the intrinsic nucleonic degrees of freedom are decoupled from macroscopic collective degrees of freedom such as multipole moments (deformations) of the mass distribution and pairing fields [1].Numerous studies of spontaneous fission, based on NEDFs, have analyzed the effects of the choice of collective coordinates (shape degrees of freedom), approximations used to calculate the collective inertia, and coupling between shape and pairing degrees of freedom on fission half-lives [12][13][14][15][16][17][18]. A quantitative description of induced fission is, in this framework, conceptually and computationally more challenging and this process has been explored less systematically. In particular, several recent studies have used the time-dependent gener...

Heavy-ion collisions and fission dynamics with the time-dependent Hartree–Fock theory and its extensions

“…One of the most important contributions of pairing to self-consistent mean-field calculations is the ability of the system to allow for level crossings, which results in fragments establishing their identity between the saddle and scission points [166,167,[170][171][172][173]. Pairing is also expected to play a role as a residual interaction in dynamical calculations of heavy-ion collisions, giving flexibility to the system to attain more compact shapes in fusion, influence transfer and breakup, or lowering the effect of spherical magic shells and open other magic numbers for final fragment formation in fission and quasifission studies [174]. While it is clear that pairing interaction plays an important role in multi-nucleon transfer reactions and for fission fragments acquiring their identity after passing the saddle point, the influence of pairing in fusion, which involves high excitation, is not so well established and is still under investigations [175][176][177][178][179][180].…”

Effect of shell structure on the fission of sub-lead nuclei

“…A direct comparison can then be made with the centroids of experimental fission fragment mass distributions for asymmetric modes. Widths and shapes of these distributions, as well as a quantitative study of the competition between symmetric and asymmetric modes are beyond the scope of this work and would require a more advanced treatment of fluctuations via, e.g., the time-dependent generator coordinate method [58][59][60][61][62][63], stochastic dynamics on top of a potential energy surface [28,64,65], or stochastic mean-field calculations [66]. Figure 1 shows the evolution of the potential energy as a function of quadrupole moment for a symmetric path and in the asymmetric valley.…”

Microscopic self-consistent description of induced fission dynamics: Finite-temperature effects

“…As in our recent calculations of Refs. [17][18][19][20], the parameters of the additional imaginary absorption potential that takes into account the escape of the collective wave packet in the domain outside the region of calculation [6] are: the absorption rate r = 20 × 10 22 s −1 and the width of the absorption band w = 1.0.…”

“…Relativistic energy density functionals [12][13][14] have also been employed in the description of both spon-taneous [15,16] and induced nuclear fission [17][18][19][20]. The microscopic input for these studies is generated using either the multidimensionally constrained relativistic mean-field (MDC-RMF) [21] or the relativistic Hartree-Bogoliubov model (MDC-RHB) [22].…”