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Physics of Atomic Nuclei

Quantum properties of deformation modes of fissile-nucleus motion

Stanislav G. Kadmensky

Published Jul 1, 2008• 14 citations
Publisher

Abstract

The intrinsic mechanisms that are responsible for the pumping of high values of the spins and relative orbital angular momenta of deformed and spherical primary fission fragments and which are induced by the connection between the quantum-mechanical uncertainty principle and the shape of a fissile nucleus are investigated.
DOI
10.1134/s1063778808070107

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The generation of angular momentum (intrinsic spin) in fission fragments has recently attracted renewed attention. While several microscopic approaches reproduce the spin distribution qualitatively using projection techniques, the physical origin of the fragments' angular momentum in density functional theory remains unclear. In this work, we investigate the mechanisms responsible for the spin distribution of fission fragments within a microscopic TDDFT framework. We compare spin distributions obtained from projection operators with those predicted by a simple expression derived from the uncertainty relation between angle and angular momentum, where angular fluctuations are estimated using a Monte Carlo sampling of nucleon positions. We find that a large portion of the spin distribution obtained from projection methods can be explained by the uncertainty principle. Our results thus show that, within microscopic approaches, the spin of fission fragments originates primarily from quantum uncertainty associated with their orientation angle with respect to the fission axis, mainly due to quadrupole deformation and, to a lesser extent, octupole deformation.
In the first part, calculated lifetimes for spontaneous fission from the ground and from the isomer state are presented. The agreement reached with experiments correponds to the crude approximations done, but is better than expected. The calculations are based on the shell correction approach for the potential energy and on the cranking model for the collective mass. In the second part we discuss the behaviour of the so-called least action trajectories: there are two of them, one for symmetric and one for asymmetric shapes. The systematic behaviour of the dynamic barriers and of the peak-to-peak ratio of the fission fragment mass distribution and their correlation with the experimental in formation support this point of view.
Nuclear time-dependent density functional theory is used to investigate spin generation and entanglement of fission fragments in spontaneous fission of ^{252}Cf, incorporating both axial and nonaxial deformations. Axially symmetric fission trajectories enforce strict constraints: counterrotation (twisting mode) along the fission axis and equiprobable bending and wriggling modes perpendicular to it. Nonaxial modes broaden the distributions of fission fragment spin projection on the fission axis, and allow for axial (tilting) collective rotations, which are forbidden on axially symmetric trajectories. Mutual information analysis reveals that axial-symmetry breaking reduces spin-spin correlations along the fission axis of symmetric cases, while perpendicular correlations remain more resilient. The effect of triaxial degrees of freedom on the opening angle distribution between the spins of the fission fragments is analyzed.
Nuclear time-dependent density functional theory is used to investigate spin generation and entanglement of fission fragments in spontaneous fission of 252^{252}252Cf, incorporating both axial and non-axial deformations. Axially symmetric fission trajectories enforce strict constraints: counter rotation (twisting mode) along the fission axis and equiprobable bending/wriggling modes perpendicular to it. Non-axial modes broaden the distributions of fission fragment spin projection on the fission axis, and allow for axial (tilting) collective rotations, which are forbidden on axially symmetric trajectories. Mutual information analysis reveals that axial-symmetry breaking reduces spin-spin correlations along the fission axis of symmetric cases, while perpendicular correlations remain more resilient. The effect of triaxial degrees of freedom on the opening angle distribution between the spins of the fission fragments is analyzed.