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arXiv:2106.10371

Hidden variables in angular correlations of the particles emitted in fission

F. F. Karpeshin

Published Jun 18, 2021• 0 citations
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Abstract

A comparative analysis of experiments on studying the (n, f), on one hand, and (n, n), on the other hand, angular correlations in fission is carried out, based on the model proposed by muonic conversion in fragments of prompt fission of 238U with negative muons. Their fundamental difference is shown in the sense of the information that can be inferred from them. Historically, the situation resembles the EPR paradox. An experimental check of the empirical relation between the alignment and polarization parameters, the former is twice as small as the latter one.

DOI
10.48550/arxiv.2106.10371

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A comparative analysis of experiments on studying the (n, f), on one hand, and (n, n), on the other hand, angular correlations in fission is carried out, based on the model proposed by muonic conversion in fragments of prompt fission of 238U with negative muons. Their fundamental difference is shown in the sense of the information that can be inferred from them. Historically, the situation resembles the EPR paradox. An experimental check of the empirical relation between the alignment and polarization parameters, the former is twice as small as the latter one.
A comparative analysis of experiments devoted to studying, in the fission process, ( n,fn,fn,f ) angular correlations, on one hand, and ( n,nn,nn,n ) and ( n,nfn,nfn,nf ) angular correlations, on the other hand, is performed on the basis of the model proposed earlier for describing muon conversion in fragments originating from the prompt fission of 238{}^{238}238 U nuclei that is induced by negatively charged muons. It is shown that each of these experiments may provide information that does not depend on the results of the other experiments and which is complementary to them. Historically, the situation resembles the Einstein–Podolsky–Rosen (EPR) paradox. An experimental verification of the theoretical relation between the alignment and polarization of fragment spins in the CORA experiment is of crucial importance.
The EPR-Bohm experiment is studied in a classical model with hidden variables. The main hypothesis of Bell about this experiment must be modified in a non-trivial way to allow for the fact that our model is non-linear and so non fully deterministic. With our classical model, we then arrive at the same angular behaviour than the one that is predicted by Quantum Mechanics for the correlated measurement of spin projections on the polarizer axis. If the spin-spin interaction predicted by our particle model, or more precisely in the present case, the spin-polarizer field axis interaction, is not able to align the spin axis with the polarizer axis, then our classical result differs by a factor 3 from the quantum mechanical result. It is surprising to find that the angular behaviour is easier to reproduce by a classical model than the amount of probability. Naively, one would have expected the reverse.
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.
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.