Intrinsic generation of angular momenta and entanglement in fission

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 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.