Uncertainty Principle and Angular Momentum Generation in Microscopic Fission Models

Abstract

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.

Figures (3)

• Figure 1: Top: Slice of the density at $x=0$ at the time when the surface of the fragments are separated by a distance of 6 fm for each fissioning system. Bottom: Corresponding angular distribution obtained by the procedure described in the text for the light fragment (blue) and heavy fragment (red). The fitted curve from eq. \ref{['eq:gauss_sin']} is also shown for each fragment.
• Figure 2: Spin distribution obtained from the projection (eq. \ref{['eq:Prob_JK']}) compared to the spin cut-off formula (eq. \ref{['eq:spin_cut_off']}) assuming the uncertainty principle (eq. \ref{['eq:uncert_principle']}) for the light (top) and heavy (bottom) fragments.
• Figure 3: Fragment-mass dependence of the angular-momentum width $\sigma_J$ (top) and the quadrupole and octupole deformation parameters $\beta_2$ and $|\beta_3|$ (bottom) for the fissioning nuclei $^{230}$Th, $^{240}$Pu, and $^{250}$Cf. Only fragments with more than 300 events are included. The angular-momentum widths $\sigma_J$ are extracted from the folded angular distributions of the fragments, whereas the deformation parameters are computed from the quadrupole (solid symbols) and octupole (open symbols) moments of the fragment nucleon distributions.