Spin distribution of fission fragments involving bending and wriggling modes

Abstract

We present a closed analytical description of the spin distributions of the fragments produced in low-energy induced and spontaneous fission. In our model the high fragment spins and the relative orbital angular momentum arise from the zero-point transverse wriggling and bending oscillations of the two pre-fragments, under the postulate that the fissioning system remains ``cold'' up to scission -- its available energy being stored as non-equilibrium deformation rather than as heat. From the probability distributions of the two modes we derive a closed expression for the spin distribution of each fragment and for its mean value. The decisive quantities are the fragment moments of inertia, which we evaluate in the hydrodynamic model from the non-equilibrium scission deformations reconstructed from the measured prompt-neutron multiplicities. Confronted with the recent data on $\rm ^{232}Th(n, f)$, $\rm ^{238}U(n, f)$, and $\rm ^{252}Cf(sf)$, the model reproduces both the magnitude of the mean spins and their characteristic sawtooth dependence on the fragment mass. Comparison with the statistical and microscopic approaches indicates that the differences for individual fragments can be traced largely to the deformation dependence of the moments of inertia.