Spin distribution of fission fragments involving transverse vibrational modes
A closed analytical description of fragment-spin distributions in low-energy induced and spontaneous fission is presented. The high fragment spins and the relative orbital angular momentum are assumed to arise from zero-point bending and wriggling oscillations of the pre-fragments near the scission point. The corresponding probability distributions yield the joint distribution of the fragment spins, the distribution of each spin, and the associated mean value. The fragment moments of inertia are calculated in a hydrodynamic model from non-equilibrium deformations at the scission point reconstructed from prompt-neutron multiplicities. For $\rm ^{232}Th(n,f)$, $\rm ^{238}U(n,f)$, and $\rm ^{252}Cf(sf)$, the model reproduces the magnitude and sawtooth mass dependence of the measured mean spins. The zero-point approximation is applied only to the bending and wriggling oscillations and does not require dissipationless motion of the fissioning nucleus from saddle to scission.