Number of Particles in Fission Fragments

In current simulations of fission, the number of protons and neutrons in a given fission fragment is almost always obtained by integrating the total density of particles in the sector of space that contains the fragment. Because of the antisymmetry of the many-body wave function of the whole nucleus, this procedure systematically gives noninteger numbers of particles in the fragments. We introduce a novel sampling method to estimate rigorously the probability of finding $Z$ protons and $N$ neutrons in a fission fragment without resorting to projectors, which can sometimes give unwieldy results. When applied on standard Hartree-Fock-Bogoliubov many-body states, we show that our approach reproduces indeed the results of full particle-number projection. We then estimate the charge and mass number dispersion of several scission configurations in $^{240}$Pu with and without pairing correlations included. We show that odd-even effects in the charge probability naturally occur within our approach, which could explain the well-known odd-even staggering of charge distributions. Our method is applicable either in static calculations of scission configurations such as, e.g., in the macroscopic-microscopic approach or energy density functional theory, but also in explicitly time-dependent density functional theory simulations of fission.