  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.
