Scission neutrons for U, Pu, Cm, and Cf isotopes: Relative multiplicities calculated in the sudden limit

The multiplicities of scission neutrons ${\ensuremath{\nu}}_{sc}$ are calculated for series of U, Pu, Cm, and Cf isotopes assuming a sudden transition between two different nuclear configurations (${\ensuremath{\alpha}}_{i}\ensuremath{\rightarrow}{\ensuremath{\alpha}}_{f}$): one just before the neck rupture and one immediately after the disappearance of the neck. This calculation requires only the knowledge of the corresponding two sets of neutron eigenstates. The nuclear shapes around the scission point are described in terms of Cassinian ovals with only two parameters: $\ensuremath{\alpha}$ (that positions the shape with respect to the zero-neck shape) and ${\ensuremath{\alpha}}_{1}$ (that defines the mass asymmetry). Based on these shapes, a neutron mean field of the Woods-Saxon type is constructed using two prescriptions to calculate the distance to the nuclear surface. The accent in the present work is put on the dependence of ${\ensuremath{\nu}}_{sc}$ on the neutron number ${N}_{f}$ of the fissioning nucleus and on the mass asymmetry ${\mathrm{A}}_{L}/{\mathrm{A}}_{H}$ of the primary fission fragments. The relative dependence of these multiplicities, averaged over the mass yields, $\ensuremath{\langle}{\ensuremath{\nu}}_{sc}\ensuremath{\rangle}$, are finally compared with existing experimental data on prompt fission neutrons $\ensuremath{\langle}{\ensuremath{\nu}}_{p}\ensuremath{\rangle}$.