Structures in the energy distribution of the scission neutrons: Finite neutron-number effect

Abstract

The scission neutron kinetic energy spectrum is calculated for $^{236}\mathrm{U}$ in the frame of the dynamical scission model. The bidimensional time-dependent Schr\"odinger equation with a time-dependent potential is used to propagate each neutron wave function during the scission process, which is supposed to last $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}$ sec. At the end, we separate the unbound parts and continue to propagate them as long as possible (in this case $50\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}$ sec) in the frozen fragments approximation. At several time intervals, the Fourier transforms of these wave packets are calculated in order to obtain the corresponding momentum distributions, which lead to the kinetic energy distributions. The evolution of these distributions in time provides an interesting insight into the separation of each neutron from the fissioning system and asymptotically gives the kinetic energy spectrum of that particular neutron. We group the results in substates with given projection $\mathrm{\ensuremath{\Omega}}$ of the angular momentum on the fission axis to study its influence on the spectrum. Finally, the sum over all $\mathrm{\ensuremath{\Omega}}$ values is compared with a typical evaporation spectrum as well as with recent precise measurements in the reaction $^{235}\mathrm{U}({n}_{th},f)$. Structures are present both in the scission-neutron spectrum and in the data.