Effect of nuclear dissipation on neutron emission prior to fission.

Abstract

We present a formalism for calculating three effects of nuclear dissipation on neutron emission prior to fission: (1) Kramers's modification of the Bohr-Wheeler statistical-model result for the fission width; (2) the transient time required to build up the quasistationary probability flow over the barrier; and (3) the mean time required for the system to descend from the saddle point to scission. Each of these effects increases the average multiplicity of neutrons emitted prior to fission relative to that calculated with a standard statistical model. The multiplicity calculation includes the dependence of the ratio ${a}_{f}$/${a}_{\mathrm{n}}$ of level-density parameters for fission and neutron emission upon dissipation that is imposed by the low-energy fission probability. We use this formalism to analyze recent experimental results of Gavron et al. for the reaction $^{16}\mathrm{O}$${+}^{142}$Nd\ensuremath{\rightarrow}${\mathrm{}}^{158}$Er at 207 MeV, where 2.7\ifmmode\pm\else\textpm\fi{}0.4 neutrons are emitted prior to fission compared to 1.6 neutrons calculated with a standard statistical model. This determines the limit \ensuremath{\beta}\ensuremath{\lesssim}5\ifmmode\times\else\texttimes\fi{}${10}^{21}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ for the reduced nuclear dissipation coefficient \ensuremath{\beta} defined as the ratio of the dissipation coefficient to the inertia.