Dependence of Neutron Production in Fission on Rate of Change of Nuclear Potential

Abstract

Most prompt neutrons from fission are thought to come from separated fission fragments excited during scission. Can some come out in a prior process: excitation of individual nucleons in the dividing nucleus by nonadiabatic changes in the nuclear potential? The question can be raised: Can enough energy be transferred to some neutrons to free them by the nonadiabatic distortion of the potential as the nucleus fissions? To study this possibility we consider a square well containing a Fermi sea of nucleons in the middle of which is "erupting" an inverted square well "volcano." It rises and divides the original square well into the two fission fragments. The energy transferred to the nucleons can be calculated analytically for the two limiting cases, adiabatic and sudden changes of potential. The transition between these limiting situations has been studied on a computer. One finds that there exist reasonable rates of rise of the volcano (i.e., scission times ≅5×${10}^{-22\mathrm{}}$ sec) for which the number of neutrons ejected is of the same order of magnitude as the total number of neutrons ejected on the average per act of fission due to all mechanisms. By varying the ratio of the width of the volcano to the width of the square well, or by smoothing the volcano out in space (rounded volcano instead of an inverted square well volcano), the number of particles ejected can be changed also. For a particular set of parameters, consistent with the experimentally known facts, we find that about 1% of the neutrons in the nucleus are ejected. For a heavy nucleus such as ${\mathrm{Cf}}^{252}$ this corresponds to about 1.5 neutrons per fission.