Through using the basic probability theory and establishing the law of finite chains near the prompt criticality, we deduce the formula of relation between the neutrons number and time in the process of persistent chains initiated by a single-pulse neutron source in burst reaction. The formula is validated by the experiments of CFBR-Ⅱ. The formula is the development of Hansen theory model because it can describe not only the developing tendency in the later stages but also the rapid increasing of neutron number in the early stage. Furthermore, according to the relation between the initial time of burst reaction and the intensity of neutron source, we illustrate that the initial time is hardly dependent on the intensity of weak neutron source.