Nuclear Science and Engineering / Volume 161 / Number 1 / January 2009 / Pages 111-118
The concept and calculation techniques of multiplicities in nuclear safeguards are applied to the calculation of the traditional fast fission factor of reactor physics. The concept is the assumption that the original source neutrons from spontaneous or induced fission, and the further neutrons given rise through fast fission in the sample before leakage, are considered as being generated simultaneously with the source neutrons. The number distribution of the neutrons arising from such a "superfission" process will be different from that of the nuclear fission process. Concerning the mathematical treatment, in safeguards literature the master equation approach is used to calculate the moments of such a distribution. Hence, to follow suit, a derivation of the fast fission factor is given here by a backward master equation. This method has the advantages that the derivation of the fast fission factor becomes more transparent than the traditional method, and that it also allows the determination of higher-order moments, notably the variance, of the total number of neutrons generated, i.e., when account is also taken of the contribution of fast fission to these moments. The results show that the relative standard deviation increases quickly with the increase of the nonleakage probability of neutrons, and hence, with the increase of the fast fission factor itself. Also, the Diven factor of the superfission process (neutrons from fast fissions included) is significantly larger than that of thermal fission. We argue that the traditional model, in which the Feynman- and Rossi-alpha models are derived, does not account correctly for the extra branching represented by the fast fission process. Hence, the Diven factor traditionally used in those formulas should be used in a modified form. We show how the effect of fast fission needs to be included in the model to obtain the correct formula and give explicit expressions. Some quantitative examples are given for illustration.