A compact Monte Carlo method for the calculation of k∞ and its application in analysis of (n,xn) reactions

To explore the Monte-Carlo definition of multiplication factor and the impact from specific reactions, a compact Monte Carlo method is established, which obtains k(infinity) simply based on neutron balance, without concerning geometry or time; the neutron transport is merely of one dimension, the kinetic energy; the neutron-multiplying reactions (n, xn), which are significant in a fast spectrum, are treated as fission. This paper tries to demonstrate the accuracy of such a method in k(infinity) calculation. Based on continuous-energy ACE data format, a Monte Carlo code is developed and validated with intermediate-spectrum benchmarks and pseudo fast-spectrum materials; the state-of-the-art Monte Carlo code RMC is used to make comparative calculations. It is found that the code gives satisfactory predictions on benchmark values and the relative differences with RMC are within 100 pcm for all materials and reactivity levels. In fast spectra a tendency of difference of k(infinity) between the two codes is found and well explained by a quantitative study of different treatments of the (n, xn) reactions.

Automated summary

A compact Monte Carlo method is established to calculate the multiplication factor k(infinity) based on neutron balance, showing satisfactory predictions in fast spectra with relative differences within 100 pcm compared to an advanced Monte Carlo code. Differences in the treatment of neutron-multiplying reactions (n, xn) between the two codes are found and quantitatively explained as the cause of the divergence in k(infinity) values observed in fast spectra.