Introducing time in derivation of the scaling factor for MCNP criticality calculations

Abstract Žerovnik et al. have derived a scaling factor for criticality calculations which is different from the one given in the MCNP5 manual. These researchers started with the neutron balance definition of k eff and ignored integrals over time because the problem is quasi steady state. In addition, they did not explain the difference between their scaling factor and the one given in the MCNP5 manual. This paper begins with the definition of the neutron lifetime and includes time in derivation of the scaling factor. After the derivation, the scaling factor derived by Žerovnik et al. will be corroborated and the difference between the two scaling factors will be interpreted.