Review and comparison of effective delayed neutron fraction calculation methods with Monte Carlo codes

• Review of several Monte Carlo effective delayed neutron fraction calculation methods.
• These methods have been implemented with the Monte Carlo code MCNPX.
• They have been benchmarked against against some critical and subcritical systems.
• Several nuclear data libraries have been used.

The calculation of the effective delayed neutron fraction, βeffβeff, with Monte Carlo codes is a complex task due to the requirement of properly considering the adjoint weighting of delayed neutrons. Nevertheless, several techniques have been proposed to circumvent this difficulty and obtain accurate Monte Carlo results for βeffβeff without the need of explicitly determining the adjoint flux. In this paper, we make a review of some of these techniques; namely we have analyzed two variants of what we call the k-eigenvalue technique and other techniques based on different interpretations of the physical meaning of the adjoint weighting. To test the validity of all these techniques we have implemented them with the MCNPX code and we have benchmarked them against a range of critical and subcritical systems for which either experimental or deterministic values of βeffβeff are available. Furthermore, several nuclear data libraries have been used in order to assess the impact of the uncertainty in nuclear data in the calculated value of βeffβeff.