Calculation of effective delayed neutron fraction with Monte Carlo perturbation techniques

New methods are proposed to estimate the effective delayed neutron fraction β_eff in Monte Carlo calculations: the eigenvalue methods jointly used with the differential operator sampling and correlated sampling techniques. In particular, the eigenvalue method with the differential operator sampling technique has a distinct feature that it theoretically gives an exact β_eff value. To verify the proposed methods, Monte Carlo calculations are performed for several systems with simple geometry. It is found that the results obtained with the proposed methods agree with the reference deterministic results within sufficiently small statistical uncertainties. The indirect perturbed source effect must be taken into account to estimate an exact β_eff value.