A Monte Carlo approach is proposed in which the random walk chains generated in particle transport simulations are segmented. Forward and adjoint-mode estimators are then used in conjunction with the first-event source density on the segmented chains to obtain multiple estimates of the individual terms of the Neumann series solution at each collision point. The solution is then constructed by summation of the series. The approach is compared to the exact analytical and to the Monte Carlo nonabsorption weighting method results for two representative slowing down and deep penetration problems. Application of the proposed approach leads to unbiased estimates for limited numbers of particle simulations and is useful in suppressing an effective bias problem observed in some cases of deep penetration particle transport problems. These results are relevant to fusion reactor shielding.
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