This paper focuses on generating accurate 1-g cross section values that are necessary for evaluation of nuclide densities as a function of burnup for coupled Monte Carlo codes. The proposed method is an alternative to the conventional direct reaction rate tally approach, which requires extensive computational efforts. The method presented here is based on the multi-group (MG) approach, in which pre-generated MG sets are collapsed with MC calculated flux. In our previous studies we showed that generating accurate 1-g cross sections requires their tabulation against the background cross-section (σ0) to account for the self-shielding effect. However, in previous studies, the model that was used to calculate σ0 was simplified by fixing Bell and Dancoff factors. This work demonstrates that 1-g values calculated under the previous simplified model may not agree with the tallied values. Therefore, the original background cross section model was extended by implicitly accounting for the Dancoff and Bell factors. The method developed here reconstructs the correct value of oo by utilizing statistical data generated within the MC transport calculation by default. The method does not carry any additional computational burden and it is universally applicable to the analysis of thermal as well as fast reactor systems.