The Big Bang Nucleosynthesis (BBN) model predicted that the abundances of the lithium isotopes should be a factor of two or three times larger than what has been observed in the universe. A common response to this discrepancy is the assumption that certain nuclear reaction cross sections that deal with the creation or destruction of lithium isotopes within the current BBN model are incorrect, which caused theoretical calculations to provide incorrect abundances of lithium. This work investigated the effect that the primordial nuclear fusion reaction 7Be(alpha, gamma ) 11C had on BBN calculations in regards to the resultant abundances of lithium once theoretical calculations were completed. This research examined the possibility of a magnied cross section for the 7Be(alpha, gamma ) 11C reaction by utilizing the potential model as well as the Breit-Wigner method. The nuclear reaction cross sections that were obtained by these methods were later used within the BBN model in order to compute the final calculations that provided the results discussed in this paper.