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We calculate the radiative capture cross section for $^7$Be($\alpha,\gamma$)$^{11}$C and its reaction rate of relevance for the big bangnucleosynthesis. The impact of this reaction on the primordial $^7$Li abundanceis revised including narrow and broad resonances in the pertinent energyregion. Our calculations show that it is unlikely that very low energyresonances in $^{11}$C of relevance for the big bang nucleosynthesis wouldemerge within a two-body potential model. Based on our results and a comparisonwith previous theoretical and experimental analyses, we conclude that theimpact of this reaction on the so-called "cosmological lithium puzzle" iscompletely irrelevant.

Impact of the $^7$Be($\alpha, \gamma$)$^{11}$C reaction on the primordial abundance of $^7$Li