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

TL;DR

This study calculates the $^7$Be($ ext{α}$,γ)$^{11}$C reaction rate to assess its effect on primordial lithium abundance, concluding it is negligible for the cosmological lithium problem.

Contribution

It provides a detailed calculation of the reaction rate including resonances, showing this reaction's impact on lithium abundance is insignificant.

Findings

Reaction rate calculations show negligible impact on $^7$Li abundance.

No low-energy resonances in $^{11}$C significantly affect big bang nucleosynthesis.

The reaction is unlikely to resolve the cosmological lithium puzzle.

Abstract

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