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In the standard Big-Bang nucleosynthesis (BBN) model, the primordial $^7$Liabundance is overestimated by about a factor of 2--3 comparing to theastronomical observations, so called the pending cosmological lithium problem.The $^7$Be($n$,$\alpha$)$^4$He reaction, which may affect the $^7$Li abundance,was regarded as the secondary important reaction in destructing the $^7$Benucleus in BBN. However, the thermonuclear rate of $^7$Be($n$,$\alpha$)$^4$Hehas not been well studied so far. This reaction rate was firstly estimated byWagoner in 1969, which has been generally adopted in the current BBNsimulations and the reaction rate library. This simple estimation involved onlya direct-capture reaction mechanism, but the resonant contribution should bealso considered according to the later experimental results. In this work, wehave revised this rate based on the indirect cross-section data available forthe $^4$He($\alpha$,$n$)$^7$Be and $^4$He($\alpha$,$p$)$^7$Li reactions, withthe charge symmetry and detailed-balance principle. Our new result shows thatthe previous rate (acting as an upper limit) is overestimated by about a factorof ten. The BBN simulation shows that the present rate leads to a 1.2\%increase in the final $^7$Li abundance compared to the result using the Wagonerrate, and hence the present rate even worsens the $^7$Li problem. By thepresent estimation, the role of $^7$Be($n$,$\alpha$)$^4$He in destroying $^7$Beis weakened from the secondary importance to the third, and the$^7$Be($d$,$p$)2$^4$He reaction becomes of secondary importance in destructing$^7$Be.

A revised thermonuclear rate of $^{7}$Be($n$,$\alpha$)$^{4}$He relevant to Big-Bang nucleosynthesis