A revised thermonuclear rate of $^{7}$Be($n$,$\alpha$)$^{4}$He relevant
  to Big-Bang nucleosynthesis
  In the standard Big-Bang nucleosynthesis (BBN) model, the primordial $^7$Li
abundance is overestimated by about a factor of 2--3 comparing to the
astronomical 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 $^7$Be
nucleus in BBN. However, the thermonuclear rate of $^7$Be($n$,$\alpha$)$^4$He
has not been well studied so far. This reaction rate was firstly estimated by
Wagoner in 1969, which has been generally adopted in the current BBN
simulations and the reaction rate library. This simple estimation involved only
a direct-capture reaction mechanism, but the resonant contribution should be
also considered according to the later experimental results. In this work, we
have revised this rate based on the indirect cross-section data available for
the $^4$He($\alpha$,$n$)$^7$Be and $^4$He($\alpha$,$p$)$^7$Li reactions, with
the charge symmetry and detailed-balance principle. Our new result shows that
the previous rate (acting as an upper limit) is overestimated by about a factor
of 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 Wagoner
rate, and hence the present rate even worsens the $^7$Li problem. By the
present estimation, the role of $^7$Be($n$,$\alpha$)$^4$He in destroying $^7$Be
is 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.
