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

In the standard Big-Bang nucleosynthesis (BBN) model, the primordial ${}^7\mathrm{Li}$ abundance is overestimated by about a factor of 2 to 3 compared to astronomical observations; this is the so-called pending cosmological lithium problem. The ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$ reaction was regarded as the secondary important reaction in affecting the ${}^7\mathrm{Li}$ abundance by destructing the ${}^7\mathrm{Be}$ nucleus in BBN. However, the reaction rate of ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$ has not been well studied so far. This reaction rate was first estimated by Wagoner in 1969, which has been primarily adopted in the current BBN simulations. This simple estimate involved only a direct reaction contribution, but the resonant component should also be considered according to the later experimental results. In the present work, we revised this rate based on the indirect cross-section data available for the ${}^4\mathrm{He}(\alpha ,n){}^7\mathrm{Be}$ and ${}^4\mathrm{He}(\alpha ,p){}^7\mathrm{Li}$ reactions by applying the charge symmetry and the principle of detailed balance. 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 ${}^7\mathrm{Li}$ abundance compared with the result using the Wagoner rate and, hence, the present rate even worsens the ${}^7\mathrm{Li}$ problem. By the present estimation, the role of ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$ in destroying ${}^7\mathrm{Be}$ is weakened from the second most importance to the third and, in turn, the ${}^7\mathrm{Be}(d,p)2{}^4\mathrm{He}$ reaction becomes of secondary importance in destroying ${}^7\mathrm{Be}$.

Figure 1

Comparison of different cross sections of ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$ among present work and other two different origins (Wagoner's work [21] and TENDL-2014 evaluation [41]).

Figure 2

The time-integrated reaction flow for BBN network with new rate of ${}^7\mathrm{Be}(n,\alpha ){}^4\mathrm{He}$. Here, $X$ and $A$ denote the mass fraction and molar mass, respectively.