QED corrections to Big-Bang nucleosynthesis reaction rates

We compute radiative corrections to nuclear reaction rates that determine the outcome of the big-bang nucleosynthesis (BBN). Any nuclear reaction producing a photon with an energy above $2m_e$ must be supplemented by the corresponding reaction where the final-state photon is replaced by an electron-positron pair. We find that pair production brings a typical $0.2\%$ enhancement to photon-emission rates, resulting in a similar size corrections to elemental abundances. The exception is ${}^4\mathrm{He}$ abundance, which is completely insensitive to the small changes in the nuclear reaction rates. We also investigate the effect of vacuum polarization on the Coulomb barrier, which brings a small extra correction when reaction rates are extrapolated from the measured energies to the BBN Gamow peak energies.

Figure 1

Solid is electric-dipole ratio, dashed is magnetic-dipole ratio. The result of the full numerical integration of Eq. (16) without approximation is depicted in thick lines, and the analytic approximations (23a) and (23b) are in thin lines.

Figure 2

The electric-dipole (magnetic-dipole) contribution to ${\langle \sigma v\rangle }^{\left(ee\right)}$ is shown by the dashed (dotted) line. The total correction is shown by the gray line while the reference value for ${\langle \sigma v\rangle }^{\left(\gamma \right)}$ [based on Eqs. (29)] is shown by the solid line.

Figure 3

Relative variation of the Gamow penetration factor $\mathrm{\Delta }\left(E\right)$ for the reaction (1b) when ignoring the centrifugal barrier ($r_{min}=0$ in continuous line and $r_{\min }=3\mathrm{fm}$ in dashed line), and with $\ell =1$ centrifugal (and also $r_{\min }=3\mathrm{fm}$) barrier in dotted line.

Figure 4

Corrective ratio ${\langle \left[\sigma v\right]\rangle }_{\mathrm{C}+\mathrm{U}}/{\langle \left[\sigma v\right]\rangle }_{\mathrm{C}}$ for the reaction (1b).