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Revisiting $^7$Be Weak and Radiative Transition Rates in Big Bang Nucleosynthesis: Implications for the Primordial Lithium Problem

The primordial 7Li abundance predicted by standard Big Bang Nucleosynthesis (BBN) exceeds that inferred from old, metal-poor stars by a factor of about 3-4. In standard BBN, most primordial 7Li is produced as 7Be in the early Universe and later converted by electron capture. Additional production or destruction channels of 7Be, such as proton capture or antineutrino capture during BBN, may therefore affect the final lithium yield. We quantify the depletion of 7Be due to in-situ electron capture, including the associated antineutrino channel, positron decay from nuclear excited states, and proton capture through the radiative 7Be(p,gamma)8B reaction. We also investigate stimulated emission induced by the dense photon background during the nuclear statistical equilibrium epoch, as well as a three-body Auger-like variant transferring the capture energy to a continuum electron. Decay rates are computed using first-order perturbation theory, modelling weak interactions with a Fermi contact term and factorising hadronic and leptonic currents. Thermally averaged rates are obtained by folding cross-sections with Maxwell-Boltzmann distributions and accounting for particle densities in the temperature range 10-100 keV. We find that the electron-capture rate decreases rapidly with temperature and is significantly enhanced by the inclusion of the antineutrino channel. Stimulated emission and plasma screening increase the radiative proton-capture rate by only 1-3 percent at temperatures around 87 keV. The Auger-like channel contributes at the level of a few thousandths of a percent and becomes negligible at lower temperatures. Overall, our total rate revises previous estimates by nearly an order of magnitude. Electron capture, proton capture, and positron decay provide corrections to the dominant depletion channel 7Be(n,p)7Li.