Variation of fundamental constants and the role of A=5 and A=8 nuclei on primordial nucleosynthesis

We investigate the effect of a variation of fundamental constants on primordial element production in big bang nucleosynthesis (BBN). We focus on the effect of a possible change in the nucleon-nucleon interaction on nuclear reaction rates involving the A = 5 (Li-5 and He-5) and A = 8 (Be-8) unstable nuclei. The reaction rates for He-3(d, p)He-4 and H-3(d, n)He-4 are dominated by the properties of broad analog resonances in He-5 and Li-5 compound nuclei, respectively. While the triple alpha process He-4(alpha alpha, gamma)C-12 is normally not effective in BBN, its rate is very sensitive to the position of the Hoyle state'' and could in principle be drastically affected if Be-8 were stable during BBN. The nuclear properties (resonance energies in He-5 and Li-5 nuclei, and the binding energies of Be-8 and D) are all computed in a consistent way using a microscopic cluster model. The n(p, gamma)d, He-3(d, p)He-4, H-3(d, n)He-4, and He-4(alpha alpha, gamma)C-12 reaction rates are subsequently calculated as a function of the nucleon-nucleon interaction that can be related to the fundamental constants. We found that the effect of the variation of constants on the He-3(d, p)He-4, H-3(d, n)He-4, and He-4(alpha alpha, gamma)C-12 reaction rates is not sufficient to induce a significant effect on BBN, even if Be-8 was stable. In particular, no significant production of carbon by the triple alpha reaction is found when compared to standard BBN. Finally, we complement our earlier work on the effect of coupled variation of fundamental constants inducing variations of the binding energy of deuterium, the Fermi constant, and the neutron-proton mass difference, that affect the weak rates and the n(p, gamma)d, A = 2 bottleneck reaction.