  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
and complement earlier work on its effect on the binding energy of deuterium.
The reaction rates for He3(d,p)He4 and H3(d,n)He4 are dominated by the
properties of broad analog resonances in He-5 and Li-5 compound nuclei
respectively. While the triple alpha process 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, He3(d,p)He4 and H3(d,n)He4 and
triple-alpha 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 He3(d,p)He4 and
H3(d,n)He4 and triple-alpha 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. We also update our previous analysis on the effect of
a variation of constants on the n(p,gamma)d reaction rate.
