  Using the recent WMAP determination of the baryon-to-photon ratio, 10^{10}
\eta = 6.14 to within a few percent, big bang nucleosynthesis (BBN)
calculations can make relatively accurate predictions of the abundances of the
light element isotopes which can be tested against observational abundance
determinations. At this value of \eta, the Li7 abundance is predicted to be
significantly higher than that observed in low metallicity halo dwarf stars.
Among the possible resolutions to this discrepancy are 1) Li7 depletion in the
atmosphere of stars; 2) systematic errors originating from the choice of
stellar parameters - most notably the surface temperature; and 3) systematic
errors in the nuclear cross sections used in the nucleosynthesis calculations.
Here, we explore the last possibility, and focus on possible systematic errors
in the He3(\alpha,\gamma)Be7 reaction, which is the only important Li7
production channel in BBN. The absolute value of the cross section for this key
reaction is known relatively poorly both experimentally and theoretically. The
agreement between the standard solar model and solar neutrino data thus
provides additional constraints on variations in the cross section (S_{34}).
Using the standard solar model of Bahcall, and recent solar neutrino data, we
can exclude systematic S_{34} variations of the magnitude needed to resolve the
BBN Li7 problem at > 95% CL. Additional laboratory data on
He3(\alpha,\gamma)Be7 will sharpen our understanding of both BBN and solar
neutrinos, particularly if care is taken in determining the absolute cross
section and its uncertainties. Nevertheless, it already seems that this
``nuclear fix'' to the Li7 BBN problem is unlikely; other possible solutions
are briefly discussed.
