  Standard Big Bang Nucleosynthesis (BBN) predicts the abundances of the light
elements in the early universe. Even if the overall agreement with the
experimental data is good, still some discrepancies exist on the relic
abundances of ${}^7$Li and ${}^6$Li. In order to exclude or confirm these
scenarios, the BBN model needs precise input parameters, in particular the
cross-sections of the BBN nuclear reaction network. However, the suppression of
the cross-sections due to the Coulomb barrier makes the measurement very
difficult and so affected by large systematic errors. Therefore, reliable
theoretical calculations result fundamental in order to reduce the
uncertainties. In this work we present a theoretical study of two nuclear
reactions connected to ${}^6$Li abundance and recently the
$\alpha$+d$\rightarrow$ ${}^6$Li + $\gamma$ and the
p+${}^6$Li$\rightarrow$${}^7$Be+$\gamma$ radiative captures. For the first
reaction we use a so-called ab-initio approach in which we solve the full
six-body problem by using realistic nuclear potentials to describe the nucleon
interactions. In particular we concentrate on the calculation and
characterization of the final state of the reaction, the ${}^6$Li ground state,
focusing on the electromagnetic static structure and the quantities relevant
from the astrophysical point of view such as the asymptotic normalization
coefficient. For doing this we use the Hyperspherical Harmonic approach
developed by the Pisa group providing for the first time the possibility of
using this approach beyond A = 4 nuclear systems. The second reaction is
instead studied by using a two-body cluster approach where the proton and
${}^6$Li are considered as structureless particles. The angular distribution of
the emitted photon obtained in this work were used by the LUNA Collaboration to
determine the efficiency of the detector used in the measurement of the
reaction.
