  During the Big Bang, ${}^{6}{\rm Li}$ was synthesized via the ${}^{2}{\rm
H}(\alpha,\gamma){}^{6}{\rm Li}$ reaction. After almost 25 years of the failed
attempts to measure the ${}^{2}{\rm H}(\alpha,\gamma){}^{6}{\rm Li}$ reaction
in the lab at the Big Bang energies, just recently the LUNA collaboration
presented the first successful measurements at two different Big Bang energies
[M. Anders {\it et al.}, Phys. Rev. Lett. {\bf 113}, 042501 (2014)]. In this
paper we will discuss how to improve the accuracy of the direct experiment. To
this end the photon's angular distribution is calculated in the potential
model. It contains contributions from electric dipole and quadrupole
transitions and their interference, which dramatically changes the photon's
angular distribution. The calculated distributions at different Big Bang
energies have a single peak at $\sim 50^{\circ}$. These calculations provide
the best kinematic conditions to measure the ${}^{2}{\rm
H}(\alpha,\gamma){}^{6}{\rm Li}$ reaction. The expressions for the total cross
section and astrophysical factor are also derived by integrating the
differential cross section over the photon's solid angle. The LUNA data are in
excellent agreement with our calculations using a potential approach combined
with a well established asymptotic normalization coefficient for ${}^{6}{\rm
Li} \to \alpha +d$. Comparisons of the available experimental data for the
$S_{24}$ astrophysical factor and different calculations are presented. The Big
Bang lithium isotopic ratio ${}^{6}{\rm Li}/^{7}{\rm Li} = (1.5 \pm 0.3)\times
10^{-5}$ following from the LUNA data and the present analysis are discussed in
the context of the disagreement between the observational data and the standard
Big Bang model, which constitutes the second Lithium problem.
