  We review the Bogoliubov theory in the context of recent experiments, where
atoms are scattered from a Bose-Einstein Condensate into two well-separated
regions. We find the full dynamics of the pair-production process, calculate
the first and second order correlation functions and show that the system is
ideally number-squeezed. We calculate the Fisher information to show how the
entanglement between the atoms from the two regions changes in time. We also
provide a simple expression for the lower bound of the useful entanglement in
the system in terms of the average number of scattered atoms and the number of
modes they occupy. We then apply our theory to a recent "twin-beam" experiment
[R. B\"ucker {\it et al.}, Nat. Phys. {\bf 7}, 608 (2011)]. The only numerical
step of our semi-analytical description can be easily solved and does not
require implementation of any stochastic methods.
