  The sensitivity of atom interferometers depends on their ability to realize
long pulse separation times and prevent loss of contrast by limiting the
expansion of the atomic ensemble within the interferometer beam through
matter-wave collimation. Here we investigate the impact of atomic interactions
on collimation by applying a lensing protocol to a $^{39}$K Bose-Einstein
condensate at different scattering lengths. Tailoring interactions, we measure
energies corresponding to $340 \pm 12$ pK in one direction. Our results are
supported by an accurate simulation, which allows us to extrapolate a 2D
ballistic expansion energy of $438 \pm 77$ pK. Based on our findings we propose
an advanced scenario, which enables 3D expansion energies below $16$ pK by
implementing an additional pulsed delta-kick. Our results pave the way to
realize ensembles with more than $1\times10^5$ atoms and 3D energies in the
two-digit pK range in typical dipole trap setups without the need for
micro-gravity or long baseline environments.
