  Recently, attention has been given to a system of He$^3$ bi-layers where a
quantum criticality similar to the one in heavy fermion compounds has been
observed [Science 317, 1356 92007)] In our previous analysis [Phys. Rev. B 79,
045112 (2007)], based on the Kondo breakdown scenario, we addressed
successfully most of the features observed in that experiment. Here, we
consider the activation energy $\Delta$ observed experimentally in the specific
heat measurements at low temperatures in the heavy Fermi liquid phase. Within
our previous study of this system, this is identified with the gap opening when
the upper hybridized band is emptied due to a strong hybridization between the
nearly localized first layer and the fluid second one. We discuss the successes
and limitations of our approach. An additional prediction is proposed.
