  Recent experimental results on two hcp phases of barium under high pressure
show interesting variation of the lattice parameters. They are here interpreted
in terms of electronic structure calculation by using the LMTO method and
generalized pseudopotential theory (GPT) with a NFE-TBB approach. In phase II
the dramatic drop in c/a is an instability analogous to that in the group II
metals but with the transfer of s to d electrons playing a crucial role in Ba.
Meanwhile in phase V, the instability decrease a lot due to the core repulsion
at very high pressure. PACS numbers: 62.50+p, 61.66Bi, 71.15.Ap, 71.15Hx,
71.15La
