  Solid He is studied in the pressure and temperature ranges 1-40 TPa and
0-10,000 K using first-principles methods. Anharmonic vibrational properties
are calculated within a self-consistent field framework, including the internal
and free energies, density-pressure relation, stress tensor, thermal expansion,
and the electron-phonon coupling renormalization of the electronic band gap. We
find that an accurate description of electron-phonon coupling requires us to
use a non-perturbative approach. The metalization pressure of 32.9 TPa at 0 K
is larger than found previously. The vibrational effects are large; for example
at P=30 TPa the band gap is increased by 2.8 eV by electron-phonon coupling and
a further 0.1 eV by thermal expansion compared to the static value. The
implications of the calculated metalization pressure for the cooling of white
dwarfs are discussed.
