  We have calculated the ground state electronic structure of He under pressure
from 0 to 1500 GPa using both all-electron full-potential and pseudopotential
methods based on the density functional theory (DFT). We find that throughout
this pressure range, pseudopotentials yield essentially the same energy-volume
curve for all of bcc, fcc, and hcp configurations as does the full-potential
method, a strong indication that pseudopotential approximation works well for
He both as the common element in some giant planets and as detrimental
impurities in fusion reactor materials. The hcp lattice is always the most
stable structure and bcc the least stable one. Since the energy preference of
hcp over fcc and bcc is within 0.01 eV below 100 GPa and about 0.1 eV at 1500
GPa, on the same order of the error bar in local or semi-local density
approximations in DFT, phase transitions can only be discussed with more
precise description of electron correlation in Quantum Monte Carlo or DFT-based
GW methods.
