  An enhanced static approximation for the electron self energy operator is
proposed for efficient calculation of quasiparticle energies. Analysis of the
static COHSEX approximation originally proposed by Hedin shows that most of the
error derives from the short wavelength contributions of the assumed adiabatic
accumulation of the Coulomb-hole. A wavevector dependent correction factor can
be incorporated as the basis for a new static approximation. This factor can be
approximated by a single scaling function, determined from the homogeneous
electron gas model. The local field effect in real materials is captured by a
simple ansatz based on symmetry consideration. As inherited from the COHSEX
approximation, the new approximation presents a Hermitian self-energy operator
and the summation over empty states is eliminated from the evaluation of the
self energy operator. Tests were conducted comparing the new approximation to
GW calculations for diverse materials ranging from crystals and nanotubes. The
accuracy for the minimum gap is about 10% or better. Like in the COHSEX
approximation, the occupied bandwidth is overestimated.
