  The energies, widths, and shapes of features observed in the total energy
distributions in field emission from W(100) and W(111) are compared with the
results of a full-potential LAPW calculation of the surface density of states
based on a supercell model of the crystal structure at the metal-vacuum
interface. The Swanson hump on W(100) is attributed to two bands of surface
states and surface resonances of dz^2 symmetry that are highly localised at the
center of the surface Brillouin zone (Gamma_bar), and a second peak observed at
lower energy is attributed to a band of surface resonances, also of dz^2
symmetry, centred at 0.11 A^(-1) along Gamma_bar to X_bar. The energy scale of
the calculated total energy distribution is compressed by about 20% relative to
the experimental data. The present calculation yields strong evidence that the
broad asymmetric peak observed on W(111) is due to emission from a band of
surface resonances. Further calculations for W(111) are proposed both to test
the accuracy of the band model and to take into account the velocity factor
that enters in a calculation of the emission current.
