Result (23) also leads to some understanding of what happens when atomic-level effects are taken into account, and the band-structure is no longer free-electron like. Due to the presence of the atomic ion-cores, the surface barrier, and also the electron wave-functions at the surface, will be different. This will affect the values of the correction factor ν ν , the prefactor P, and (to a limited extent) the correction factor λ d. These changes will, in turn, affect the values of the parameter D F and (to a limited extent) the parameter d F. For a real metal, the supply density will vary with position in energy space, and the value at point "F" may be different from the Sommerfeld supply density. We can take account of this effect by introducing an electronic-band-structure correction factor λ B into eq. (23). Modinos has discussed how this factor might be calculated: he estimates that it is most likely to be between 0.1 and 1; it might lie outside these limits but is most unlikely to lie outside the range 0.01< λ B <10.